Oh you are very welcome Amin! We must always remember to never look down on anyone unless we are helping them up. People like yourself inspire me to do what I do. Stay positive my friend! Best, B.
I am glad that someone pointed out the typo. The typo itself, did a good job in challenging my critical thinking skills. 'This row does not add up to one, is that OK?". I enjoyed the apparent simplicity of the tutorial in the beginning, but found that I had to dig deeper to teach myself matrix math, and prove to myself that the matrix multiplication is doing the job to add up all the probabilities for N steps of roulette. It is such a powerful technique!
I started teaching FM in 1979 and am currently rewriting a chapter on M.c.'s. Professor Foltz's video is the best explanation I've seen! Will ABSOLUTELY follow his other videos. Thanks!
Hi, Thank you very much for the videos. It's a great help for me. To help back let me point a typo error. There is a typo in 10:39. The row probabilities of P2 does not add up to 1. It should be [1,] 1.00 0.00 0.00 0.00 [2,] 0.50 0.25 0.00 0.25 [3,] 0.25 0.00 0.25 0.50 [4,] 0.00 0.00 0.00 1.00
You're so nice calling it a typo, I'd simply call it an error. I spent 15 mins thinking how can that be, subconsciously thinking that he cannot have made such an obvious mistake since he's going on about how "the rows should always add up to 1"! I mean, he is not listening to his own video, he fails to pass his own test:)
These have saved my 4.0 lol so I am eternally grateful. I will graduate soon and have put off math for so long because I'm terrified of it. I thought this might be the one to kill my perfect run until u found these. Thank you thank you thank you! 🙏🙏🙏
UPDATE 2015/02/10. Added annotation around 9:55 correcting a copy/paste typo I did not catch. Thanks to everyone who pointed it out in the comments. Thanks!
Friends I am gоing tо share with you the same seecret that a smallhandful of other lucky people have used to win lotterу…heres the link ==> twitter.com/b9005288ed9df93f6/status/742626059930198016 Finiteee Maath Markov Chain Example Theee Gambler s Ruin
actually i'm not in school so i'm not struggling in class. also when calculating these scenarios considering 50 to 100 plays+ using smaller bets. there is a number generally at a 1/3 loss or gain threshold in which if passed gamblers ( emotionally committed to the outcome) will typically alter previous patterns either intelligently or emotionally both of these create a whole new set of variables stacked on the previous 2 probability matrices. MarKov chain probability matrix ( used for base odds ) tier 2 matrix after >1/4 gains/losses tier 3 Matrix after 1/3 gains/losses Down based off of a) intelligent event based betting ( Active recall and event based probability that plays off of the belief they are out smarting their opponent i.e leading can't get too far behind mentality original balance at entry is the new 0 point for when to quit betting ) in this scenario the gambler will proactively alter betting patterns based off of previous wining placement meaning the gambler will repeat a winning placement less often and either aim for a pattern such as wwl wlw lww (this seems obvious but its not surprisingly) gambler continues betting while experiencing patterns based off of 2/3 outcomes but never 4 consecutive losses or more than 3 consecutive 1/3 outcomes. ( again there will always be a 2/3 association either with sets of 3,6,or 9 bets) if these happen its almost guaranteed they quit while ahead b) Emotional event based betting ( Active recall and event based probability that plays off of the belief they are being outsmarted I.e Being lead ) this is typically the slippery slope that guarantees a gamblers ruin. and is almost like a preset that activates after initial money slips below 2/3's (or 7/9 when ahead by 1/3 or more at any given time) during emotional phases the gambler will perform an opposite placement of their bet after a loss and hardly ever after a single win ( unless a wwl lwwl is seen a gambler in emotional state bets opposite to the losing color in this situation meaning a loss from red will mean a bet on black next) take into mind these are all based on consecutive same color bets like Red RED RED or Black Black Black (reality is that a sub matrix can be developed to account for a non consecutive color bet placement) much like 1/3*1/3= 1/9 when dealing with RbRbRb wlwlwl even at an even probability this is the last step before quitting. you may be interested in doing a video on the subject i'm about to tell you of ( also Event based probability, N+1 theory should be taken into account) first off i just happen to be good at pattern recognition. and have taught myself these things so be nice if they are either obvious or simply illegible ! i really like math and this is something i thought was very interesting while i was looking for a pattern. secondly Quantum mechanics as related to Quantum computing primarily the equally dispersed odds of determining the location of a particular subatomic particle particle wave theory allows for a shotgun blast method of finding such a location but markov chains and byzantine fault models allow for better understanding when processing billions of results. then by determining the current location as relevant to 1. unix time and 2. the given relation to any previous pattern after multiple tests. ( taking into consideration the result of the next outcome being directly affected by the event of "testing" which becomes the base event to attain singularity with when determining the odds of being correct at the positioning of the particles or at least its on off spin orientation as related to its counterparts spin orientation )" NOW with all of this being said (took longer than i intended but believe me i left out other long term factorial matrices that would have literally exponentially increased the amount of writing as these are all related and dont account for high being up then slightly below even then up then down and so on and so forth. the longer the game is played the harder it gets. ok so bitcoin dice games use event based probability with bilateral orientations Up Down LEFT RIGHT ( some extend to include *10bet UP DOWN ( and after enough computation LEFT RIGHT or vice versa depending on the pattern that is first established ) Using Deep leaning AI bots to determine the random rolls it starts out fairly random, but after close analysis it was obvious they are not, through trial and error i discovered that the bots have a fairly simple algorithm based off of the gamblers ruin theory only they implement a level of psychology that i tried to explain metaphorically with the emotional states ( charged/uncharged i.e happy/sad producing these outcomes: intelligent/emotional responses) i'm able to reach 10-15 consecutive correct guesses when playing the btc dice games fairly consistently (consider (up down patterns) .........(left right patterns), then all that is inverse once a threshold of consecutive wins or losses is crossed. (maintains the random factor when encountering an equally random equation regularly cancels out to generate only wins or only losses.)
There's a trick that works at the casino , and I have tested it a few times outside of one and it works at the roulette table . You are always guaranteed to go up , but you will get kicked out if they catch you and banned for life .
Thank you for your video! Through this video, I perfectly can understand Markov Chain!! Your accent and speed of telling is very suitable for non-native English (like me) to study this. Thank you for your sensible video! Have a nice day~
My final exam is at the end of the week and our last lesson was on this, and game theory. I feel a lot more confident than I did a week ago. I actually think I have a fighting chance to pass this difficult class! Thank you so much for make me finally understand this!
I just heard about Markov Chains and decided to look it up. I like the way you explain things and your motivating speech at the beginning. Keep doing these tutorials!
I usually do not watch educational videos but you are great!!! I do not get bored, I understand everything you explained, you're funny...you're great!!
I greatly appreciate your help. This presentation gave me the support needed to better understand the Markov Process chapter I am working on. The example and explanation were right on point. Thanks!
I am a biologist, and we are studying gambler;s ruin in matlab which is worse than i imagine. and Sir Brandon Foltz thanks a lot for your engouragement for worried students like me.
Thanks for this very clear explanation! Could anyone, however, say more about the initial state vector, as I am clarifying for myself how do we get to [1/3 0 0 2/3] as the final result?
+Hikaru Akiyama It would be great if a definition of initial state vector can be given here and how exactly do we calculate the multiplication of the matrix by an initial state vector, thanks!
Matrix P2 must be wrong as pointed out by various friends here before. Explanation seems to be that you take $25 to gamble two times, first hand lose is 0.5 in probability, win once and then lose once is 0.5x0.5 = 0.25 in probability, win twice is 0.5x0.5 =0.25 in probability; adding all these up will be 1 in probability. So, no case is possible to carry $50 after playing twice and thus the 2nd row 3rd column should be "0" instead of ".5".
zckfu Hello! Yes and thank you. I copied and pasted P1 and didn't change two numbers. I just added an annotation at that point so others would not be confused. Thanks again!
One small over in the second state when starting with 25$ the odds of learning with 75$ was one third but that would be a profit of 50$ not 25$ as it says in the sequence
It wasn't until 2 1/2 minutes into the video that you stated we should already know what Markov Chains are. It would be good if that was mentioned immediately at the beginning. Thanks!
Brandon, great video, I would love to see some of the Markov Chain sample problems for some of the textbook examples that are readily available, especially for scenarios where absorbing states are outnumbered by non-absorbing states (2 absorbing states, say and 4 non-absorbing states). I am at a loss how to calculate the necessary long-term states. Thanks!
Your matrix P2 is incorrect, which should be evident from the observation that rows 2 and 3 each do not sum to one. The correct P2 is: {{1., 0., 0., 0.}, {0.5, 0.25, 0., 0.25}, {0.25, 0., 0.25, 0.5}, {0., 0., 0., 1.}}
The P^2 matrix at 11:34 is wrong. The 2nd row - 3rd column element and the 3rd row - 2nd column element should both be zeros. (A good way to check is the fact that sum of all elements in a column should be equal to 1)
Good explanation of markov chain and steady state. However, misleading from gambling point of view. As you showed, there is always lower chance for bigger profit. basically the chance of winning $25 is twice higher than losing $50 and vice versa. So in long run, the money you make might not depend on what state you start at.
Coming (very) late to this party, but what if you flip the focus of the question to read "how many games can he expect to play before either of his end states ($75 or $0) are reached?" I can do it manually, but is there some matrix magic with which you can work it out? intuitively you'd be looking for the lowest value of k for which your Pk matrix has the center four probabilities all equal to zero
Interesting. So if I create a 2 steps down and 1 step up, would it be best to have that as that would give me a 2/3 chance of making money. So if I started with 75 dollars and stopped at 100, it would give me a 2/3 chance of winning. The structure of gambling is more important than the gambling itself. I am trying to figure out the optimal duration of gambling a set of independently identically distributed events. See if I can do it.
I need some help with forming the transition probability matrix for the following problem : I have a 6 face dice and the condition below : if i roll and get the value as 4,5,6 . i will get 4,5,6 dollars accordingly if i roll and get 1,2,3 . my account will be deducted to go to $0 ● What is the expected amount of dollars for this game if you follow an optimal policy? That is, what is the optimal state-value function for the initial state of the game? Expected Output: 2.5833
If he starts wish $50 then he is 2/3 of the way to 75 already but he has to lose 2/3 of total to get to 0 so it makes sense seeing as he is twice as close to his winning threshold than his losing threshold.
I'm a little confused about the statement at 18:29. Doesn't the problem change if you start at $25? In order to come out $25 ahead the gambler needs to transition to the $50 state so the entire chain is defunct isn't it? The wording is what makes it, if the gambler cashes out when they are $25 ahead you need a seperate chain for each starting point. If the gambler cashed out when he hits $75 then the logic of the video holds.
the odds of winning roulette on black or red on an american wheel are 0.473684210526...47.3%. far from 50% if you want to make money. 48.6% on a european wheel if you're curious. Don"t think in terms of 50/50 or 1/3...there are one or two greens depending on which country you live in and these 2 numbers change everything.
Jeremiah this is what he should mention when he talks about games in casinos being rigged for the house. He mentions they are biased towards the house but never says how - ppl probably assume the groupier looks at the bets and presses a button to change the behavior of the wheel on the fly like in Bond movies or some silly stuff like that :)
This is more complicated than it needs to be, you assume right away the game is fair, i.e. a wheel with no zero's, betting $2.08 on 24 out of 36 numbers gives you $75 when you win and 0 when you lose, chance of ending up with $75 is 24/36 = 2/3. If you think it's different because we're betting red/black then look up the law of independent event, basically states that it doesn't matter, you can't combine a bunch of 0 EV bets to make a +EV or -EV bet.
It's kind of problematic to say that you "only changed what the gambler came in with", when what you really did was change the ratio between [the gambler's bet each turn] and [what the gambler came in with]. I get that you want as many people as possible to understand what is going on (which I guess is why you used numbers instead of variables), but I would really appreciate it if you had added in an algebraic approach after the arithmetic one.
I noticed a mistake where one of the rows had a sum greater than one, representing a probability greater than one. I posted a screenshot with the correction at gist.github.com/dmaust/0884e14bc0f9dd2b1ae4
How can the probability after 50 runs be zero for the in between values (25,50,etc.). Isn’t it possible that the gambler wins and loses in repeated fashion 25 times? The probability that the game reaches an absorbing state should only be 100% if the game is played an infinite amount of times.
The positivity in this video made me smile
:) You...saved you. Seeking help for yourself when you need it is where the battle is won. All the best, B.
Oh you are very welcome Amin! We must always remember to never look down on anyone unless we are helping them up. People like yourself inspire me to do what I do. Stay positive my friend! Best, B.
I am glad that someone pointed out the typo. The typo itself, did a good job in challenging my critical thinking skills. 'This row does not add up to one, is that OK?". I enjoyed the apparent simplicity of the tutorial in the beginning, but found that I had to dig deeper to teach myself matrix math, and prove to myself that the matrix multiplication is doing the job to add up all the probabilities for N steps of roulette. It is such a powerful technique!
I started teaching FM in 1979 and am currently rewriting a chapter on M.c.'s. Professor Foltz's video is the best explanation I've seen! Will ABSOLUTELY follow his other videos. Thanks!
Hi,
Thank you very much for the videos. It's a great help for me. To help back let me point a typo error.
There is a typo in 10:39. The row probabilities of P2 does not add up to 1. It should be [1,] 1.00 0.00 0.00 0.00
[2,] 0.50 0.25 0.00 0.25
[3,] 0.25 0.00 0.25 0.50
[4,] 0.00 0.00 0.00 1.00
yes this makes a lot more sense
You're so nice calling it a typo, I'd simply call it an error. I spent 15 mins thinking how can that be, subconsciously thinking that he cannot have made such an obvious mistake since he's going on about how "the rows should always add up to 1"! I mean, he is not listening to his own video, he fails to pass his own test:)
These have saved my 4.0 lol so I am eternally grateful. I will graduate soon and have put off math for so long because I'm terrified of it. I thought this might be the one to kill my perfect run until u found these. Thank you thank you thank you! 🙏🙏🙏
until I* found these.
UPDATE 2015/02/10. Added annotation around 9:55 correcting a copy/paste typo I did not catch. Thanks to everyone who pointed it out in the comments. Thanks!
Friends I am gоing tо share with you the same seecret that a smallhandful of other lucky people have used to win lotterу…heres the link ==> twitter.com/b9005288ed9df93f6/status/742626059930198016 Finiteee Maath Markov Chain Example Theee Gambler s Ruin
actually i'm not in school so i'm not struggling in class. also when calculating these scenarios considering 50 to 100 plays+ using smaller bets. there is a number generally at a 1/3 loss or gain threshold in which if passed gamblers ( emotionally committed to the outcome) will typically alter previous patterns either intelligently or emotionally both of these create a whole new set of variables stacked on the previous 2 probability matrices.
MarKov chain probability matrix ( used for base odds )
tier 2 matrix after >1/4 gains/losses
tier 3 Matrix after 1/3 gains/losses
Down
based off of
a) intelligent event based betting ( Active recall and event based probability that plays off of the belief they are out smarting their opponent i.e leading can't get too far behind mentality original balance at entry is the new 0 point for when to quit betting ) in this scenario the gambler will proactively alter betting patterns based off of previous wining placement meaning the gambler will repeat a winning placement less often and either aim for a pattern such as wwl wlw lww (this seems obvious but its not surprisingly) gambler continues betting while experiencing patterns based off of 2/3 outcomes but never 4 consecutive losses or more than 3 consecutive 1/3 outcomes. ( again there will always be a 2/3 association either with sets of 3,6,or 9 bets) if these happen its almost guaranteed they quit while ahead
b) Emotional event based betting ( Active recall and event based probability that plays off of the belief they are being outsmarted I.e Being lead ) this is typically the slippery slope that guarantees a gamblers ruin. and is almost like a preset that activates after initial money slips below 2/3's (or 7/9 when ahead by 1/3 or more at any given time) during emotional phases the gambler will perform an opposite placement of their bet after a loss and hardly ever after a single win ( unless a wwl lwwl is seen a gambler in emotional state bets opposite to the losing color in this situation meaning a loss from red will mean a bet on black next) take into mind these are all based on consecutive same color bets like Red RED RED or Black Black Black (reality is that a sub matrix can be developed to account for a non consecutive color bet placement) much like 1/3*1/3= 1/9 when dealing with RbRbRb wlwlwl even at an even probability this is the last step before quitting.
you may be interested in doing a video on the subject i'm about to tell you of ( also Event based probability, N+1 theory should be taken into account)
first off i just happen to be good at pattern recognition. and have taught myself these things so be nice if they are either obvious or simply illegible ! i really like math and this is something i thought was very interesting while i was looking for a pattern.
secondly Quantum mechanics as related to Quantum computing primarily the equally dispersed odds of determining the location of a particular subatomic particle particle wave theory allows for a shotgun blast method of finding such a location but markov chains and byzantine fault models allow for better understanding when processing billions of results. then by determining the current location as relevant to 1. unix time and 2. the given relation to any previous pattern after multiple tests. ( taking into consideration the result of the next outcome being directly affected by the event of "testing" which becomes the base event to attain singularity with when determining the odds of being correct at the positioning of the particles or at least its on off spin orientation as related to its counterparts spin orientation )"
NOW with all of this being said (took longer than i intended but believe me i left out other long term factorial matrices that would have literally exponentially increased the amount of writing as these are all related and dont account for high being up then slightly below even then up then down and so on and so forth. the longer the game is played the harder it gets.
ok so bitcoin dice games use event based probability with bilateral orientations Up Down LEFT RIGHT ( some extend to include *10bet UP DOWN ( and after enough computation LEFT RIGHT or vice versa depending on the pattern that is first established )
Using Deep leaning AI bots to determine the random rolls it starts out fairly random, but after close analysis it was obvious they are not, through trial and error i discovered that the bots have a fairly simple algorithm based off of the gamblers ruin theory only they implement a level of psychology that i tried to explain metaphorically with the emotional states ( charged/uncharged i.e happy/sad producing these outcomes: intelligent/emotional responses)
i'm able to reach 10-15 consecutive correct guesses when playing the btc dice games fairly consistently (consider (up down patterns) .........(left right patterns), then all that is inverse once a threshold of consecutive wins or losses is crossed. (maintains the random factor when encountering an equally random equation regularly cancels out to generate only wins or only losses.)
There's a trick that works at the casino , and I have tested it a few times outside of one and it works at the roulette table . You are always guaranteed to go up , but you will get kicked out if they catch you and banned for life .
Thank you for your video! Through this video, I perfectly can understand Markov Chain!! Your accent and speed of telling is very suitable for non-native English (like me) to study this. Thank you for your sensible video! Have a nice day~
Great clarity and patience! Lecturer is very personable, and leads us to want more.
My final exam is at the end of the week and our last lesson was on this, and game theory. I feel a lot more confident than I did a week ago. I actually think I have a fighting chance to pass this difficult class! Thank you so much for make me finally understand this!
I just heard about Markov Chains and decided to look it up. I like the way you explain things and your motivating speech at the beginning. Keep doing these tutorials!
I usually do not watch educational videos but you are great!!! I do not get bored, I understand everything you explained, you're funny...you're great!!
I greatly appreciate your help. This presentation gave me the support needed to better understand the Markov Process chapter I am working on. The example and explanation were right on point. Thanks!
God Bless you !!!!!!
No amount of compliment is enough for this service of yours !!!!
These videos are simply fantastic. I'm really in mathematics class. Very grateful.
excellent excellent excellent --please make each lecture of 10 minutes --thank u my lord
The best video on mathematics i ever saw on youtube... Keep spreading more knowledge
Very helpful. Thank you! Explained the process better than my University lecturers thats for sure!
I am a biologist, and we are studying gambler;s ruin in matlab which is worse than i imagine. and Sir Brandon Foltz thanks a lot for your engouragement for worried students like me.
Lucid lecture. Thank you for your great effort.
The video is so helpful and the outro and intro was just what I needed, so sweet .Tysm :')
your motivation at the beginning actually made me more positive! thank you
Great video! P2 calculation @ timestamp 09:59 looks wrong. Sums of second and third rows are greater than 1. Row sums should equal to 1.
Brandon,
I would like to thank you for this video. I was struggling with Gambler's Ruin at Uni, Also your motivation inspires me!
Another very clear, well delivered, tutorial. Thanks
Very instructive video for beginners like me. Keep up the good work !
I am so grateful for your videos, you are great at explaining!
Thanks for this very clear explanation! Could anyone, however, say more about the initial state vector, as I am clarifying for myself how do we get to [1/3 0 0 2/3] as the final result?
+Hikaru Akiyama It would be great if a definition of initial state vector can be given here and how exactly do we calculate the multiplication of the matrix by an initial state vector, thanks!
Matrix P2 must be wrong as pointed out by various friends here before. Explanation seems to be that you take $25 to gamble two times, first hand lose is 0.5 in probability, win once and then lose once is 0.5x0.5 = 0.25 in probability, win twice is 0.5x0.5 =0.25 in probability; adding all these up will be 1 in probability. So, no case is possible to carry $50 after playing twice and thus the 2nd row 3rd column should be "0" instead of ".5".
zckfu Hello! Yes and thank you. I copied and pasted P1 and didn't change two numbers. I just added an annotation at that point so others would not be confused. Thanks again!
I am pleased to have your reply and I appreciated your videos a lot and hope everyone can learn statistics from you.
Best explanation I found!
One small over in the second state when starting with 25$ the odds of learning with 75$ was one third but that would be a profit of 50$ not 25$ as it says in the sequence
Clearity= 💯
very nice lecture and simple to follow. Thank you.
hey!! that's a great video ..i wish you could upload some more problems to practise ..
It wasn't until 2 1/2 minutes into the video that you stated we should already know what Markov Chains are. It would be good if that was mentioned immediately at the beginning. Thanks!
Brandon, great video, I would love to see some of the Markov Chain sample problems for some of the textbook examples that are readily available, especially for scenarios where absorbing states are outnumbered by non-absorbing states (2 absorbing states, say and 4 non-absorbing states). I am at a loss how to calculate the necessary long-term states. Thanks!
Very good video.. just a small correction P2[2][1] will be equal to 0 and not 0.5.
I like it, very clear gotta have an A score for my operational research! thx
Your matrix P2 is incorrect, which should be evident from the observation that rows 2 and 3 each do not sum to one.
The correct P2 is:
{{1., 0., 0., 0.},
{0.5, 0.25, 0., 0.25},
{0.25, 0., 0.25, 0.5},
{0., 0., 0., 1.}}
Thank you!
Haha...this confused me for 15mins. Now things make sense. Thanks man!!
The P^2 matrix at 11:34 is wrong. The 2nd row - 3rd column element and the 3rd row - 2nd column element should both be zeros. (A good way to check is the fact that sum of all elements in a column should be equal to 1)
I love every bit of this video
Very resourceful material
Great material, thanks a lot for the message to keep the head up ;)
Great video 🎉
THANK YOU!!! CLEAR AND SIMPLE
Great video, keep up the good work!
Good explanation of markov chain and steady state. However, misleading from gambling point of view. As you showed, there is always lower chance for bigger profit. basically the chance of winning $25 is twice higher than losing $50 and vice versa. So in long run, the money you make might not depend on what state you start at.
In the long run probabilities section, you show matrix P2. How did you create this? Where did it come from?
He multiplied the P matrix by itself
Shouldn't each row still only add to 1?
wonderful explaination
thank you for your video, i understand all. I'm really exited
Good presentation ,,,,, best teacher ;) , from Montreal
Coming (very) late to this party, but what if you flip the focus of the question to read "how many games can he expect to play before either of his end states ($75 or $0) are reached?"
I can do it manually, but is there some matrix magic with which you can work it out? intuitively you'd be looking for the lowest value of k for which your Pk matrix has the center four probabilities all equal to zero
Thank you so much . Great explanation.
you sound like a really nice ron swanson XD thanks for explaining so well!
Great work.
Great video, thank you very much.
Thanks so much !! You are an awesome teacher. !! :)
Thanks a lot!
Thnx sooo much for your vides,they r really helpful!
Great work, kindly correct P2 if possible
thank you for the video!
Great work .. explained well .. thanks .. i did subscribed (because its worth )... Thank you
Interesting. So if I create a 2 steps down and 1 step up, would it be best to have that as that would give me a 2/3 chance of making money. So if I started with 75 dollars and stopped at 100, it would give me a 2/3 chance of winning. The structure of gambling is more important than the gambling itself. I am trying to figure out the optimal duration of gambling a set of independently identically distributed events. See if I can do it.
sick vids Brandon. thanks a lot!
Thank you sir, it helped a lot.
very clear
superb !!
I have a question, how does the probability change if you vary the bets every time? Is there a way to acheive an advantage? 🤔
wonderful
Nice video!
You good sir are awesome
I need some help with forming the transition probability matrix for the following problem : I have a 6 face dice and the condition below :
if i roll and get the value as 4,5,6 . i will get 4,5,6 dollars accordingly
if i roll and get 1,2,3 . my account will be deducted to go to $0
● What is the expected amount of dollars for this game if you follow an optimal policy? That is, what is the optimal state-value function for the initial state of the game?
Expected Output: 2.5833
This one is missing in the playlist.
Great
Brandon, and if I am wondering what is the probability that there are at least 4 rounds ?
helpful, thanks
If he starts with only $25, I don't think he can end in the $75 state, since he should stop when he is $25 up.
Well played.
Absorbing states: Also known as riches and poverty.
Though they can be recurring, rags to riches, riches to rags, rags to riches.
If he starts wish $50 then he is 2/3 of the way to 75 already but he has to lose 2/3 of total to get to 0 so it makes sense seeing as he is twice as close to his winning threshold than his losing threshold.
This Video explains how to use Transition Matrices but it is definitely not about the gamblers ruin problem
I'm a little confused about the statement at 18:29. Doesn't the problem change if you start at $25? In order to come out $25 ahead the gambler needs to transition to the $50 state so the entire chain is defunct isn't it?
The wording is what makes it, if the gambler cashes out when they are $25 ahead you need a seperate chain for each starting point. If the gambler cashed out when he hits $75 then the logic of the video holds.
Put your Markov videos in a playlist.
Add the P1 Matrix. Otherwise very clear
Thank you. That helps a lot. I would rather subscribe your channel with fees instead of paying tuition fees to my uni
the odds of winning roulette on black or red on an american wheel are 0.473684210526...47.3%. far from 50% if you want to make money. 48.6% on a european wheel if you're curious. Don"t think in terms of 50/50 or 1/3...there are one or two greens depending on which country you live in and these 2 numbers change everything.
Jeremiah this is what he should mention when he talks about games in casinos being rigged for the house. He mentions they are biased towards the house but never says how - ppl probably assume the groupier looks at the bets and presses a button to change the behavior of the wheel on the fly like in Bond movies or some silly stuff like that :)
You forgot to put this in the finite mathematics playlist
How to convert a FSM Model into a Markov Chain Model? Please Help!!!
Man you really saved me ^_^
This should be called "Intro to Day Trading" lol
what if the probability of winning is reduced? the person will end up penniless in lesser no of games? How can we explain that mathematically?
I'm here because read "The lost world" and wanna know more about.
This is more complicated than it needs to be, you assume right away the game is fair, i.e. a wheel with no zero's, betting $2.08 on 24 out of 36 numbers gives you $75 when you win and 0 when you lose, chance of ending up with $75 is 24/36 = 2/3. If you think it's different because we're betting red/black then look up the law of independent event, basically states that it doesn't matter, you can't combine a bunch of 0 EV bets to make a +EV or -EV bet.
18:10 should be ahead 50 dollars not 25
18:00
The text in the lower right corner _should_ say "...coming out ahead *_$50_*." Not $25.
yup!! I thought so too..
Nice nice nice
It's kind of problematic to say that you "only changed what the gambler came in with", when what you really did was change the ratio between [the gambler's bet each turn] and [what the gambler came in with].
I get that you want as many people as possible to understand what is going on (which I guess is why you used numbers instead of variables), but I would really appreciate it if you had added in an algebraic approach after the arithmetic one.
I noticed a mistake where one of the rows had a sum greater than one, representing a probability greater than one. I posted a screenshot with the correction at gist.github.com/dmaust/0884e14bc0f9dd2b1ae4
I should have watched your video instead of going to class.
How can the probability after 50 runs be zero for the in between values (25,50,etc.). Isn’t it possible that the gambler wins and loses in repeated fashion 25 times? The probability that the game reaches an absorbing state should only be 100% if the game is played an infinite amount of times.