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Thread: Convert probabilities to bet

  1. #1


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    Convert probabilities to bet

    Hi all,

    I've been doing JAVA for some time, and as a practice I'm making a Blackjack program, which calculates my probabilities of winning and equality given a certain shoe (number of cards).

    Ultimately I would like to have a program which gives me my probabilities of winning the following hand given a certain shoe.
    (forget about doubling, splitting etc., even forget about equality, let's assume we play a game where when winning you double your bet, and losing or equality you loose your bet).

    Imagine I would have 30% chance of winning my next hand, how would I have to calculate how much I have to bet to be winning on the long term?
    Knowing of course one time I have 30% chance of winning, the following hand 50% chance of winning, the following hand 70% chance of winning, the next one again 25% of winning).
    What comes into the calculations to know how much I would have to bet?

    In other words, how do Card Counters know how much to bet each hand?
    I suppose I would have to be able to calculate a % of my bankroll to bet, given a certain probability to win?
    What comes into account for this calculation? The number of hands played, the amount in your bankroll?

    Maybe it's way more simple than I'm imagining, maybe it's way more complicated.
    I'm just trying to find out how the logic works behind betting and winning in long run, with the advantage I can calculate for every hand my chances of winning (and therefore as well my chances of loosing).

  2. #2


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    Quote Originally Posted by MSimonart View Post
    Hi all,

    I've been doing JAVA for some time, and as a practice I'm making a Blackjack program, which calculates my probabilities of winning and equality given a certain shoe (number of cards).

    Ultimately I would like to have a program which gives me my probabilities of winning the following hand given a certain shoe.
    (forget about doubling, splitting etc., even forget about equality, let's assume we play a game where when winning you double your bet, and losing or equality you loose your bet).

    Imagine I would have 30% chance of winning my next hand, how would I have to calculate how much I have to bet to be winning on the long term?
    Knowing of course one time I have 30% chance of winning, the following hand 50% chance of winning, the following hand 70% chance of winning, the next one again 25% of winning).
    What comes into the calculations to know how much I would have to bet?

    In other words, how do Card Counters know how much to bet each hand?
    I suppose I would have to be able to calculate a % of my bankroll to bet, given a certain probability to win?
    What comes into account for this calculation? The number of hands played, the amount in your bankroll?

    Maybe it's way more simple than I'm imagining, maybe it's way more complicated.
    I'm just trying to find out how the logic works behind betting and winning in long run, with the advantage I can calculate for every hand my chances of winning (and therefore as well my chances of loosing).
    Your percentage of winning the hand is not what determines your bet size; rather, the advantage that you have for the next round does, and those two are not the same thing. Simulation tells us what our edge is. Armed with that knowledge, there are now optimal-bet algorithms that relate your optimal bet size to the size of your bankroll, the aforementioned edge for the next hand, and the variance of outcomes for that hand.

    With caveats and limitations, your optimal bet is often (bankroll x edge)/variance. And since variance is about 1.33, that makes the reciprocal 0.75, so a rule of thumb is to bet your 75% of your bankroll multiplied by your edge for the upcoming hand.

    Next rule of thumb: if you use a count system such as Hi-Lo, your edge is approximately 0.5% per each true count.. So, if the true count were, say, +4, that would be a 2% edge, except for the fact that we don't have an even game to start! So, if the house edge off the top is, say, 0.5%, then the edge at +4 would be only 1.5%.

    Hope this helps. Write back with more questions.

    Don

  3. #3


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    Hi Don,

    Thanks a lot for you answer, this already helps me categorize this matter much better, though I think I didn't fully grasp your explanation.

    Basically I have 2 questions:

    How is edge calculated precisely?

    You tell me simulation tells us what our edge is, and that with card counters, if you have a certain true count, you have a certain edge (of course minus the house edge).
    - First, I can imagine which factors play a role in the simulation of your edge (deck-penetration, rules of the game(house edge), knowing the exact amount of every card present in the shoe helps, etc...)
    - Could you tell me or send me somewhere where this simulation is explained, which factors come into calculating your edge?


    What is variance?
    plain and simple, no idea what this is or what it stands for.
    Again if you have a webpage with info, that's more than enough.
    But feel free to answer directly if you can make it not too long for yourself.

    Last thing:
    'With caveats and limitations, your optimal bet is often (bankroll x edge/variance).
    Which caveats and limitations?

    I'm so sorry, I think I really didn't grasp a lot of your answer, only the 'Your percentage of winning the hand is not what determines your bet size; rather, the advantage that you have for the next round does' and the term bankroll i seemed to understand

    At least now I'm positive that calculating the odds of winning a hand before any card is played has no reason at all, and that calculating winning chances only matter when you have to do something, like standing, hitting, doubling, splitting etc.... Correct right?

  4. #4


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    Edge or advantage is calculated by multiplying your chance to win by the payoff and subtracting the amount you may lose by the chance of a loss. In many games, it's quite simple to calculate, because those figures are easy to get. It's harder in blackjack due to card removal as well as the chance to double, split, 3:2 BJ, etc. You can lose up to 8 units, push, win up to 8 units, as well as win 1.5 units, assuming you can only split to 4 hands and double after split. You CAN do the math by hand, but that would take forever. Better off to do a simulation.


    Variance is basically how much difference there is or there can be between expectation and actual. Flip a coin 10 times and you expect 5 heads and 5 tails. But you can get 4 heads and 6 tails. That's variance. It's certainly useful to know how "off" of expectation you can be with a certain level of confidence, so that you can bet an amount so that your risk isn't too high. IE: You wouldn't bet your entire net worth on a coinflip where you're getting a 1% edge. Knowing variance and other formulas I'm too lazy to write about, you can calculate the optimal amount of money to wager.


    A caveat would be table maximum (you can't bet more than that) or heat in a casino, where you don't want to attract attention to yourself by betting more than you think the casino will toleratev
    "Everyone wants to be rich, but nobody wants to work for it." -Ryan Howard [The Office]

  5. #5


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    Quote Originally Posted by RS View Post
    A caveat would be table maximum (you can't bet more than that) or heat in a casino, where you don't want to attract attention to yourself by betting more than you think the casino will toleratev
    In general, the formula I quoted for a precise Kelly bet is exact for all intermediate bets that aren't the minimum or the maximum of the spread you choose. The latter two are subject to different math and other constraints.

    Don

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