Pro Card Counter Answers Casino Odds Questions From Twitter | Tech Support | WIRED

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  • Опубліковано 15 тра 2023
  • Yuchun Lee, professional blackjack player and former member of the MIT card counting team, answers the internet's burning questions about casinos and odds. What are the odds of winning a slot machine? What's the best blackjack strategy? How does card counting work? What's the best poker strategy? What casino games make the house the most money? Yuchun answers all these questions and much more!
    Director: Justin Wolfson
    Director of Photography: Francis Bernal
    Editor: Louville Moore
    Expert: Yuchun Lee
    Line Producer: Joseph Buscemi
    Associate Producers: Paul Gulyas; Brandon White
    Production Manager: Eric Martinez
    Production Coordinator: Fernando Davila
    Casting Producer: Nick Sawyer
    Camera Operator: Eric Brouse
    Audio: Sean Paulsen
    Production Assistant: Ryan Coppola
    Post Production Supervisor: Alexa Deutsch
    Post Production Coordinator: Ian Bryant
    Supervising Editor: Doug Larsen
    Additional Editor: Paul Tael
    Assistant Editor: Andy Morell"
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  • Розваги

КОМЕНТАРІ • 1,7 тис.

  • @ryanmanning2846
    @ryanmanning2846 11 місяців тому +18464

    Gambling at the casino helped my family get much closer. We had to move into a smaller house

    • @eternalselph
      @eternalselph 11 місяців тому +152

      😂😂😂😂

    • @mdubb9621
      @mdubb9621 11 місяців тому +71

      😂😂😂😂😂😂😂

    • @admiralthrawn7754
      @admiralthrawn7754 11 місяців тому +73

      I don't know why everyone else is laughing at your misery. I apologize for their treatment.

    • @daytonabeachh
      @daytonabeachh 11 місяців тому +293

      @@admiralthrawn7754 it was probably a joke..

    • @vadimakdav1357
      @vadimakdav1357 11 місяців тому +302

      ​@@admiralthrawn7754 you can clearly see tears in the emojis, no one is laughing.

  • @AhmedMostafa-gu8ot
    @AhmedMostafa-gu8ot Рік тому +9102

    For amateurs, the reasonable way to go to casinos is by deciding how much money you're willing to lose ahead of time, and thinking of that amount as a fee for entertainment.

    • @PanchoPonceN
      @PanchoPonceN 11 місяців тому +852

      This. This is exactly how common people should see casinos. As entertainment, not as an investment.

    • @zesolodar
      @zesolodar 11 місяців тому +243

      thats exactly what my dad taught me the first time i went to a casino. he said you have to set a number your comfortable with loosing- some people thats 100 bucks, others its a thousand, and your just there to have a good time.

    • @HyperionFive
      @HyperionFive 11 місяців тому +56

      But how are people comfortably entertained by knowing they gonna lose anyway?!
      I just can't do that! I hate losing and I can't be entertained knowing I am gonna lose.
      That being said, I am still curious about going to a casino just out of curiosity for the atmosphere and for the sake of the experience (one time in life), but I definitely wouldn't be finding it entertaining knowing I will loose even just 100 bucks 😄 I would probably be anxious all that time and not finding any joy in playing anything. That would change IF I had someone else's money to play with.
      The whole thing feels like a nicer way of being robbed, like a thief asking for your permission to rob you 🤦‍♂

    • @aarushvemuganti9947
      @aarushvemuganti9947 11 місяців тому +161

      @@HyperionFive i think its because everyone has to have that tiny feeling in the back of their mind "what if I do win" that's what's enough to get them to a casino and gamble

    • @FMSkyLoL
      @FMSkyLoL 11 місяців тому +129

      Yeah, always do it with the mindset "How much money am I willing to spend?". Other hobbies cost money too. If you have fun doing it, go ahead

  • @Nikkiflausch
    @Nikkiflausch Рік тому +6366

    I like how this guy‘s fully transparent about casinos just always being a losing game. The entire framing already starts with „you lose less“, never even implying you could (= should) try to win.

    • @kiyokiyoko
      @kiyokiyoko Рік тому +226

      transparency would be if he worked at a casino, he has no incentive to lie about raw stats

    • @TheExdraconian
      @TheExdraconian Рік тому +94

      You know he used to go after casinos right? Why would he care about hiding info to benefit them?

    • @userac-xpg
      @userac-xpg Рік тому +78

      that's because the only way to win long term against the casino is to play a game at an advantageous state (to the player) This is only possible in blackjack if counting cards, or in progressive slots if the Jackpot is high enough. All other games this is impossible UNLESS there is some kind of defect like a biased roulette wheel or other mechanical error

    • @TheIbney00
      @TheIbney00 Рік тому +7

      @@userac-xpgas Richard Munchkin says, it is probably possible to beat every game in a casino. You just gotta know where to look.

    • @charliekeane2520
      @charliekeane2520 Рік тому +32

      @@kiyokiyoko Not true, there's countless people out there claiming to have a system and trying to get people on board. Whether they want to sell a book, views on a video, etc.

  • @wonderwhyiwonder3458
    @wonderwhyiwonder3458 Рік тому +3473

    I love when you can see him catching himself and thinking "How can I say this, but on a random UA-cam watcher level?"

    • @realpillboxer
      @realpillboxer Рік тому +370

      Being able to take in complex knowledge and distill it for succinct consumption is an incredibly underrated, yet highly valuable, skill.

    • @Zzyzzyzzs
      @Zzyzzyzzs Рік тому +116

      Scientists always get accused of talking over or patronising people. I don't know why, but people get incredibly insecure about how little they know, even when they're actively seeking knowledge and asking questions about something they don't know. In that context, being able to explain stuff in a way that doesn't prick that insecurity, puts people at ease and they still end up learning the information accurately is valuable. Because the alternative is they get hostile, mentally block you out and end up just as ignorant as before, having learned nothing.

    • @ramshacklealex7772
      @ramshacklealex7772 11 місяців тому +1

      Was that why he said "law of large numbers" when what he was describing seemed to be regression to the mean?

    • @jcs3146
      @jcs3146 11 місяців тому

      ​@@Zzyzzyzzs this really resonated with me

    • @rickysmith6041
      @rickysmith6041 11 місяців тому +33

      ​@@ramshacklealex7772 no that's literally a law you can look it up. Math and physics degree holder here.
      Personally, I don't think he's holding back, they were pretty simple questions. He's answered them properly and concisely. Also, I don't see anyone accusing scientists of talking over them. Real professionals know how to explain things in simple terms, if someone is sounding confusing check their education. I see a lot of uncredible sources on youtube try to use big words when they don't know anything. In an academic or professional setting, that would be cringe and no one would ever do that. I instead see people more so saying they KNOW MORE THAN THE SCIENTISTS 🤦‍♂I think that's way more common than people saying they talk over them.
      I think it's just the way he talks that makes you feel like he's struggling to explain it simply, you can feel confident that he didn't hold back telling you anything. It's just his mannerisms.

  • @jopo7996
    @jopo7996 Рік тому +4975

    Your best bet is staying outside the casino.

    • @punchmadedmacka
      @punchmadedmacka Рік тому +21

      lol

    • @androiduberalles
      @androiduberalles Рік тому +52

      🤷🏻‍♂️ if you don't go crazy and stick to video poker or something, you can have a pretty good time on $20 over an hour or so. You can easily blow $20 doing something else.

    • @Morgan423Z
      @Morgan423Z Рік тому +53

      You could do what my mother in law did, and stick fifty cents in a low-fry slot machine on the Vegas trip. She didn't gamble anything else the rest of the trip, but she only paid half a dollar for the right to truthfully say, "I gambled in Vegas." 😆

    • @alexandermutsaers2693
      @alexandermutsaers2693 Рік тому +40

      That’s loser talk

    • @ro_achterberg
      @ro_achterberg Рік тому +2

      😅😮

  • @RoomOne001
    @RoomOne001 Рік тому +2800

    I love how he basically goes 'you make the most money in poker when you play against people that are really bad. Also, sidenote: my friend created a software to track really bad poker players online so he can make a lot of money'.

    • @sethkang4410
      @sethkang4410 Рік тому +55

      going against people vs machine is easier

    • @userac-xpg
      @userac-xpg Рік тому +28

      online poker is for cheaters.

    • @TheStein36
      @TheStein36 Рік тому +266

      You make money over other players in poker by having a skill edge over other players. If you can’t spot the fish you are the fish.

    • @Shipdacheese
      @Shipdacheese Рік тому +8

      @@userac-xpg haha ok

    • @ajm5007
      @ajm5007 Рік тому +89

      With poker, you still can't beat the house, but you can beat the other players. The table as a whole will lose money, but some players at that table might come out WAY ahead.

  • @jacobsweet9270
    @jacobsweet9270 Рік тому +1089

    Another fun fact is that casinos like to put out tons of slot machines so that if they hit a jackpot, lets say, every hour, then having 60 machines makes it sound like they are winning every minute to people hearing the jackpot sounds. This helps the psychology to get players to want to play them as they hear the jackpots more often even though they may only be happening 6 times in a whole day on a machine

    • @CorwinPatrick
      @CorwinPatrick 7 місяців тому +24

      Also, the layout of Slot Machines are Strategic. Machines near thruways and places where lines form can be set at the lower end of the dial. So tired and bored line holders will sit down and throw quarters away (or dollars).

    • @janos5555
      @janos5555 3 місяці тому +12

      Yes, I have only played ones and it is not just the jackpots. You habe a constant feeling you are winning. You put in 10 Cents per game, will lose 4 games and win 1 for 20 Cents, so you lost 30 Cents, but the maschine will use sound and lights in a way that you will forget your 4 losses and remember that 1 win.

    • @MeanBeanComedy
      @MeanBeanComedy 2 місяці тому +3

      Wouldn't that be 24?

    • @yjlom
      @yjlom 2 місяці тому +1

      @@MeanBeanComedy if it's at full occupancy around the clock, then yeah, but how many people are playing in eg the early morning?

    • @PorkBoy69
      @PorkBoy69 2 місяці тому +2

      @@MeanBeanComedy Wow bro u can do arithmetic, clap clap

  • @andrewjames9132
    @andrewjames9132 10 місяців тому +509

    I worked at a casino as a bartender, the casino I worked at had the hot machines at the bar. It was great for me but it made me realize casinos do what they need to to benefit the house. A guy wins 200 at the bar, he buys the bar a round of shots, the house makes back 60 and I make 30

    • @konigstiger3252
      @konigstiger3252 8 місяців тому +3

      😂

    • @cmd31220
      @cmd31220 6 місяців тому +37

      That's the biggest thing I feel like people don't fully appreciate about casinos. Vegas built a global brand and dozens of multi-billion dollar hotels and casinos off of a 2-3% edge. They lure you in with promises of riches and keep you at the table as long as possible because even if you break even, they win. Even if you win, everyone around you lost. But only enough where they think it's bad luck and/or worth the fun.
      If you're trying to actually make money, you need to know your math and ignore everything else around you.

    • @paulcooper1046
      @paulcooper1046 6 місяців тому +4

      That's a win for everyone involved.

    • @cypobos
      @cypobos 2 місяці тому +5

      ironically, because of those kind of reasons, if they managed incredibly well all the things outside of the money games part, casino could still come out positive without having an edge in games. games would not be here to make money, but just to bring people in and incite them to spend money outside of the games.
      that's close to the business plan of some video games. gacha games, they make you pay to randomly roll for rewards with odds stacked in your favor, if that wasn't enough, they even make you more likely to win big if you lose repeatedly. thing is, regardless of winning or losing, you're not winning back money. and all they are ever spending on you is simply their initial development costs.

    • @SupraSav
      @SupraSav 2 місяці тому +3

      That's pretty much the reason I stopped going to casinos and venture cautiously anywhere - everything has been psychologically designed. Pure oxygen pumped in, free drinks, and tailored experiences like you mention, there's plenty more under the woodwork, I'm sure.

  • @mindbomb2000
    @mindbomb2000 9 місяців тому +1081

    I'm just an average poker player, but his point about playing bad poker players is spot on.
    One time I was in Vegas at an open table (hold 'em), and these 3 guys entered the game...they seemed like they knew the game and probably played a weekly game, but I started noticing a rhythm in their betting and all three played the same type of game. I folded a bunch of hands and watched.
    They tended to bluff early, but with small bets. If they had a good hand, they would open strong. So I started to only play really strong hands (occasionally showing my cards to prove this), and folding if they ever raised, making them think that I never bluffed. I could see them talking to each other pointing this out. So I let them steal a few blinds that I would normally play.
    Within ten hands I could literally predict when they had a strong hand. I made around $500 off of the three of them.
    The point: Any good player would have crushed me but you don't have to be the best, just be better than the others.

    • @isaacmendes1926
      @isaacmendes1926 8 місяців тому +70

      now you ruined their weekly poker lol

    • @carlosbaquerizo1589
      @carlosbaquerizo1589 8 місяців тому +53

      So you are telling me if i want to win.. i just have to be better than my opponent? Wow never tought obout that before

    • @mindbomb2000
      @mindbomb2000 8 місяців тому

      Ha ha... yeah I know, it's kind of a dumb post by me if you look at it that way, but I'm still surprised at how many people can't read the table and take advantage of the weaker players. Honestly I wasn't even the best player at the table, so I avoided hands with the better players and capitalised of those guys. @@carlosbaquerizo1589

    • @lovelessissimo
      @lovelessissimo 7 місяців тому +85

      ​@@carlosbaquerizo1589No need to be rude.

    • @farrel_ra
      @farrel_ra 7 місяців тому +60

      ​@@carlosbaquerizo1589on top of that, he's telling his experience to back it up. I don't see u do the same.

  • @peppygrowlithe
    @peppygrowlithe 11 місяців тому +1066

    These are really well-explained. He explains these sometimes very complex things in a quick, straightforward, intelligent way.

    • @matthewbrealey2026
      @matthewbrealey2026 11 місяців тому +20

      too many errors:
      * house edge of baccarat is 1%, not 0.5%
      * best odds in the casino for dumb player is technically craps, because the odds bet has no house edge and the pass/don't pass bets stay on the table for multiple rolls (at 1.4% HA)
      * the number for blackjack edge at the beginning are weird; not as much as 3% (unless it's 6:5 bj), but below 1%
      * house edge for casino games calculation is deterministic, not Monte Carlo/RNG.
      * Martingale is not reason for bet limit, but simple risk reduction.
      * Volatility of slots wasn't answered
      * Casino games aren't rigged, he should have challenged that
      * he got the odds of 8 reds in a row wrong (18/38^8, not 1/2^8)

    • @reivang7196
      @reivang7196 9 місяців тому +17

      @@matthewbrealey2026 I bet you try to correct a Nobel promise winner in the comments of you the chance 😂, just stop it.

    • @Cowtymsmiesznego
      @Cowtymsmiesznego 3 місяці тому

      @@matthewbrealey2026 Thank you. I noticed a few of those but it's nice to see a summary

  • @dragon6irl
    @dragon6irl 8 місяців тому +100

    2:40 I like how his hand just phases through the PNG of cards and chips on the table.

    • @jukeboxygo4353
      @jukeboxygo4353 2 місяці тому +2

      lol just noticed

    • @BladedAngel
      @BladedAngel Місяць тому +4

      They didn't even try to crop wiht a magic wand tool either. Thing was a giant smudge of white LMAO.

  • @sciencebunny
    @sciencebunny 11 місяців тому +599

    You can tell he’s truly studied everything around gambling at casinos

    • @jimklemens5018
      @jimklemens5018 11 місяців тому +6

      He doesn't know craps.

    • @timoofthenight1432
      @timoofthenight1432 11 місяців тому +5

      I could've answered all of these with little experience

    • @CloverJam
      @CloverJam 10 місяців тому +23

      These are super basic questions

    • @KrazzeeKane
      @KrazzeeKane 10 місяців тому +38

      @@timoofthenight1432 yet somehow you aren't the one they asked, hmm...almost like he's an actual expert or something

    • @timoofthenight1432
      @timoofthenight1432 10 місяців тому +5

      @@KrazzeeKane he might be an expert but this video doesn't show it like the original comment said

  • @The_BigB
    @The_BigB Рік тому +82

    Not the cgi chips and cards XD 2:40

  • @patricksingleton7516
    @patricksingleton7516 4 місяці тому +41

    "the best poker strategy is to be good at poker"
    This is basically the best answer he could give, since it would take maybe hundreds of hours to actually describe something close to optimal strategy. The set of possible gamestates is just so much larger than any table game, alnost infinitely so for any given stack depth

  • @kahlzun
    @kahlzun Рік тому +203

    I've had fun at a casino before. The trick is to think of it as spending money, the same as you would at a cinema or something. If you walk away with a win, thats a bonus. Otherwise, you're paying for the thrill of the risk.

    • @HaircombMan
      @HaircombMan Рік тому +18

      I'm so stealing that "you're paying for the thrill of the risk". You worded it so nicely.

    • @doublestrokeroll
      @doublestrokeroll 10 місяців тому +6

      For me the "thrill" disappeared after learning the odds. Table games just became boring to me. Even the winning.

    • @lionbear7078
      @lionbear7078 6 місяців тому

      This is what gambling addicts say

  • @AsylumOfSolitude
    @AsylumOfSolitude Рік тому +670

    I’ve worked at many casinos, and for a very long time. Something like to mention to players who say something like, “It’s landed on Red 8 times in a row! The odds of that are crazy!” And I’m seeing people in the comments saying (correcting) the math he mentioned in this video. HOWEVER, something to consider is those crazy odds are ONLY the odds if you were to make the bet BEFOREHAND. For example, “I bet it’ll be Red 8 times in a row.” THEN, the odds would be crazy difficult. Playing in REAL TIME, and betting red each time…the odds will always be slightly LESS than 50%. Each and every outcome is totally independent of the last.

    • @sarabsinghmonga1927
      @sarabsinghmonga1927 Рік тому +19

      Yeah its called regression to the mean.

    • @benjaminaltube8731
      @benjaminaltube8731 Рік тому +34

      Yeah people tend to forget it isn't a cumulative chance the chance of you getting a color is always 50%
      Same as 0, the chance of getting it is the same as getting any other single number. It only isn't affected by color so you're forced to bet individually

    • @setcheck67
      @setcheck67 Рік тому +61

      This is what makes slot machines particularly dirty. In the real world probability is always the same every time, but in software probability DOES follow mathematical statistic formulas because it frankly is a simulated mathematical statistic formula for pseudo randomness. So that slot machine IS keeping track of how many wins/losses and will reward it's payout according to that. Likewise in online gambling you're dealing with the same problems, the computer can and will streak you into a number of wins and losses.

    • @AsylumOfSolitude
      @AsylumOfSolitude Рік тому +22

      @@benjaminaltube8731 well it’s fair to correct your comment as well: the chances of getting a red/black in roulette is not 50%. It is less, because there are (typically) two green options on the wheel as well.

    • @monkeySkulls
      @monkeySkulls Рік тому +1

      omg. I have understood this concept for years. I have never been able to explain it at all. and now I even have a name for what this is.
      thank you

  • @jarrakul
    @jarrakul 9 місяців тому +75

    Loving how much he's just using/explaining statistics concepts. Which makes perfect sense, but he's doing a really good job of laying this stuff out.

  • @Ojisan642
    @Ojisan642 Рік тому +140

    I’m glad he mentioned craps. That is the best game in the casino because if you play basic strategy, you have odds that are almost as good as blackjack, and so you can play a long time without losing too much money, get free drinks, and the craps table is more fun and exciting than blackjack. You’ll still lose, but you’ll have more fun doing it than blackjack. Also nobody yells at you for “doing it wrong” which does happen at blackjack tables.

    • @kruks
      @kruks 11 місяців тому +37

      The best thing about craps is that you're playing to win with the rest of the table. It's one of the few social games where you're not trying to beat the other players and you can celebrate wins together.

    • @djm5687
      @djm5687 11 місяців тому +11

      ​@kruks ...unless you bet on Don't Pass. Which can be very fun....

    • @evergreenrider
      @evergreenrider 10 місяців тому +3

      ​@@kruksunless you're betting big red lol

    • @fluffysheap
      @fluffysheap 4 місяці тому +2

      Yes. I disagree with the video about baccarat. While it does have a good payout per hand, baccarat is a very fast playing game, even faster than blackjack. That means you can lose your money faster. Roulette and craps have odds that aren't quite as good, but are close (especially for craps, if you bet most of your money on the odds). But roulette and craps are very slow games so you can play for a long time before you inevitably lose.
      The other thing about roulette and craps is that because of the wide variety of bets available, you can adjust your play style for the kind of gambling you enjoy. Baccarat has only player and banker, which are almost the same, and the tie, which is a sucker bet. There is not really very much variety.
      I do not think baccarat is a very good game 🙃

    • @brandon7957
      @brandon7957 4 місяці тому +1

      ​@@fluffysheapbacc is the easiest casino game by far. Lol. Its 2 bets. You say you can lose money quickly but it also goes the other way as well. It can be gained just as fast.

  • @TheBlunk86
    @TheBlunk86 Рік тому +54

    I like how he has the Blackjack Apprenticeship basic strategy chart there. 5:09

    • @AdamAarts
      @AdamAarts Рік тому +3

      I have the same chart saved on my
      Phone hahah

    • @misterchubbikins
      @misterchubbikins 2 місяці тому +3

      Umm. . . You do know the chat BJ Apprenticeship uses was designed in 1956 and that this guy was using that same chart in the 90s as part of the mit blackjack team before Colin even knew what blackjack was, right?

  • @NovaHorizon
    @NovaHorizon 10 місяців тому +181

    As a former casino employee (specifically in the gaming department) I only have 1 math correction and 1 linguistic correction for all of this.
    1) 0:40 Lee states that a regular player loses $1.5-$3 per $100 in blackjack (1.5-3% hold for the house.) However that's too optimistic of the regular player's base skill level. We almost always had a hold of around 20% on our Blackjack tables because players are regularly quite bad at the game. (Our house had 3:2 blackjack and no continuous shuffle machine.)
    2) 7:48 Lee says "The follow on bets are even odds." In a casino, "even odds" would be used to describe a 1:1 payout. What Lee is intending to say is they are "true odds" bets. These are bets where the payout is identical to the chance to lose the bet. What he describes is correct, it was just the wrong phrase.

    • @thedemon2149
      @thedemon2149 10 місяців тому +23

      I got one more:
      At 10:44 he says the odds of eight reds in a row is 1 in 256, but the chances of red are only 18/38, not 1/2, so the odds are actually closer to 1 in 394

    • @NovaHorizon
      @NovaHorizon 10 місяців тому +17

      @@thedemon2149 yeah, I was going to ignore that though since he was doing mental math and powers of 2 are a lot easier lol. But you are technically correct. The best kind of correct. 😅

    • @casper14301
      @casper14301 10 місяців тому +6

      ​@@Marvininini How did you get ≈0.000172? I got ≈0.00253 which is about a 1 in 394 chance. You didn't even use mental math and you're way off, so don't insult his mental math. Unless you're trolling of course lol.

    • @Paul-vf2wl
      @Paul-vf2wl 7 місяців тому +1

      The side bets on blackjack tables are the money makers for casinos.

    • @NovaHorizon
      @NovaHorizon 7 місяців тому

      @@casper14301 oh I missed what ever you were replying to. I tried to figure out what number the guy must have done and the best I can figure it 0.000175 is hitting red 12 consecutive times on a single 0 wheel. 🤔

  • @barthalen
    @barthalen Рік тому +803

    As a kid, I felt so smart for thinking of a way how to win at roulette by betting on a color and doubling my bet every time I’d lose, until I’d eventually win. So cool to now discover there’s a name for that, haha. Never put it in practise though.

    • @ok-nq8mr
      @ok-nq8mr Рік тому +48

      Martingale System i think

    • @Lukethetiger
      @Lukethetiger Рік тому +162

      Yeah cause it can get you bankrupt 😅
      Even if it’s unlikely to let’s say lose a 100 rounds in a row, it’s still possible and will happen to you eventually if you play over the long run. Even if you start with 50 cents and then double that every time you lose, you will be bankrupt very early already if you are not a multi billionaire being able to back up the extremely high doubling that comes at some point.

    • @mechmat12345
      @mechmat12345 Рік тому +127

      ​@@Lukethetiger correct. And if you show me the billionaire who will bet the rest of his fortune on a single spin at roulette after losing 99 times in a row, I'll show you a fool.

    • @VikramSingh-fw8hb
      @VikramSingh-fw8hb Рік тому +139

      @@Lukethetiger The idea with that strategy is to keep doubling till you win, and then never ever play the game again. That’s where most people falter, they keep playing after doubling up and then essentially the Casino is now playing with the Martingale system

    • @gozer825
      @gozer825 Рік тому +80

      The problem is when u win that really big bet you only win back the amount of ur original bet as profit subtracting all the previous losses.

  • @devdog7409
    @devdog7409 Рік тому +66

    6:55 It’s not really to stop the martingale betting strategy (though it does) because they know eventually the player will go on a losing streak and they will get their entire bankroll. It is more to cut down on variance. If someone goes in and bets a million on one outside bet in roulette, then the law of big numbers hasn’t really come into play because it is only one bet. The player has a pretty good chance at winning and then walking away with a million. By having limits it forces them to play more rounds to win a substantial amount of money and thus the law of big numbers kicks in.

    • @CarlosSamuel-ms9ee
      @CarlosSamuel-ms9ee 8 місяців тому +17

      Yeah I really don't know why he said that, martingale is completely flawed. Like you say variance is a big factor. Another consideration would be if someone found a way to cheat, they would have more chance to catch then before they walked away with a huge profit.

    • @lynco3296
      @lynco3296 3 місяці тому +9

      The martingale strategy is a good reason for the betting limit. Without these limits Elon Musk could pretty easily bankrupt pretty much any casino before the law of big numbers would save them.

    • @devdog7409
      @devdog7409 3 місяці тому +10

      @@lynco3296 nope.

    • @bonusmeme4691
      @bonusmeme4691 3 місяці тому

      @@lynco3296 The only reason for betting limits is to decrease variance. Casinos need to control the variance because they are in the business of making steady but certain profits, so they don't want to let Elon Musk walk in and put 100 million on 00. Martingale or any other betting strategy is not going to change the probability of the huge bet making the casino lose a year's worth of profit

    • @Cowtymsmiesznego
      @Cowtymsmiesznego 3 місяці тому

      @@lynco3296 You're right about the conclusion but wrong about the reason. It's a mathematical fact that a billionaire will have a better chance of outlasting the casino by taking the biggest possible bet over and over than by making any low bets (like he would in Martingale).
      Yes, Elon Musk could bankrupt the casino if there were no table limits, but Martingale has nothing to do with it. Musk would just bet on red against the casino's entire bankroll over and over until he won. He wouldn't start with any small bets (like Martingale would suggest) because that's just helping the casino build their bankroll for no gain.

  • @ryangraham9623
    @ryangraham9623 11 місяців тому +150

    this guy was very entertaining to watch and did a good job of explaining everything.

  • @mechmat12345
    @mechmat12345 Рік тому +303

    To expand of one of his answers: casinos in Las Vegas are allowed to kick you out for any reason. They do not need to justify their decision. So they can kick out card counters because card counters win money, and for no other reason at all.

    • @anderfu8273
      @anderfu8273 Рік тому +19

      Same with any store really, like Walmart.

    • @midknightcrisis8612
      @midknightcrisis8612 Рік тому +51

      I mean, isn't that the trespassing law he mentioned? The moment you as the owner arbitrarily consider someone a trespasser, you're legally allowed to throw them out since it's he's on your property? However you are formulating the justification afterward, if there was an actual court over this, wouldn't it lead back to that exact law?

    •  Рік тому +14

      He essentially said this lol

    • @tmtmtlsml
      @tmtmtlsml Рік тому +34

      @@midknightcrisis8612 Not necessarily. In order to trespass someone, there are certain steps you have to go through such as formally and unequivocally informing them that they are no longer welcome on the property. You cannot trespass someone without letting them know and then arrest them later. Also, you cannot trespass someone or deny services to someone if the reason is discriminatory such as their religion, ethnicity, etc.

    • @ronblack7870
      @ronblack7870 Рік тому +20

      unless you are cheating they may just tell you you are welcome to play any other game there but not blackjack. your play is too strong for us they can even say. you are there for entertainment not to run a financial enterprise. they are there to run a financial enterprise , not you.

  • @SoloAdventureDiva
    @SoloAdventureDiva Рік тому +49

    Lol as someone who works in a casino look at it as entertainment or a fun night out and never spend more than you can afford.

  • @SplittingProductions
    @SplittingProductions Рік тому +12

    2:39 *gasp!
    Those chips are edited in!!

  • @TMJJack
    @TMJJack 11 місяців тому +68

    Love the MIT guys. Colin taught me everything I know, and you all were part of his inspiration. Thanks for everything!

  • @stanleyroberts4381
    @stanleyroberts4381 Рік тому +13

    I agree, I took the Bobby Singer blackjack course and did very well with it back in the 80s.

  • @GaryLiseo
    @GaryLiseo 11 місяців тому +208

    My brother worked in a casino where he was taught how to count cards to catch counters. He had to memorize a cheat sheet (strategy outline) and would keep the count on an entire floor’s tables. He even admitted counting wasn’t illegal and the best he could do was ask someone to leave (can’t force them out)

    • @benhardin6095
      @benhardin6095 11 місяців тому +71

      It isn't illegal, but they can absolutely force anyone out. They just can't take any of the money you have already won. Any business can trespass any person for any reason.

    • @gilbertjacobs3705
      @gilbertjacobs3705 11 місяців тому +6

      @@benhardin6095 yep once they ask you to leave you're then on a countdown

    • @JasonEngland
      @JasonEngland 11 місяців тому +15

      This is not true in all jurisdictions.

    • @cthomas025
      @cthomas025 11 місяців тому +12

      @@benhardin6095 I mean he literally said in this video that in New Jersey they cannot kick you out for counting.

    • @failtolawl
      @failtolawl 10 місяців тому +1

      you can force them out...

  • @RA-dq4ro
    @RA-dq4ro Рік тому +32

    More of this guy please!

  • @brycedaugherty9211
    @brycedaugherty9211 7 місяців тому +5

    Super informative and analytical. Thanks!

  • @legendarymoshko3613
    @legendarymoshko3613 8 місяців тому +18

    The expert was very well spoken. Enjoyed this video!

  • @Joonzi
    @Joonzi 8 місяців тому +34

    The best guest you had in terms of clarity and giving actual answers.

  • @spaghettioso2799
    @spaghettioso2799 Рік тому +52

    Great video, he did a really great job of explaining!

  • @misterchubbikins
    @misterchubbikins 2 місяці тому +1

    This is argueably the most unbiased, straight foreward explanation I have heard on this topic.
    Props

  • @cmel7841
    @cmel7841 Рік тому +42

    I always use the time strategy, enter casino, play a certain predetermined amount if you win at ANY TIME, stop, walk out, works for me a lot, it takes a lot longer for me to get to the casino than I end up playing but leaving $5 up is fine by me

  • @billdodson5703
    @billdodson5703 Рік тому +104

    this was great! Need a part 2 with Mr Lee!

  • @captainkeller2792
    @captainkeller2792 Рік тому +18

    Its amazing how many people with strange professions you find. listening to those is so much fun.

    • @TheIbney00
      @TheIbney00 Рік тому +1

      If you find this stuff fun check out gambling with an edge. Just ended this week but they have 12 years of people talking about their advantage play exploits.

  • @jackie6786
    @jackie6786 2 місяці тому +2

    One of the best videos ever, especially the last part

  • @nickzhaosun
    @nickzhaosun 8 місяців тому +2

    Thank you for your expertise. I enjoyed it.

  • @ScreamsPenguin
    @ScreamsPenguin Рік тому +9

    This was a great video, this guy rocks.

  • @nepmobile3583
    @nepmobile3583 Рік тому +15

    This guys awesome! Really interesting explanations

  • @davidodonohoe1773
    @davidodonohoe1773 11 місяців тому +1

    Loved this. Just straight up answers.

  • @tobin1677
    @tobin1677 10 місяців тому +18

    I have heard some video poker setups have positive payout rates, the explanation I saw was that because the bets were capped at 25 cents or so the actual theoretical payout on a machine with 107% return (double bonus 7/10 iirc) if you play perfectly is only about $8 an hour, so the casino would still be fine since you have other expenses in those cases.

    • @bartfromnl
      @bartfromnl 2 місяці тому

      No other expenses when the beers are for free :-) I can see how this little loss can be accaptable, or even smart, if it makes players more confident to try bigger games tho. One game of roulettes and the casino has more than it's money back.

    • @glennyee184
      @glennyee184 2 місяці тому

      I was surprise he did not mention video poker as a game where you can be favored. As you mentioned 7/10 double bonus has a positive expected value of 100.17% (not 107%). So you are favored by 0.17%. That game is available in LV in the $1 denomination. But you are correct you can probably make $8 to $10 an hour playing this particular game in the long run. Not a fortune make by any means.

  • @EwokPanda
    @EwokPanda Рік тому +17

    If you're wondering how to figure out what bank value becomes +EV on a progressive slot machine, you need to know your odds of winning on that machine.. You can then calculate "the amount per play * number of plays needed to reach those odds" and figure out the amount. Usually you'd want the value to be quite a bit higher than that cost, as odds aren't a gaurantee.

    • @mrburns805
      @mrburns805 Рік тому +5

      @@roamingthereal4060 not always true. Some machines have a “this machine must hit bonus by x amount of spins and will actually have a counter. If it’s near the max then it will be very +EV. Good luck finding one that’s open though lol

  • @RobinPoker
    @RobinPoker 8 місяців тому +8

    Love it! Fancy having a professional poker player on this series guys?

  • @Ryan256
    @Ryan256 Рік тому +3

    Excellent summary of casino odds.

  • @dkoppenol
    @dkoppenol Рік тому

    Very nice vid! These are the best

  • @glenns.2676
    @glenns.2676 Рік тому +74

    Great video! Small point, but the chances of rolling red in roulette is 18/38 on a standard double zero roulette table, so getting eight reds in a row is about a 0.25% chance. 1/256 is about 0.39%

    • @cosisthebest
      @cosisthebest Рік тому +21

      He probably simplified the answer for the purpose of the average viewer but you're right

    • @urd3adnow
      @urd3adnow Рік тому +19

      he clearly knew this and just simplified lol

    • @criticalthinker3262
      @criticalthinker3262 10 місяців тому

      He knew that, but it's still surprising how much of a difference that makes. That's casinos for ya

    • @ThisHandleFeatureIsStupid
      @ThisHandleFeatureIsStupid 8 місяців тому

      @@urd3adnowSimplified? Clearly?
      Nah, man. He was just dead wrong there.
      The actual odds against the described event are 394:1, not 256:1.

    • @Romans8-9
      @Romans8-9 4 місяці тому +1

      ​@@ThisHandleFeatureIsStupid He simplified by assuming getting red was 50-50 when it is in fact 18/38. It is much harder to calculate 18/38. That accounts for the final difference.

  • @rudymartin8583
    @rudymartin8583 10 місяців тому +5

    10:54 This is really profound actually, and helps me understand gambling addictions way better

  • @nextari
    @nextari 2 місяці тому

    One of the best gambling videos I've seen!

  • @juggler314
    @juggler314 Рік тому +39

    took the easy way out - odds of 8 reds in a row is not 256-1 it's actually quite a bit worse since it's (18/38)^8 which works out to about 395-1 (changed more to "worse" as that didn't really make sense in context - odds are worse now - not better!)

    • @cadamdo1982
      @cadamdo1982 Рік тому +2

      Did he forget the green ones? I was thinking the same thing.

    • @rolandoftheeld
      @rolandoftheeld Рік тому +7

      While you are right that the odds of 8 reds in a row is 1/395, neither that nor 1/256 answer the question that SHOULD have been asked. The question should have been, "What are the odds of losing on 8 black bets in a row?" That becomes (20/38)^8, or 1/170 - more than DOUBLE the odds of specifically 8 reds.

    • @TueChristensenDK
      @TueChristensenDK Рік тому

      Was looking for this comment. Mr. Lee already talked about the green numbers, and it seems the are forgotten in this calculation

    • @marblemadness22
      @marblemadness22 10 місяців тому

      I also came here for this comment. How does a gambling expert forget about the green tiles on a roulette table?!? Sheesh

  • @eschiedler
    @eschiedler Рік тому +4

    Excellent presentation in such a short period about general statistics, probability, and game theory concepts.

  • @adog3129
    @adog3129 10 місяців тому +15

    imagine playing blackjack with the MIT card counting team and not knowing it. soul crushing experience

    • @RonJohn63
      @RonJohn63 2 місяці тому +4

      Players only tangentially play against other players; they play against the dealer.

  • @michaelworsham2724
    @michaelworsham2724 3 місяці тому

    Thank you for the clear explanations.

  • @Ramonatho
    @Ramonatho 11 місяців тому +35

    That point about a true gambler is someone who loves winning more than they hate losing really rings with me. A lot of my friends are gambling addicts where when I'm out on my money at the casino I don't go back to the ATM.

    • @CarlosSamuel-ms9ee
      @CarlosSamuel-ms9ee 8 місяців тому

      Yeah, you could almost say that is the definition of a gambler.

  • @Cheapiebeepie
    @Cheapiebeepie 10 місяців тому +10

    Gosh. Knowing all this, I sure would be embarrassed if I ran casinos and had to declare bankruptcy, say, 5 times.

    • @bob456fk6
      @bob456fk6 9 місяців тому +3

      You might move on to some other job, oh...like being President of the United States.

  • @michaeldegrave5905
    @michaeldegrave5905 Рік тому +8

    For what it's worth, the expected value of using the Martingale system is that you'll lose all your money even without limits. Your wins are so small and your losses are so tremendously large that you'll eventually hit a streak of losses that costs you everything. Plus by the end you're betting a billion dollars on one spin to win back the $10 or whatever you bet on the first bet, so it would never make practical sense anyway.

    • @aheroictaxidriver3180
      @aheroictaxidriver3180 Рік тому

      Murphy's law.

    • @aheroictaxidriver3180
      @aheroictaxidriver3180 Рік тому +1

      Even a very high table limit, like 10,000 times the initial bet, defeats the strategy.

    • @cyrannodb
      @cyrannodb 3 місяці тому +1

      Yeah, I suspect the tables having a fairly narrow range between their minimum and maximum limits is more of a logistical consideration, like not needing to stock the table with a wide range of denominations of chips.

    • @gyroninjamodder
      @gyroninjamodder 2 місяці тому

      This is why you take out debt to make sure you don't run out of money.

  • @exdejesus
    @exdejesus 4 місяці тому

    Very interesting! Thank you!

  • @ExtraVictory
    @ExtraVictory Рік тому

    Awesome video, awesome guest

  • @outsidethebox218
    @outsidethebox218 Рік тому +60

    I saw 12 red in a row at a table in reno. Some bet tons on red and made their rent... others almost took the luck personally and were betting on black just to go against whatever happened.
    At the height of it the past roll board was 90% red for like 20 some odd rolls....just insane and people were screaming. I was playing safe at the black jack table.

    • @lipslide101
      @lipslide101 Рік тому +6

      12 times is insane. That's a 1/4096 chance to happen

    • @Heopful
      @Heopful Рік тому +9

      Must've had something to do with the dealer having done it 9999 times

    • @seanbirtwistle649
      @seanbirtwistle649 Рік тому +15

      insider tip - always go with the run. you don't have better odds, but by the time you lose 20 spins in a row the only thing you're thinking of is how much you could have won. and yeah the christmas tree turns a solid colour sometimes. ive seen 22 hands lost in a row on baccarat - once in 10 years

    • @Migustinder
      @Migustinder Рік тому +6

      I used to be a casino dealer for 5 years and my record is 14 black numbers in a row.

    • @peterdrogan6926
      @peterdrogan6926 Рік тому +4

      I was a croup and I once did 23 reds, normally everyone is on it, it's nice to give money away

  • @hannahpumpkins4359
    @hannahpumpkins4359 11 місяців тому +8

    i love playing the penny and nickel slots - one time in the Bahamas I won the jackpot on the nickel slot machine (this was back when you put actual coins into the machine). It was around $75, and all these nickels started pouring out and were falling out of the tray onto the floor. I was really drunk, and was crawling on the floor to get my nickels, like under people's legs at the machines next to me, etc! My sister who was there with me took one look, and was like, "I have no idea who this crazy drunk girl is" and walked away!!! It was awesome - I felt like I won a million dollars.

  • @TerriPlunkett
    @TerriPlunkett 8 місяців тому

    Really good video & info

  • @kailinaleekuk
    @kailinaleekuk 4 місяці тому

    Thanks for the laymen explanation of GTO!

  • @Studeb
    @Studeb 11 місяців тому +3

    Awesome compact information, I'm always surprised at how many ways AI will be used, only now I considered it being used to find patterns with gamblers and poker players, they will definitely use it to win tournaments.

  • @travisdk84
    @travisdk84 8 місяців тому +7

    that former colleague that used an algorithm to hunt whales on online poker sites has bond villain energy. Equal parts genius and evil.

  • @jeffploetner
    @jeffploetner 10 місяців тому

    Awesome info!

  • @lancearmada
    @lancearmada 9 місяців тому +1

    I had never thought about some of these things. This was interesting.

  • @k0olmini11
    @k0olmini11 Рік тому +5

    This guy like a legend. Legit a movie was made out of them

  • @plunder3624
    @plunder3624 10 місяців тому +27

    goes to MIT . becomes professional card counter . well done .

    • @jimlahey3919
      @jimlahey3919 8 місяців тому +6

      Doesn’t hurt to have a 6 figure degree to fall back on. Backup plans are nice to have

    • @chrisss689
      @chrisss689 Місяць тому

      It's a wonderful feeling to know that you could do something entirely different in your life whenever you feel like doing that and still being in a comfortable spot financially :)

  • @LegendaryVideoVlogs
    @LegendaryVideoVlogs 8 місяців тому

    loved the video. very informal. i play baccarat, poker, and blackjack mostly.

  • @AshaiTides
    @AshaiTides Місяць тому

    This was a great video!

  • @warrensnook9435
    @warrensnook9435 Рік тому +45

    I’m a math and computer science teacher who worked as a dealer and floor supervisor during my college days.
    These are all spot on. 👍🏻

  • @questionmark1152
    @questionmark1152 Рік тому +19

    "There are people that value the thrill of winning money over the misery of losing money."
    🤣🤣🤣🤣🤣

  • @flow6156
    @flow6156 Рік тому

    Buffer Overflow, so much information

  • @ExTAzY101
    @ExTAzY101 Місяць тому

    Very informative . this guy knows what he is talking about.

  • @quietlychattering
    @quietlychattering Рік тому +4

    This really fun for a maths nerd like me. And i dont gamble but still it’s interesting to know. This one is the best. Neuroscience and the optical illusion was equally fun

  • @JohnSendrey
    @JohnSendrey Рік тому +17

    Odds of 8 consecutive reds is 1 in (19/9)⁸ (1 in 395 approx.), not 1 in 2⁸ (1 in 256). Also Martingale in a negative-EV game always loses eventually, even when there are no table limits.

    • @tmtmtlsml
      @tmtmtlsml Рік тому +13

      Theoretically, you can only lose using a Martingale strategy with no table limits is if you run out of money. If you have infinite money to bet, you will eventually win. There is no infinite series of losses in an infinite series of spins, at least as far as my understanding of statistics goes

    • @Fast148
      @Fast148 Рік тому +2

      @@tmtmtlsml which is, unfortunately, how real world works. Even a bilionare will lose with Martingale, as they have limited money

    • @aheroictaxidriver3180
      @aheroictaxidriver3180 Рік тому

      @@tmtmtlsml Murphy's law.

  • @rodneyzurek4900
    @rodneyzurek4900 8 місяців тому

    Great video!

  • @JustMe-xb4ey
    @JustMe-xb4ey 2 місяці тому

    Great explanation. Smart dude!

  • @jamess870
    @jamess870 Рік тому +28

    Wow, he's one of the legends of gambling! Cool to see him here!

  • @latchdoorlatch996
    @latchdoorlatch996 Рік тому +10

    Never stepped foot in a casino but this was so interesting

    • @jliller
      @jliller 2 місяці тому +1

      I walked through one in Vegas while in town for a convention. The place reeked of stale cigarette smoke and dead dreams.

  • @wildfoodietours6702
    @wildfoodietours6702 18 днів тому

    Love this guy! I learned so much in so little time. He's really good and I wish I could gamble with him.

  • @gordonhodgson8266
    @gordonhodgson8266 Рік тому

    Outstanding!

  • @The-Dom
    @The-Dom 8 місяців тому +9

    I'd be so interested to see this guy analyze some online gambling stuff. I used to play roulette online. when I played for free, my system worked extremely well, but as soon as i started playing for money (tiny bits) i noticed the behavior of the random generator change and my system was defeated.

    • @paulcooper1046
      @paulcooper1046 6 місяців тому +1

      I didn't even know online roulette existed. Cheers, mate.

  • @manbuckets
    @manbuckets Рік тому +8

    Should get Blackjack Apprentice for this too!

  • @RayDusso
    @RayDusso 2 місяці тому +2

    I can understand Blackjack and Poker but I never understood the entertainment value of losing money in a slot machine.

    • @OGdadpool
      @OGdadpool 26 днів тому

      Lights and sounds go "brrrr"

  • @briannelby7480
    @briannelby7480 2 дні тому

    Great honest video!

  • @doublestrokeroll
    @doublestrokeroll 10 місяців тому +26

    When I was getting into poker I read a book that broke down the odds of the various games. Roulette and Craps were terrible. Somewhere around 55% to the house if I recall correctly. As he said, Blackjack is a little better if you know what your doing but only tip in your favor if you can count cards.
    Still though...after reading that book, I basically never wanted to play any casino games again. Before that I used to enjoy the odd sit down at a blackjack table, not thinking I would win mind you. I always knew the odds were against me, but it was the degree. After that, I literally found it super boring to play. Basically it killed whatever idea I had in my head about it being "just entertainment." Like if I were to throw money into a fire and try to call that "entertainment".
    Poker on the other hand, is amazing. Even there though, the house gets it's cut for hosting the game and you've gotta factor in the rake to see if it's worth it. Some casino's are a complete ripoff on the rake and that can cripple your returns to the point of not being worth it.

    • @fluffysheap
      @fluffysheap 4 місяці тому

      Roulette and craps aren't nearly that bad. The only game in the casino that pays around 50% is Keno. And the state run lottery (but at least that funds schools or parks or whatever your state does with the money).
      Roulette and craps pay better than 90% (the exact amount depending on the exact bet and rules of the game) so long as you avoid the handful of really bad sucker bets.

  • @BlueShellshock
    @BlueShellshock 9 місяців тому +15

    2:46 - I used to own a roulette wheel like this. It somehow got damaged, and it would always lean towards all the numbers around the 00. If you guessed any number on that side of the roulette, or 00 itself, you would tend to win pretty reliably. Because of where it was leaning, it make black and red worse, but my sis and I could reliably win by guessing 00, and eventually it'd hit.

    • @NeZCheese
      @NeZCheese 6 місяців тому

      Can you even bet on 00?

    • @cyrannodb
      @cyrannodb 3 місяці тому +2

      ​@@NeZCheese yes. You can bet on any number. The thing with the 0 and 00 is that when it hits, it's a loser for every other number and every flavor the grouped bets (like "1st/2nd/3rd 12", "red/black", "even/odd", the full column bets and the half board bets). It wipes out every possible bet except for four: straight 0, straight 00, "0/00", "0/00/1/2/3"
      And it's the presence of the 0 and 00 that makes even money bets like red or black a losing proposition. It's like betting even money on a coin flip when there's a non-zero possibility of the coin landing on it's edge.

  • @stephanschmidt2334
    @stephanschmidt2334 2 місяці тому

    Excellent explainer.

  • @jeffreytackett3922
    @jeffreytackett3922 Місяць тому

    Nice. Wired finally puts someone in one of these videos who actually knows what they're talking about. Love it. Well done.

  • @ThisAintAStupidName
    @ThisAintAStupidName Рік тому +51

    The best way to leave a casino with a small fortune, is to go into the casino with a large fortune.

  • @Sunless1337
    @Sunless1337 10 місяців тому +3

    No one in the comments talking about this guy's friend and the online poker games. That's just brilliant. 😂

  • @ChonkySlotDonkey
    @ChonkySlotDonkey 8 місяців тому +1

    Awesome video, this guy has a galaxy brain!!

  • @MegaJackolope
    @MegaJackolope 2 місяці тому

    Going to apply this knowledge to my Balatro games

  • @emaster01
    @emaster01 Рік тому +7

    As a mathematician who has studied the martingale, I am triggered by god explanation. The martingale does not win. Even if you have trillion $ it still loses. It’s a losing algorithm.

    • @admiralsap
      @admiralsap Рік тому

      I've always loved the subtle snark of a martingale in mathematics being essentially defined as a game in which there is no winning strategy.

  • @nickmeyer238
    @nickmeyer238 Рік тому +15

    Along with the progressive slot chasing (he called it bank) these are known as advantage play slots. There are many more than just progressives but you have to real know what you're doing to beat them. And since in one casino the odds of that game could be set at 95% and in another 85% it might be an advantage at your local casino and then at another its no longer EV+.

  • @Kataang101
    @Kataang101 Рік тому

    I love that blackjack apprenticeship chart that they used

  • @isettech
    @isettech Рік тому +3

    Taking a class on statistical process control and the statistics class cured me of any interest in games of chance with a probability under unity. When expanded into large sample sizes, the bell curve of distribution becomes very narrow and eventually narrow enough that no points are in the overall gains side of the middle of the distribution.
    In the stock market, overall, the odds are in the investor's favor. Unlike very well planned games of chance, the odds on stocks vary widely to where winning is like looking for a needle in a stack of needles. I leaned to buy companies which are undervalued as they are likely to correct up, where overvalued stocks are more likely to correct down.
    I highly use the Price/Earnings ratio. A low price for each dollar earned per share increases your chance of getting a larger dividend yield.
    When the P/E starts to rise, this is a warning, either the price is rising and the earnings are not rising also, or the earnings are falling and the price didn't. A high P/E is a warning to sell or place stop loss orders to lock in your gains.
    A temporary condition that causes the price to fall, but earnings fall much less results in a low P/E. This is golden buying opportunities. As the event passes and earnings return, the low cost can result in outstanding yield on cost, as cost was at a discount.
    Example, during the pandemic, the price of crude oil crashed. The price of oil transportation cashed. Bought a bunch of oil pipeline stocks at about 80% off the tradional price. Earnings fell, but not near as far as the price, so the P/E dropped to about 2. 3 years later, the price is up more than 4 times what I paid for it. Paid under 6 per share. Forward dividends of $2 per share is more than 33% yield on cost. Love the odds much better in the market. About doubled my holdings value twice in 3 years.
    I thank my statistics class for showing me the odds in well made games of chance, and the odds of doing well in the market.