Finite Math: Markov Chain Example - The Gambler's Ruin

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  • Опубликовано: 25 ноя 2024

Комментарии • 129

  • @sabihaakhtaruddin6703
    @sabihaakhtaruddin6703 8 лет назад +61

    The positivity in this video made me smile

  • @BrandonFoltz
    @BrandonFoltz  11 лет назад +23

    :) You...saved you. Seeking help for yourself when you need it is where the battle is won. All the best, B.

  • @BrandonFoltz
    @BrandonFoltz  11 лет назад +4

    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.

  • @sdsa007
    @sdsa007 10 лет назад

    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!

  • @r4nd8m
    @r4nd8m 10 лет назад +24

    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

    • @cutieb32
      @cutieb32 5 лет назад +1

      yes this makes a lot more sense

    • @yianpap6093
      @yianpap6093 4 года назад +1

      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:)

  • @benbrink3567
    @benbrink3567 4 года назад

    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!

  • @seonjoopark5669
    @seonjoopark5669 9 лет назад +7

    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~

  • @johngale1000
    @johngale1000 4 года назад

    Great clarity and patience! Lecturer is very personable, and leads us to want more.

  • @ashleymckerall5128
    @ashleymckerall5128 8 лет назад +1

    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! 🙏🙏🙏

  • @3m1lu
    @3m1lu 10 лет назад

    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!!

  • @solidstatedevices
    @solidstatedevices 6 лет назад

    God Bless you !!!!!!
    No amount of compliment is enough for this service of yours !!!!

  • @lasisitaiwo7075
    @lasisitaiwo7075 2 года назад

    These videos are simply fantastic. I'm really in mathematics class. Very grateful.

  • @robbiep.5497
    @robbiep.5497 10 лет назад +1

    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!

  • @ExplorewithDrYasir
    @ExplorewithDrYasir 6 лет назад

    The best video on mathematics i ever saw on youtube... Keep spreading more knowledge

  • @TheDoombreath
    @TheDoombreath 10 лет назад

    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!

  • @anushka_5163
    @anushka_5163 2 года назад

    The video is so helpful and the outro and intro was just what I needed, so sweet .Tysm :')

  • @crownt97
    @crownt97 5 лет назад

    Very helpful. Thank you! Explained the process better than my University lecturers thats for sure!

  • @kaursingh637
    @kaursingh637 3 года назад

    excellent excellent excellent --please make each lecture of 10 minutes --thank u my lord

  • @edavis4663
    @edavis4663 5 лет назад +1

    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!

  • @shanadhikari3383
    @shanadhikari3383 Месяц назад

    Lucid lecture. Thank you for your great effort.

  • @AHAA9
    @AHAA9 11 лет назад

    your motivation at the beginning actually made me more positive! thank you

  • @CutePokapipi
    @CutePokapipi 10 лет назад

    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.

  • @clydehillbellevue
    @clydehillbellevue 11 лет назад +8

    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.

  • @BrandonFoltz
    @BrandonFoltz  9 лет назад +13

    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!

    • @ahmet41907
      @ahmet41907 8 лет назад

      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

    • @andrewadams2793
      @andrewadams2793 7 лет назад +1

      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.)

    • @BarbRogersMs.SolarTerror
      @BarbRogersMs.SolarTerror 6 лет назад

      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 .

  • @jackryanvn
    @jackryanvn 11 лет назад

    Brandon,
    I would like to thank you for this video. I was struggling with Gambler's Ruin at Uni, Also your motivation inspires me!

  • @MidLifeDad
    @MidLifeDad 10 лет назад

    Another very clear, well delivered, tutorial. Thanks

  • @Mikeybikey88
    @Mikeybikey88 10 лет назад

    I am so grateful for your videos, you are great at explaining!

  • @ttctoh
    @ttctoh 8 лет назад

    Very instructive video for beginners like me. Keep up the good work !

  • @dishasingh6591
    @dishasingh6591 7 лет назад

    Best explanation I found!

  • @simoncausyn1466
    @simoncausyn1466 7 лет назад +3

    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

  • @zckfu
    @zckfu 9 лет назад +3

    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".

    • @BrandonFoltz
      @BrandonFoltz  9 лет назад

      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!

    • @zckfu
      @zckfu 9 лет назад +1

      I am pleased to have your reply and I appreciated your videos a lot and hope everyone can learn statistics from you.

  • @alighafourian5456
    @alighafourian5456 5 лет назад

    very nice lecture and simple to follow. Thank you.

  • @virginiamore
    @virginiamore 6 лет назад

    THANK YOU!!! CLEAR AND SIMPLE

  • @srinathk6137
    @srinathk6137 5 лет назад +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)

  • @marynsabagwa7492
    @marynsabagwa7492 6 лет назад

    I love every bit of this video

  • @jonihoppen
    @jonihoppen 4 года назад +1

    Great material, thanks a lot for the message to keep the head up ;)

  • @SnoozeDog
    @SnoozeDog 8 лет назад

    Great video, keep up the good work!

  • @EricOtieno1
    @EricOtieno1 6 лет назад

    Very resourceful material

  • @Shtercus
    @Shtercus 5 лет назад +1

    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

  • @hikaruhiyama1152
    @hikaruhiyama1152 9 лет назад +2

    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?

    • @hikaruhiyama1152
      @hikaruhiyama1152 9 лет назад +1

      +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!

  • @gnso01
    @gnso01 6 лет назад

    thank you for your video, i understand all. I'm really exited

  • @optimistshivasheesh
    @optimistshivasheesh 10 лет назад

    Thanks so much !! You are an awesome teacher. !! :)

  • @zackattack7967
    @zackattack7967 5 лет назад

    Thank you so much . Great explanation.

  • @nv_spartan1771
    @nv_spartan1771 7 лет назад +4

    In the long run probabilities section, you show matrix P2. How did you create this? Where did it come from?

    • @dorukeski2519
      @dorukeski2519 5 лет назад

      He multiplied the P matrix by itself

    • @2inthemorning
      @2inthemorning 5 лет назад

      Shouldn't each row still only add to 1?

  • @eliosgreek8028
    @eliosgreek8028 5 месяцев назад

    Great video 🎉

  • @nesyamaliaify
    @nesyamaliaify 11 лет назад

    I like it, very clear gotta have an A score for my operational research! thx

  • @ngandjuicynthia9168
    @ngandjuicynthia9168 10 лет назад

    Thnx sooo much for your vides,they r really helpful!

  • @TheNapishtim
    @TheNapishtim 9 лет назад

    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!

  • @ranitchatterjee5552
    @ranitchatterjee5552 5 лет назад

    Clearity= 💯

  • @waynehughes6967
    @waynehughes6967 9 лет назад

    Great video, thank you very much.

  • @mohit0356
    @mohit0356 9 лет назад

    wonderful explaination

  • @ehabALsharairi
    @ehabALsharairi 11 лет назад

    Great work.

  • @mattdavisrn
    @mattdavisrn 10 лет назад +20

    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.}}

  • @umagunturi7442
    @umagunturi7442 6 лет назад +1

    hey!! that's a great video ..i wish you could upload some more problems to practise ..

  • @soothingTrench
    @soothingTrench 7 лет назад

    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.

  • @johncise3908
    @johncise3908 5 лет назад

    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!

  • @amanmaghan9146
    @amanmaghan9146 5 лет назад

    Very good video.. just a small correction P2[2][1] will be equal to 0 and not 0.5.

  • @ThilankaMunasinghe
    @ThilankaMunasinghe 11 лет назад

    Great work .. explained well .. thanks .. i did subscribed (because its worth )... Thank you

  • @mangopurple
    @mangopurple 7 лет назад

    sick vids Brandon. thanks a lot!

  • @MrAdelromio
    @MrAdelromio 10 лет назад

    Good presentation ,,,,, best teacher ;) , from Montreal

  • @PukeSkinwalker
    @PukeSkinwalker Год назад

    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.

  • @aronhegedus
    @aronhegedus 10 лет назад

    thank you for the video!

  • @jatinjeena7877
    @jatinjeena7877 6 лет назад

    Thank you sir, it helped a lot.

  • @Yourhavingagaff
    @Yourhavingagaff 7 лет назад

    I have a question, how does the probability change if you vary the bets every time? Is there a way to acheive an advantage? 🤔

  • @Se7Olutionyg
    @Se7Olutionyg 6 лет назад

    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

  • @nunyabidness5232
    @nunyabidness5232 5 лет назад

    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.

  • @TheFeldhamster
    @TheFeldhamster 7 лет назад

    This one is missing in the playlist.

  • @bigbossfan007
    @bigbossfan007 11 лет назад

    Great work, kindly correct P2 if possible

  • @brunobilchegomide7954
    @brunobilchegomide7954 8 лет назад

    Brandon, and if I am wondering what is the probability that there are at least 4 rounds ?

  • @acatindisguise
    @acatindisguise 4 года назад

    you sound like a really nice ron swanson XD thanks for explaining so well!

  • @Speak4Yourself2
    @Speak4Yourself2 2 года назад

    Thanks a lot!

  • @BrenoSaravalli
    @BrenoSaravalli 9 лет назад

    Nice video!

  • @JimmyCroissant69
    @JimmyCroissant69 6 лет назад

    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.

  • @samuelswiswa3553
    @samuelswiswa3553 10 лет назад +1

    superb !!

  • @kentcaspersen2310
    @kentcaspersen2310 10 лет назад +3

    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.

  • @nskartik66
    @nskartik66 7 лет назад

    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?

  • @Nasim_Hamid
    @Nasim_Hamid 7 лет назад

    How to convert a FSM Model into a Markov Chain Model? Please Help!!!

  • @rmutatina
    @rmutatina 11 лет назад

    very clear

  • @Konzor
    @Konzor 7 лет назад

    This Video explains how to use Transition Matrices but it is definitely not about the gamblers ruin problem

  • @kamzilla3000
    @kamzilla3000 11 лет назад

    You good sir are awesome

  • @Polarcupcheck
    @Polarcupcheck 10 лет назад +6

    Absorbing states: Also known as riches and poverty.

    • @GloriousAssam
      @GloriousAssam 5 лет назад

      Though they can be recurring, rags to riches, riches to rags, rags to riches.

  • @workichoable
    @workichoable 7 лет назад

    wonderful

  • @matthewftinogiannis1644
    @matthewftinogiannis1644 9 лет назад

    helpful, thanks

  • @JeremiahJesmok
    @JeremiahJesmok 8 лет назад

    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.

    • @TheFeldhamster
      @TheFeldhamster 7 лет назад

      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 :)

  • @sinan_islam
    @sinan_islam Год назад

    Put your Markov videos in a playlist.

  • @tomminterbobby
    @tomminterbobby 7 лет назад

    Add the P1 Matrix. Otherwise very clear

  • @dr.4453
    @dr.4453 6 лет назад

    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.

  • @trial000000000000001
    @trial000000000000001 11 лет назад

    Man you really saved me ^_^

  • @dmaust1
    @dmaust1 10 лет назад

    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

  • @ericwinny
    @ericwinny 10 лет назад

    Thank you. That helps a lot. I would rather subscribe your channel with fees instead of paying tuition fees to my uni

  • @tomasedasonno2
    @tomasedasonno2 5 лет назад +1

    18:10 should be ahead 50 dollars not 25

  • @curiewilhelm5062
    @curiewilhelm5062 4 года назад

    Great

  • @whattoexpect8731
    @whattoexpect8731 3 года назад

    You forgot to put this in the finite mathematics playlist

  • @PokerOCD
    @PokerOCD 7 лет назад

    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.

  • @SonLuther
    @SonLuther 7 лет назад

    I'm here because read "The lost world" and wanna know more about.

  • @alexanderskae5720
    @alexanderskae5720 2 года назад

    This should be called "Intro to Day Trading" lol

  • @binizmohamed8758
    @binizmohamed8758 11 лет назад

    PLZ I WANT HIDDEN MARKOV MODELE

  • @jumpman8282
    @jumpman8282 7 лет назад +1

    18:00
    The text in the lower right corner _should_ say "...coming out ahead *_$50_*." Not $25.

  • @paulchairez939
    @paulchairez939 7 лет назад

    I should have watched your video instead of going to class.

  • @bowenchen4908
    @bowenchen4908 7 лет назад

    Nice nice nice