The Mathematics of the Casino | What people get wrong about gambling
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- Опубліковано 22 бер 2022
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let me guess you went to Vegas and you got caught counting cards and now you want to say that its not even worth arresting over because reason A and reason B are logical.
If you take their money in bundles they get pissed end of story.
Zach, if you have the spreadsheet on all the odds calculated in this video, could you post them somewhere so we can review them? Thanks...
How will you create such animated videos
Can you please tell ?
Great video. But what did your last line mean? “Never walk away from the table when you’re on the heater”. Never heard that saying before. Could you clarify?
😂😂😂
Want to know the secret for leaving a casino with a small fortune? Arrive with a large fortune.
😂😂😂😂🤣
😆
That's how making money in general works: The more you have, the easier it is to make more.
@@Kitsudote "T C" was joking. What they really meant is: "Want to know the secret for leaving a casino with a bit of money? Arrive with lots of money."
Original and funny.
So the moral of the story is, “If the odds are against you, don’t give them time to even out”
Just be aware that the game doesn't stop when you leave the casino unless it's your last time playing. You might leave with a profit the first dya because you were smart enough to walk away, but the next time you play that expected value plot keeps going right where you left off
@@wyattsullivan2714 Incorrect, actually. The true expected value always lines up with the known present value at time=0. So every time you see the results of a gamble, the expected value graph has to “update” to include the new present results.
Every roll of the dice is theoretically independent. To say that a person coming in one day with some gambling winnings has a different expected value than another person bringing in the same amount of money on their first day is an example of the “gambler’s fallacy”.
No... It's best if you don't even start playing. The risk of making a little compared to losing a lot is a huge.
Sure, you have an 88.8% chance of winning 50,000$ car but a 11.2% chance of losing your currently owned 1,000,000$ house. Is it worth it probability wise? Definitely not. So no, that's not the moral of the story..
And Wyatt is correct. He is talking about the expected value plot. Just because you play one game today and one tomorrow doesn't mean it isn't the same if you played 2 games today and none tomorrow. It's all about statistics and probability... I hope this clears things up for you and saves you from losing money if you are considering gambling at the casinos...
If you want to do something similar to gambling but with the edge on your side then I suggest learning how to trade stocks professionally.
The only way to do that is betting like twice in your whole life xD
Any new bet adds towards that tendency of losing money
@@jakobr_ He's not saying this. What he is saying is that the more you play the same strategy the closer you are going to be to the expected value of it. And the count of it approximating to this ev does not stop when you leave the casino, but continues to get closer and closer to the ev when you go back to play again.
I am a retired casino dealer living in Las Vegas and I can attest to what he is saying. Take your shot, and win, lose or draw leave. The longer you play the more chance you have of losing. I have 36 years of experience watching this happen.
I did not believe it until I read this comment. Thank you.
i’m about to start as a dealer. it’s nice to hear you were able to retire and work for 36 years doing it!
What if I walk in and win then walk out a winner, then I come back in and do it again 5 hours later ;)
It happens alot .. 😂😂😂
Are you allowed to gamble ? We're you allowed to gamble when you were a dealer
A couple of weeks ago, I walked into a casino for the first time in my life with only $5. On my very first round of the first game I played which was a slot machine, I ended up winning $107. I instantly cashed out and walked out.
Smart.
How much did you tip the purse check?
The probability of you coming back to lose all that back and more is very high. Just don't ever go back even if u just want to drink a beer or eat dinner.
@@smlbcity23 thanks for the tip haha. 😂
@@movementpk1 oops!! First time at a casino. I didn’t know that was the proper thing to do. 🤷♂️
I like to factor in the free drinks if you sit at a black jack table for a while.
Probabilities are always a fascinating subject to me.. i like the way it can predict what may happen in future just using some numbers and some expressions
When I thought I flunked out of engineering I was thrown down to what was called "finite math" which was basically probilities. Still regret not doing the work necessary to understand calculus. I drive a truck. So there are are consequences for being lazy or stupid.
@@wayneburgess2885 you flunked calculus?!
didnt you stay long enough to learn the short cut?! OMG!
calculus is simply the slope of the graph.
In truck driver terms: Speed is the slope of distance travelled vs time
acceleration is the slope of speed vs time
Jerk (change in acceleration) is just the slope of acceleration vs time
Integral is going back the other way, the area under the graph instead of the slope...
its SIMPLE
@@kenwittlief255 those are fundamentals of calculus but it can be much more complex, there are still problems in calculus which the worlds greatest mathematicians have not solved.
@@kenwittlief255 What you described is the first week of high school calculus. Anyone with half a brain could figure that out. I think he means something more involved like a complex integral or differential equations which can get very messy.
@@kenwittlief255 Mate that's year 11 GCSE stuff. It gets a lot harder after that. Don't talk about what you don't know about lol.
I'm happy to say this channel had a part, even if small since my decision was already mostly made on pursuing engineering. I'm now a junior 1 and looking to take abstract algebra next year. Amazing channel Zach! :)
This has more to do with mathematics or statistics than engineering.
@@christiantretter4605 yeah i just happened to comment on this video, i meant more of his older videos lol
Just don’t build any more slot machines. The world doesn’t need any more of those
Fun update btw, Im not taking abstract algebra because I got a D in mechanics of materials and cant afford to risk another tough class or I lose my scholarship 😎
This makes me want to watch the movie 21 again. I recommend buying the book called "Beat the dealer" by Edward Thorp. Goes into so many strategies in statistics and probability. Great video Zach.
god that's a good movie
too good; really enjoyed watching it multiple times!
Might I also recommend "The last casino", highly underrated game with a lot of the same elements.
Just watched it yesterday. Could've been a good movie but they added wayyy too many clichés
Is "Beat The Dealer" a book about casinos/games or generalized about statistics and probability? Sounds interesting.
"Edward O. Thorp is the father of card counting, and in this classic guide he shares the revolutionary point system that has been successfully used by professional and amateur card players for generations. This book provides:
o an overview of the basic rules of the game
o proven winning strategies ranging from simple to advanced
o methods to overcome casino counter measures
o ways to spot cheating
o charts and tables that clearly illustrate key concepts."
When I went to a casino and did this I used the Alice strategy. I started with $10, betting $5 at a time. I made about $80 before going all in a la Bob's strategy, lost it all in one go, and then lost $60 more trying to make it back. Just my personal experience, though.
Yep, that's why the casino is still there.
The real mistake was not walking away with those enormous wins
@@randomperson9732 Some people like casinos. For me, the mistake is going in. I hate the noise and congestion.
If you start with 10 you stop at 20.
@@randomperson9732 That depends on what constitutes walking away. Few take that to mean forever. Yet, that's what it really takes. Lugging around "winner" is an albatross that most can't handle. "I 'walked away' a winner last time and I'll do it again." This sentiment tends to become most powerful, unsurprisingly, when in need of money.
Worked for an online casino software provider for 14 years. Taught the basics of real odds vs offered odds (the difference is known as the house edge) and the only strategy to win at an odds based casino game is to own the game and encourage as much play as possible. This is why casions balk at large, single plays, and encourage the players to increase their number of plays with smaller denomination machines and bets. As game play tends to infinity, the house edge tends to a guaranteed income.
They want the grind, yep.
Online casinos are fake
That's why they put a cap on bets.
you take roulette course, can you call me on my whatsapp?
You would think so, but as someone happy to piss away money on a $10 craps table, they have a habit these days of choosing not to take my money, by only offering $25 tables.
Thank you. UA-cam is flooded with "systems" to beat these games, but the basic math ALWAYS says "no." Yet, the comments sections are filled with people in huge denial, often citing anecdotes about how they beat the odds and won.
If they did beat the odds, it's due to variance. We don't lose exactly on the trend line. Sometimes we come out ahead. More times we come out behind. And there's no way to predict when that is.
If a casino game could be beaten, they'd change they payouts to make it less profitable so players would still come out behind. This happens with video poker, where the payout table is crucial. (And usually ignored by players, to their detriment.)
The only casino game that can be beaten is blackjack. But to beat it, you have to play perfect strategy, maintain a running count, convert that to the true count, play variances on perfect strategy based on the count, and vary your bets widely when the count is in your favor. And you have to do all of this while not getting detected by the casino staff. Contrary to popular belief, counting cards is not cheating, nor is it illegal. But the casino can "back off" a player it suspects of card counting, refusing to take his/her bets. The math in card counting is easy. Managing the process is incredibly difficult.
So, why don't casinos just get rid of blackjack? Because it's incredibly popular. They also don't like to back off "advantage" or "skill" players because it looks bad. So, they've resorted to other means of drawing in the suckers and discouraging the card counters. Three important changes are (a) game variances, (b) changed payouts, and (c) automatic shuffling machines.
The casinos are offering more "blackjack-like" table games. But these are horrible, with the odds stacked in favor of the house. The house has also implemented rule changes (like eliminating the surrender rule or what you can or cannot double-down on) and payouts. (The worst of these is the switch to 6:5 payouts for blackjacks. This reduces the card counter's edge, sometimes eliminating it and making the game not worthwhile to play.) Finally, some houses have introduced automatic shuffling machines to eliminate card counting. Period.
What about all the other casino games, like craps, roulette, keno, the wheel of fortune, etc.? They're all bad bets with house odds stacked against you. Have fun. Gamble. But you're playing a losing game. Be comfortable with that.
@@Damood I contend that your statement is false. But I'd love to hear how it is true. What games and how?
@@Damood There is nothing I said that is false.
There are plenty of "systems' out there and such, but I mostly see people presenting them as ways to lessen your risk, not to beat the house long term. It may just be that I tend toward craps content, but from what I see the standard is that you expect to lose, and just want to get the most entertainment out of your money.
Anyone that thinks they can beat the casino consistently is deluded and needs a lot more help than you or I can provide, but there is plenty of fun to be had walking in with the same couple hundred bucks you'd spend at an amusement park or going to a fancy dinner, and shooting dice for a couple hours.
Although long everything this man typed is the truth!
My students often come up with questions how to win in casinos....
When I'm done with them, I have quite a number of shocked and disillusioned students that just learned how bad it is to be bad at math :-)
PS: it I was carlos, I would buy the casino....
tell me more
If you can't beat them, join them, right?
And then launder money through it and make even more money 😂😂
better answer: drive past the casino and goto a GoodWill store
you have really good odds of finding something valuable that was donated by an estate by someone who did not know what its worth,
and they seldom sell anything for more than $40
Examples: LL Bean shirts that were never worn and still have the $50 store tag on then: $6
Real leather jacket with the $450 store tag on it: $40
Hand made Japanese Classical Acoustic guitar, $700 online at the Guitar Center: $50...
the great thing about "gambling" at the Goodwill store is you dont have to pay anything if you dont see anything you want - you cant lose. Its literally a treasure hunt.
On a good day you can put $500 worth the new clothes in your closet for $60. I think sometimes stores donate clothes that didnt sell, a lot still have the store tags on them.
@@kenwittlief255 i never saw the tags at any thrift store i got some good deals over the years
1:20 "Just note: this is a probability problem so, yeah. It's a trap."
You don't really need math to figure this out - just reason. If your game gives you a less than 50% chance of winning, you can still get "lucky" playing once. with every additional play, your chances of consistently maintaining your luck decreases, and quickly approaches zero. that's why casinos want you to stay.
"you dont really need math to figure this out" they said, then proceeds to explain it mathematically
@Santosh Parvatikar But you also have to add the caveat that games of chance are specifically designed to give the house a greater chance in every round of the game. And since math doesn't rely upon feelings, the more you play, the more certain it is that the house wins.
yea, repeatedly playing a game with odds stacked against you (less than 50%?) is intuitively worse than playing once or twice as what you risk in the former just compounds more and more as you play longer
@@kabusohikaru6187 Nah. He did only use reason. Even without using probability and just common sense, you just know that its very hard to get 100 heads in a row in a coin toss. 1000 heads in a row is even harder to almost impossible. So the more head in a row you get, you can guess that its going to be a tails more and more because a lot of heads in a row simply does not happen, even though each flip is independent.
@@Ntnt11 Man was literally talking about percentages in his post, that's definitely using maths. You're using more "pure" reasoning, he wasn't
I have worked as a dealer for 26 years. Never saw a big winner. If someone wins, most probably he goes again the next day, and looses all. My advice is STAY AWAY from gambling. It’s addictive. I have seen too many people breaking up and finishing with nothing.
I'll bet I can stay away from gambling longer than you...wha?...dammit!
Got any advice for me on what I could do to try to help a friend with a gambling addiction? I assume not much until they're ready to admit it and seek help themselves, right? I just really want them to realize how unsustainable it is before it really ruins their life and before it starts fucking with my life if I stay with them... They just got sober again from drugs and were doing well up until they started going to casinos at night and neglecting friends, family, their kids because of it, and then spending all day playing real money slot machine apps on their phone... You'd think someone with Substance Abuse Disorder who's been in and out of treatment their whole life and has admitted they're a drug addict would find it easy to realize when they've developed a gambling addiction, but I guess not... -_-
@@taywimz The best therapy is CBT (Cognitive Behavioral Therapy). This deals with both the behaviors but as well the cognitive (thought based) underlying reasoning or value. The neurotransmitter involved for the most part is dopamine which people mistakenly call the "pleasure neurotransmitter" but has much less to do with pleasure as with "motivation". Your friend lives a lifestyle where he constantly has to create firing of neurons in the two dopaminergic brain pathways. He needs to reset homeostasis and one way is a "dopamine detox" look it up it's not difficult to try. It takes discipline but not skill per se.
@@datroof2262 it's not a "he" lol, but thank you. I've actually been telling her to do EXACTLY that already. She just keeps procrastinating on making the call to her therapist.
@@taywimz encourage her to self exclude herself (a legal-binding document) from the local casinos and wipe the gambling apps from her phone. then buy her a non-smart phone.
It's always good knowing what percentage odds the specific casino will allow you to take on your pass line bet. And yeah, house blackjack rules can alter odds as well as the number of decks being used.
A really excellent summary with easy to do math for figuring out the house edge. There is such a thing a beginner's luck. Bet once and walk away and you have a fair chance of winning. There is no such thing as long runner's luck. The more times you bet, in the long run, the more certain you are to lose.
actually there is no such thing as luck
its all a matter of probability
its random - with people playing 20,000 times per hour on slot machines, someone will hit the top jackpot somewhere in the casino every hour (on average)
want to be a millionaire? be a billionaire and enter the casino.
Great video. I find the 'Wizard of Odds' an excellent place to learn about gambling and the odds of going broke, which is more often than not when visiting a casino.
Our issue stems from the prevalent belief held by the majority that "having a good job is all it takes to become wealthy." Many people are unaware that these billionaires are using a different set of rules when conducting business.
That's very practical and smart goal, a wise man once said do everything you can to get outta debt, one of his tips to get rich.
The best approach for novices is to trade under the supervision of an expert, trust me you will be debt free.
Wish I knew about crypto trading earlier.stock is good but crypto is better. Brace up and get yourself a bitcoin before it's too late.
Crypto is the future, investing in it will be the wisest thing to do especially with the current rise.
Fear is one of the factors that hinder most people to invest into crypto, most people say ignorance.
Thank you so much for such a clear and concise analysis of EV and the house edge. Even if the formulas make people’s eyes glaze over, once you point out the bottom line, it becomes so much more clear.
When I go to a casino (pre-COVID days), I play poker. And depending on the day/time/etc., I may have to wait. And table games like these can be a decent way to pass the time as long as you know the odds and accept that you are going to lose.
But the one thing you didn’t cover is: how slowly will you lose? You showed the EVs for the coin toss game, the pass line in craps, and red/black choice in roulette and how much one would lose over X hands (500, I believe), but you didn’t show how much time (on average) it would take to play that many hands. I think I saw something on one of your tables, but I would have liked a section towards the end of your presentation that said that, on average, you would play X number of hands per hour for each game and, therefore, lose X*Y/hour at each.
And it’s that reason that, despite the math, I tend to play roulette while I wait. Red/black or Odd/Even might be 18/38, but the actual number of hands/hour is soooooooooo much slower than craps or blackjack that it’s a cheaper way for me to kill time.
I have a decent grasp of basic blackjack strategy, but the game is much faster, and I’m usually trying to get my head into poker, so I don’t want to think too hard.
To date, I’ve only tried craps a couple times and while I knew VERY basic strategy, the game went too fast for my taste. But if we are ever both at the same casino, I’d happily take some lessons and have some fun hanging with you and your brain!
Think of dice as a lot of little separate games going on all at once. Everyone at the table may be playing multiple games, or just one. You just choose which ones you want to play. 🎰
@@failuretocommunicate correct. You can throw a minimum bet on a single number and every time it hits you win, if the seven hits you lose. Everything in between is no change. You can play for quite a while like this if youre just looking to kill time. And also, if youre looling for the game to slow down overall try to find a busy table as it slows the game down naturally having to pay out so many people every roll.
@@TheGillenium ikr, yeah, like just play the pass or the dont's or 27 across or 6 and 8 only or if you like bad odds play the props. pay the vig to get true odds on the 4 and 10...lol omg here I am a wheel dealer raised on traditional BJ talkin shit about dice. 🎲🎲
The grand daddy of expected value calculations for the card game Blackjack (21) can be found in the classic "Beat The Dealer" written by a mathematician who later made a fortune in hedge funds by finding pricing abnormalities. This 1966 book begat generations of card counters as well as famous rules like "always split aces and eights".
"Never walk away from the table if you're on a heater". Good outro would be Bob Seger's _Still The Same._
I feel my only power in a casino is being able to leave at any chosen time. If I get up in a session I can simply cash out and leave. Not many do though lol also the sessions where you never get up are the killers.
True, we had heart attacks, people who wouldn't give up their seat in a fire and others who went into uremic shock. Two bankruptcies that I know of, one lady's son called up in tears because his mother had mortgaged her house to the hilt and still wouldn't quit. Gambling is insidious.
@@haroldwilkes598 There's no eV reason for anyone to play higher than min stakes and claim back maximum comps.
When I was travelling I would frequently visit casinos for cheaper entertainment than other places. Make sure to max your free drinks and minimum tip. Will spend heaps less than going out to bars or other fancy places.
Gambling is only insidious if people allow it to be. Sports can be insidious, you're just playing a game and WOOHH lifetime crippling injury and thousands spent in medical fees for the rest of your life.
Gambling has saved me thousands of dollars compared to my useless university degree that costs me 10's of thousands. University trapped me with lies of career prospects and large debt. Universities/Colleges are insidious.
I am glad that you started uploading videos on math again
wtf does he say at the very end?
'never walk away from the table if you dont have a heater?' - wtf?
I have the same problem understanding him. Apparently a heater is slang for someone on an extreme hot streak. But I can't make out what the strategy is supposed to be with the heater at your table.
"Heater" is a gambling slang that means "An extended winning streak".
That was a bit of a joke. It’s definitely NOT really scientific. The “common knowledge” among gamblers is that you don’t stop when your on a hit streak with the subtle counter logic being if you don’t stop until you start losing you’ll just lose your winnings…and then proceed to lose your stake as you try to win it back again.
Thank so much you, Zach!!! Subject of this video seems so paradoxical and kinda misleading. And that's probability and statistics is all about! It shakes your intuition and attempt to understand it hurts your brain! As always, a very informative and brilliant video!
A simple coin toss can show house edge. Natural odds for a coin toss are 50%, only allowing for proper outcomes. So, if a casino offers you $1.95 for heads on $1 bet and $0 for tails, using 10 flips as a proxy for infinity (note over 10 flips these will NOT be the results, but we're using 10 flips to proxy an infinite number of plays):
Over these proxied 10 flips 5 will be H, 5T. Income is $10 (10 bets at $1 each), winnings paid will be 5 x 1.95 = 9.75. Thus the house keeps 25c of every $10 when the flips tend to infinity. This is a house edge of 2.5%. As the number of plays tends to infinity, the house is almost guaranteed to keep 2.5% of the bets taken.
The casino has no control of the outcome of an individual bet, but they do have control over how much they OFFER you for a win, and this offer is always less than the natural odds. Slot machines don't 'get hot' or are about to pay out.
Knowledge is indeed power and in my mind, this is, by far, one of the the best videos explaining what a player can do to attempt to come out ahead. Of course, luck will always be a factor! Some of these principles can apply to slots as well, however, one should be very careful when playing "progressives like slot games" e.g.,, the popular firelink and dancing drums. Regardless, any player must exercise "discipline" (as taught by the great Lombardi), try to play smarter (not harder), have a drive "to win", and finally, know when to eventually stop playing and quit (just like Brady!). Thank you for sharing this informative video!!
My advice if you find yourself walking into a casino: don't
In my ECE stats class we went over a lot of gambling and writing MATLAB simulations of games deceiving expected values and things
Simplest way to think about this, I think, is a smaller bet means you have to win more to reach the total before you walk away.
U can rly change your life at the casino. Pull up in a 50k sports car, leave in a 150k bus
Thank you😊 for this video, do you offer account management or have any recommendations?
If you are using really a good broker or account manager is easier to earn from the market
@@craigbrown7886 That's true. a lot of people today have been
having a ton of disappointments in forex and
crypto trading in light of helpless direction and awful specialists
@@millerwoods1343 Any specific guide?
@@joykeating3635 check out Mrs Victoria Wilson of UCLA Anderson.
she's great and her methods are working for me at the moment
Very professional
Ever since I lost my job with the ministry, I have been surviving through my investment with Miss Victoria, I'm so glad I invested when I did.
Now I understand the relationship between time spent at the table or slot machine and comps - not necessarily just the coin in. Thank you for the info
I have to adress a special thanks for the editor of this youtube channel, that was a revealing moment when I followed your interepretation the first time and that has consequences on my vision about risk and reward attribution. Absolutly MUST wathc for any mathematic passionate !
Mathematician: The Casino always wins.
The typical Gambler: No gamble no future.
Youre on earth, youre a gambler.
No woman no Cry😮
“I know this is going to upset some people, but it’s true”. How true!!!
Good well delivered information. Long term proabilities. House edge. I found the charts helpful to understand the averages. Thank You!!
bruh i didn’t know you did this stuff
i legit thought you only made skits on your other channel 😭 respect man
Thank you. With the help of this video, I’ve been banned from several national casino chains
damn that was fast
That’s a world record
I learned a strategy a few years ago, but one that I think they'll ban you for. Every time you lose, double your bet. When you win, you'll make back at least what you've lost.
It works until it dosnt, or if you have unlimeted bankroll
They don't ban you. Because your EV is still negative. Because if you do it long enough there will come the time when you loose all the money you have. Also as a risk management strategy for the casino they can just set betting limits. If they set a limit of 10k and you start with 10 bucks you only can only lose 10 times in a row until you are wiped out.
Doubling after each loss results in a one unit profit when you win. Fibonacci sequence gets you back to zero. Math gets in the way of your plan in any case.
current wager = base wager*2^n(current losses)
zeroth loss: $5*2^0 = $5 total stake: $5
first loss: $5*2^1 = $10 total stake: $15
second loss: $5*2^2 = $20 total stake $35
third loss: $5*2^3 = $40 total stake $75
fifth loss: $5*2^5 = $160 total stake $315
tenth loss: $5*2^10 = $5120 total stake $10,235
I tried that on roulette until black came up 13 straight times one night.
Martingale is the reason for having maximum bet limits on all tables.
More about house edge and the line bet on craps (from a career dealer, not a math head)...
It is true that in any casino that offers table games, the best possible bets in terms of house edge are the line bets and come bets. However, reducing house edge *requires* betting the odds behind the line, and if one is serious about reducing house edge to the lowest possible degree, the player needs to bet the maximum odds allowed. The more odds the house allows (some only allow odds of 2x the pass line bet, others go as high as 100x), the lower the player can reduce the edge by betting the maximum odds.
Come bets and line bets are essentially the same - a flat bet with odds for a number to repeat before a 7. The strategy decision the player has to make is how many numbers to cover. Three numbers is pretty standard, but your bankroll and risk tolerance are going to determine how extended you're willing to be on default.
i remember making up a game way back, but i don't think i have the brains to calculate the expected return, it works like this:
draw 9 cards from a deck with no jokers, and place them on a 3x3 grid
if there is a line with three cards of the same suit, you lose
if there is a line with three cards of the same COLOR (but not same suit), remove the card of different suit, and replace it. do this as many times as necessary until you either have three of the same suit in a row, or no more lines with three of the same color
finally, if there are no more lines with three cards of the same color, you win. depending on the pattern the cards form, it's a different payout:
house pays 3 to 1:
R B R
B R B
B R B
kite pays 2 to 1:
R B R
R B B
B R R
other pays 1 to 1:
R B R
R B B
B R B
Carlos is a good buddy of mine, we hang out on his yacht all the time.
𝗪𝗵𝗮𝘁𝘀𝗮𝗣±𝟷𝟿𝟷𝟾𝟾𝟷𝟸𝟹𝟻𝟺𝟿
I think you did a really good job of getting the important points across!
Excellent basic math explanation of the house edge. I tell people that play roulette that they have better odds of throwing a twenty dollar bill out of the drivers side window & having it fly back in the rear window😂
It seems to me generally that casinos tend to give games with higher variance payouts a higher house advantage.
I don't know if anybody has quantified that relationship but there's some truth to it. So the greater the house advatage, the sweeter the game is to walk in with $100 and walk out with way more. Interestingly, as per initial argument.
So myself? If i want to hit and run I'd choose roulette, and craps if im passing time.
If you are good at card counting, you can get an edge in your favor of up to about 0.5% (in blackjack)
Which is basically irrelevant as you would have to be perfect, not just good to get that edge. Then theres the problem of bankroll, and the casino has a much bigger on than the players...and if youre not very careful, they will still run you down to 0 even if you have .05% edge.
@@TheGillenium If you exercise proper position size and discipline to manage your bankroll, it can be done. I did it once hopping between various casinos on the Gulf Coast of MIssissippi and Louisiana over a period of several months and playing a lot of hands. Being just a tad less than perfect, or having the need to camouflage what you're doing to avoid getting booted can reduce your edge, but you can still have one, meaning that you'll win if you play long enough.
I was a specialty contractor for many years. During the building of the casino, I was asked for a quote on a project nobody wanted and they didn't know how to do. I quoted them a cost plus price, plus % profit. They studied the proposal and everything was good. They found my profit percentage too high. So, I just said why don't we go with the same profit that the casino is projected to make while they are open and operating.
They hund up the phone on me. I DIDN'T GET THE JOB.
2:00 It was fun to sort out the logic behind this teaser in my head, thanks Zach!
I was thinking of a roulette strategy that was to bet $10 on red and every time you lose bet three more times until red comes up again and start again with $10. The problem is that the amount of money you have to have so that a losing streak does not ruin you is very high.
Best way to keep your money in a casino is to just keep walking right through.
I have never known a happy Gambler.😮
My method for casinos is to treat them as arcades. Come in with a limited supply of funds. Anything you win in a game goes into your wallet separate from the money you brought in. Then at the end of the day if you brought x amount of dollars and expected to spend x but you got some back, then you got a bargain. Because if you change your view of it you change how you play it , and then enjoy it more or less.
I never liked losing money
I never like feeling that someone took my money
Casinos guarantee you WILL lose money in the long run
enjoyable?!
@@kenwittlief255 Black jack is fun. Just like anything else you can do for fun, it costs something. You can't live life without doing so. My point is that someone hasn't taken your money, the moment you put money down at a table or in exchange for chips it's spent, not taken. It's okay to not enjoy casinos. Not everyone likes the same things. But the ideology that someone can't enjoy things simply because you have to spend something to do it, is one that will leave you dissatisfied with everything. Every action spends something.
@@captainironbat8193 you can play blackjack all day long, and not play for money - just for the game itself
if you think its not about the money, but you are paying to play... its about the money..
there are thousands of things you can do that will always make you money
and thousands of things you can do that dont cost anything
@@kenwittlief255 the prospect of winning money is the fun part, I played black jack first time in 10+ years a few weeks ago. Sat down with 200 in chips and walked out with 2 grand.
Roulette is the worst game in the house. For instance, if you place your bet on 14 and the ball lands on fourteen, you only get 35 times pay. However, there are 37 numbers showing. You should get paid 37 times.
It depends on the money management strategy. Martingale, Fibanacci, etc changes those odds. Take a $1,000. Doing a Martingale, you will win $30 more times than if you would flat bet every spin/hand. Depends on the money management the player is using.
The only game you can play in the casino with no house-edge is old-fashioned Poker (not the video/tablegames versions). And that's entirely because it's the one game where the house isn't actually playing (you only win or lose based on the other players at the table). The only money the casino makes from Poker is from their fees for hosting the table (rake/time)
Any poker variant (Texas hold em, Omaha, etc) that is against other players rather than the house you might have an edge if you understand at least the basics of poker.
And you can have a huge edge if you have studied the game in a very deeply way.
They take a 3 to 5 buck every hand dealt. They winning!!!
The rake: at 30-40 hands an hour, the casino doesn't care about individuals winning. What the casino see's is the table loosing $200-300 an hour. The house doesn't have an edge on the game, just the amount of hands at that table. So with 10 ppl at the table, you have a 1 in 10 chance of winning a hand each round. You need to be a good player and know when to get out. Sometimes you get lucky. Otherwise, the same player would win every game. Poker is the only game I play at a casino.
@@JohnBS this is true, you can give yourself a much better chance of winning playing poker, if and only if you select the game properly. If you sit at a table and youre the best player out of the 10..youre odds of winning are far greater than playing any house game. Now if you sit at a table with 9 guys who are better players than you, you now have worse odds of winning than playing the casino. The advantage is flipped drastically to the better player.
"Heres the thing...if you cant spot the sucker in your first half hour at the table...then you are the sucker."
- Mike McDermott, Rounders
You have even more of an edge if your opponents are drunk, which is also very likely in a casino.
Aye been waiting for this one
Moved to Vegas when BJ had favorable rules. Left when those rules became difficult to find. Although to be fair, I am a poker player. Table games was just entertaining. But I knew every game. And the rules! And yes I even played Roulette for fun. Well kinda. I was involved in a wheel tracking system where a famous gambler (now barred from Vegas) tracked a wheel in the Gold Coast and the Paris. He found the wheel (must be hand made wood wheel) over years even decades of play developed anomalies. Depending on the big or small ball you could predict what numbers were more likely to land.
Now I knew one of the team members and we attempted it at the TI but they switched wheels. The wood had a distinct pattern that appeared to look like an old woman in one corner. When we decided to pounce the wheel was switched. So the moral is I lost about 300.00 playing Tabasco machine on one minimum bet at a time. I tracked the roulette wheel results from Tabasco one spin at a time recording results. (This is allowed because everyone has a system in Vegas) (casinos love guys with systems) (not card counters though, another story) Then my partner was convinced the actual roulette wheel wasn’t switched (it was) we argued and basically flipped a coin. I lost the coin flip and the roulette wheel took 2k that night.
Ahh good memories though. It was very fun to attempt to slay treasure Island even though my ass was handed to me. Poker grind and selling cars gets boring! Now I live in Nebraska and have a garden! The end!
Man I had quit gambling for a while now. This vid makes my fingers itch...lol.
I once heard a story of a guy who played the casino trying to walk away with $10. He would bet $10 and lose, then $20, etc. up to $510 or something, just to come out ahead by $10. Would this strategy work given you have a large money supply compared to the amount you are trying to earn?
This is the martingale strategy and it is statistically likely to work in the short run but still has a negative EV. So it's basically just like what was discussed in the video, as you play you're going to win most of the time, and every time you win you will win $10. BUT a small percentage of the time you will lose (as in lose all the money you came in with via multiple losses in a row), and that loss will be big (let's say $630, meaning you are doubling your bet until $320). And that occasional loss of $630 will outweigh those majority of '$10 wins', if you were to plot this you would still notice it follows that best fit line with a negative slope.
But yes if you're ever in a casino and want to win $10 then definitely a good strategy to do the martingale system in terms of optimizing your odds of winning that $10, but you do risk a big loss if things don't go your way. I was once gambling with a friend and watched him do the martingale strategy at the roulette table for hours with amazing success (only got maybe 4 losses in a row max), then after going up several hundred dollars a string of 16 reds came up in a row and he lost it all. It does happen.
@@zachstar once he broke the up to 4 losses pattern he shoulda quit. I.e. on the fifth loss
@@mattstaab6399 probability works both ways though. The more you lose, the more the probability that you will win the next hand and its hard to quit when you have such high odds of winning
@@Ntnt11 no… the probability of each bet remains the same no matter what happened previously . To think otherwise is called “ the gamblers fallacy “ and has resulted in many losing everything .
@@michaelblankenau3129 exactly
You have a gift! Your math matches almost exactly the English language statements you use. In other words, a person can see the math in your English, and see the English in your math.
The House has an edge which covers all kinds of expenses and overheads and (normally) even makes a profit. But we players have an advantage over them because we are (or should be) 100% in control as to when to play, how to play, how much or little we play, when to stop etc etc. In fact when it comes to systems/strategies they can never GUARANTEE you win, are never INFALLIBLE; but what they do is they make it easier for you to exercise your free will and have preset goals and limits so you don't get emotionally involved and take the wrong decisions.
Never say never. Only time you probably want to leave a blackjack game when you’re on a heater is if someone suddenly jumps in on a hand, or another player stops playing a hand…or plays an additional hand. Great video though!
Excellent video. Why do casinos continue to have crap tables if the house edge is much lower with this game? Also, takes maybe 4 or 5 employees to run the crap tables.
The games goes very fast. I believe that's why.
Probability is one of the coolest maths
As long as you do it right. But most of the time you're not doing it right and you have virtually no way of noticing that.
As a probabilist, I approve this comment
you're probably right.....
I’d like to know how long Carlos has to play in years lol
Watching other people lose money at casinos is cheaper, but just sad. I only go for sightseeing, shows and restaurants
Interesting about the "Die" example. I used to be a roulette player (terrible house edge) but exciting then moved to Craps, which has 2 dice in play. As each die will average 3.5, added together that makes 7 - the House number (da-ding, lightbulb). Hence the reason you cannot consistently bet on 7 (compared to the other box numbers) and why lay bets (7 to win) require double the stake of back bets (betting on another box number) to gain the same return. I'm leaving out the Craps numbers, 11, Horn and other spread combinations for simplicity in the example. After 7, 6 and 8 have the next best chance of winning (and lowest return). End of the day you can mathematically strategy the game, but it comes down to blind luck or chance if you win. Although you can break even and make a little extra for tips if you use various methods. Not as much fun though! Hence the reason "The house always wins". I find the trick with casinos is to gamble for fun and casino points (for comps/rewards), rather than attempting to build a retirement fund. Doesn't take much to build up some free nights, free food, show tickets and any other freebies as the casino wants you to stay in the building as long as possible with hours of entertainment. The few that win are paid out from the majority that lose. Yes I've made the odd high (high for me) jackpot, which covered my trip costs. but I mostly "break even" or lose a little which is the cost of my entertainment. When it no longer becomes fun is when you have to quit!
I have nothing against people going to a casino for a bit of fun. Take a few hundred dollars, play, most likely lose it all, and walk away. No real harm done.
The problem comes when people think they can make money at a casino. STOP. You can't. Walk away.
Imagine a math teachers start his tution class very next to casino 😝
Still teacher and students both will lose
𝗪𝗵𝗮𝘁𝘀𝗮𝗣±𝟷𝟿𝟷𝟾𝟾𝟷𝟸𝟹𝟻𝟺𝟿
there are two types of people who shouldn,t gamble -- those with money because they don,t need it and people with no money because they do need it ---every one else should gamble.
For those whon want to dive deeper into the mathematics:
Until around 3:30 is the idea of stopping times
After 9:00 is the theory of martingales :)
I thought of the Alice case via the simulated net profit lines such as at 10:10. It's gonna take her a long time to burn through that $10,000 so probably there will be a streak of rounds during which she has a gain of $100. Or probably not, when I saw that low probability for Alice's success I realized that getting 100 more wins than losses in some number of rounds might be much more rare than I thought.
For comparison, you can see in the graph at 10:10 a gain of about $25 between rounds 500-600. The trick just is that it should happen pretty much right in the beginning, not when she's already lost some money. The graph I referenced was still losing money after that $25 gain.
I think the problem meant to make $100 more than your starting amount.
@@njgskgkensidukukibnalt7372 Yeah exactly. That's what I was trying to say when I mentioned that the gain should happen almost right in the beginning instead of when she's already lost some money.
This should be titled: _The Mathematics of Marriage_
I thought titles should be relevant?
Your coin toss example was a perfect analogy for a slot machine, it is biased towards the negative (house edge) but under gaming law it has to get back to their programmed percentage return (98%, 85%, or however the machine is programmed) over a long period to make it a "fair" game. they are not quite as fair as a honest coin toss, but within the allowed gambling laws that apply This Return to Player (RTP) has many names but "balancing" is the best one I heard. The balancing period may be millions of spins, hence the reason some people lose over long term and others win on one pull of the handle. Slot machines are programmed to be more or less "loose" (volatility) by the casino (it is actually based on the percentage payback table and the denomination of the machine) to make it seem/sound like someone is constantly winning to encourage more players to take part. On average, slot machines account for roughly 70% of the casino's income, which if you factor in the electricity bill alone of the building is a staggering number. Low volatility machines pay back more often with smaller bets, high volatility pay occasionally with a large payback and the rest are somewhere in between. Only the casino and the manufacturer know the true dynamics of each machine and like real estate it is all about "location, location, location".
The slots have variable payouts, so the casinos can usually set the % payout to what they like. Legally it can't be below 80% and I think casino have to accurately report it publicly so there is transparency. I mean some machines boast a 97% payout. Like "we're still taking your money but it could be less than other machines". Still doesn't stop people from playing
That's why I play poker. I'm not playing against the house, I'm playing against the other players at the table. Although the house does take their "rake" from the pot, it's easier to beat other players than it is to beat the house.
You can change the house edge to your favor by counting cards in blackjack, which is NOT cheating or illegal.
But you should do your research before you try. You really have to get it perfect for it to work.
Wym perfect? Preferably you would be adding or subtracting the numbers that come up(which isnt that hard with a little practice) but u can still get an edge by just thinking "ok theres been more small cards than large ones, time to go in"
Not illegal, but you will 100% get kicked out and banned if caught, and it's completely within a casino's right to do so.
@@Radi0actvChickn its better than what used to happen to people who got caught. If you were lucky, the mob would "only" break your hand
@@Radi0actvChickn Been there, done that, all depends on the particular casino, how much bet variance you do, how good they are at detecting counters, and in the very end their policy. I did the counting thing for several months many years ago on the Gulf Coast, hopping from place to place and I experienced many different combinations of the above. But I did end up with a nice pile of winnings. So it can be done. One place in Biloxi comped me a room and meals while simultaneously banning me .... haha
Hi zach ! Love this video ....I was looking for this video... I have a question. There was an old couple is united states who was able to crack lottery..have you heard about them ? .. I want to understand that math
I don't think I heard of that but I have heard of an MIT team (I think) from decades ago that found an 'error' in the lottery number payouts where there was a positive expected win for people who purchased a ticket. So a bunch of these people from MIT purchased as many tickets as possible since it was actually a smart investment (it was like the same as being 'the house') and I believe they did in fact win something.
@@zachstar here is video ....ua-cam.com/video/TJesgv3YOf8/v-deo.html
@@zachstar Casinos just end up banning those people. It's setup to be not fair.
@@edwardlulofs444 They are talking lottery though.
@@evamccray6500 I was using the word generically. I should have used the word gambling.
I always assumed when I saw 97% payout that it meant you lost 3% everytime you bet - you'd lose everything over time
We occasionally visit our local casino, never to win, purely for a fixed amount of entertainment, free buffet available, and free drinks, it's a good night out when controlled.
A quick look around the establishment clearly shows who the only winner is.
@4:10 My strategy is great. I play till I win 50, then take a break and play till I win 50 again 🤣🤣🤣
So you play until you win 100? This is no novelty.
@@danielyuan9862 I'm guessing you missed the joke.
Finally, a practical application for mathematics! Haha!
So you've been living under a rock till now??
@@vectorclassic6403 hey genius, pull out a dictionary and look up the word, Antiphrasis
There is an exception. Counting cards in blackjack, if you know how. It does take skill, but you can vary your bet based on what cards have been played and your hand and get up to a 2% advantage over the house.
Now you'll probably get kicked out before you can take advantage of that but hey.
Great explanation. Spot on.
These concepts are really valuable in financial markets as well. A lot of the trading community doesn't realize they're placing negative EV bets and they go bankrupt not even finding out!
One way to ensure some fun, likely little in losses, and maybe even leaving ahead, is to play through your bankroll just once. If you go in with $2,000 you make $2,000 in bets. Even on slots, which have the worst odds (as low as 85% RTP) you will likely leave with no less than $1700. Just size your individual bets to maximize your time, never make any individual bet over 1% of bankroll, and accept the fact that you will likely lose up to 15%. Also, set a hard limit on how much you are willing to lose and leave, no matter what, if that happens.
didnt you watch the video?! you got it completely backwards
the way to win ahead is to take your $2000 to a $25 slot machine, they payout as much as 97%.
bet $25 per spin. the 2 credit and 5 credit returns will keep you close to $2000 for a while
if you get a 10 credit win, that is $250 - good chance you will be up $200
winning $200 with $2000 is a 110% return
on a machine that has a 97% payout you beat the odds - you won $200
go spend it on something like you found it on the street and be happy - you won!
as he said in the video: 70% of the time you will be able to do this, but 30% of the time you will lose the entire $2000
@@kenwittlief255 Yes, I watched the video. Did you read my comment, though? I focused on "some fun, and likely little in losses". The problem with what you just said is it requires you to be lucky in the very beginning. You can easily end up hundreds in the whole with your system within minutes and never come back.
@@jeremywj your statement
-------------------------------------------
If you go in with $2,000 you make $2,000 in bets. Even on slots, which have the worst odds (as low as 85% RTP) you will likely leave with no less than $1700....
------------------------------------------
is false. At one session it is very unlikely that you will follow the 85% return line on a penny or quarter slot machine....
most likely you will lose half your money after playing the entire $2000
the factor you are missing is variance in the wins
with a higher payout machine, $25 for example at 97% you are more likely to keep hitting $50 or $125 wins, and keep breaking even
but what you are hoping for is an unlikely (lucky) hit: a 10X or 20X hit on a quarter machine is only $2.50 or $5
but on a $25 machine its $250 or $500 on one win.. If you have been breaking even (with the higher 97% return its more likely) than that one win is enough to walk away $200+ ahead
to put it another way, playing quarters or $1 with $2000 is what the casino WANTs you to do - play long enough and the odds always average out in their favor
if you are content with losing $300, then put it in a $25 machine and play 12 times - you have a good chance of hitting a 10X return and breaking even or coming out ahead
and you are in the game for a jackpot win on the $25 machine, which could hand you $8000
another way to look at it: You have a small chance of being hit by lightning, being eaten by a shark, a 20% chance of being in a serious car accident at some point in your life
a small chance of getting a terminal illness - there are a lot of bad things that can happen to you at random - and in the long run you cant get ahead, you cant break even, and you cant even get out of the game (of life).
there are very few good things that can happen to you at random by contrast. Taking $200 to a casino once a year, or buying lottery tickets, or browsing estate sales, Goodwill stores, looking at the listings on Craigslist.... Sometimes you will 'get lucky' and the odds will line up in your favor.
at a casino in the short run you can win, and you can get out of the game (walk out and dont go back)
Slots are different in that each spin doesn’t give you a specific win like roulette or blackjack. You bet $1 on those games, you win a set amount based on your strategy. In slots, on each spin your win total can vary wildly. You can win less than your bet or nothing at all all the way up to a bonus or huge line hit that could exceed 100 times your bet or even more. Over a very long period, slots are a bad choice but in the short run as in a single trip to a casino, doing small bets on slots generally will net a larger win. Go the casino 100 days in a row and yes you will probably lose more in slot play , a lot more.
Awesome video, man
Great video. But how do you calculate if you bet different amounts of money. Sometimes I’ll bet 10 dollar on blackjack but it can be that I double my next round
Of course. Statistically, you can't win at a casino. That's how the casino stays in business. My play: I start with $100. Then I DON'T go into the casino. I've won $100. Gambling is a tax on people who are bad at math. It's NOT fair. But people gamble for entertainment, not to win. They do it to momentarily have the illusion of winning. That's not an illusion that I want. But it's easy for me not to play - I hate the noise and congestion.
No friend, you definitively have not 'won' 100 dollars. Unless someone else handed it to you for nothing, or you found it on the sidewalk, you probably did some inordinate amount of work for it. This is why gambling is appealing...if you actually do 'win'. Take it from a degenerate gambler. 🐢
And you can win- it has nothing to do with being bad at math. Double your bankroll on a single bet sometime, and then reconsider. You're right that many people do it unthinkingly, and often fall victim to the 'gambler's fallacy', but there are plenty of people who place a single large bet and walk away much richer than they were minutes before. Kind of the point of the beginning of the video. Be well! 🌞
Or better yet, take that money and put it in a trusted index fund when it's evaluated lower than what it should be, and wait a few years. Barring a world end disaster, you beat inflation this way.
@@maynardtrendle820 True, but I like my opinion (perspective) more.
@@maynardtrendle820 And I wish that everyone who wins, would immediately leave and that the casinos (which I don't personally like) would go out of business. Again, your statement is true, but I still prefer my opinion. And I would never pass a law against gambling - I prefer democracy.
Gut instinct for the problem with Alice and Bob tryna win $100 is that for Alice, you're gonna need to use a hypergeometric distribution, but of course now that I'm writing it out, I realize that I'm probably wrong because for every dollar she wins, that's one more bet that can go wrong without cutting into her progress on trying to win $100, so the total # of trials isn't set
Setting up a markov chain would be your best bet for that problem.
That's a very rational response; I don't think you know what a gut feeling is.
@@fatsquirrel75 wait are you telling me that gut feelings have to be irrational?
Very informative. Thanks
You can TECHNICALLY make the Come and Don’t Come bets and their respective odds at the craps table and enjoy the same EV as Pass/Don’t Pass, but I guess it’s the same game :-) fun and informative video!
There is exactly one bet at the casino with no house edge. That is the "odds" bet on the craps table. The "odds" bet will pay you the exact odds on hitting that role making it a neutral EV bet.
The casino takes a small edge on the 1 to 1 payout on the pass line itself (required in order to play the "odds" bet).
Every bet you play at the craps table the house has got the edge. The best you can hope to accomplish is to minimize that edge
I knew Carlos had a bigger chance, I just knew it
And so did everyone else.
Well, you have totally convinced me to stay out of the casinos !
such a great vid!
I love that line at the end where you basically just say "You should eat that paint if it tastes good"
Some people you can't reach with reason and math, so you may as well just tell them to have fun 🤣
Here's one aspect of roulette wheels. If they are the traditional mechanical type (vs "virtual" wheels) that machine, over time, will exhibit biases which, if discovered, can actually tip things against the casino.
@@davidharris3264 Didn't some casinos lose a crapload if money? Was that made into a movie? I don't recall.
Even if the wheel is bias on a certain sector, the bias will be practically eliminated because of the frets that the ball hits before landing on the number.
That is the purpose of the frets.
@@wacky6136 the bias exhibits over the long run over thousands of games
I did that on FanDuel. They started spinning the wheel insanely fast. Called it shaking the wheel up. I think I lost my edge. I ended up calling it a day after the fifth loss in a row. I was still up about fifty bucks.
I always play corners in roulette. My strategy is to play $5 chips and place a few different bets per round. I’m yet to lose playing like this, although I’m sure statistically I’m probably just getting lucky and there’s some way I could be playing smarter