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Thread: Trying to calculate Full Kelly on 30k BR

  1. #27


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    Quote Originally Posted by Tthree View Post
    ...
    CE = EV - Var*(B/2), where B is your bet size.

    So if either variance or bet is zero CE = EV which is 5. Both variance and bet are 0 in this case.
    Variance is never zero for a non-trivial random variable. In a coin flip game, the variance is 0.5*1^2 + 0.5*(-1)^2 = 1.

    Expected Growth is the geometric mean of growth (decline) of bankroll. If you are handy with derivatives, you can calculate your Kelly bet from the Expected Growth function for a bet with known outcomes. Below is a simplified example of Blackjack with 3 possible outcomes for a bet of 1 unit:
    1: Win 1.5 with probability 0.023669;
    2: Win 1 with probability 0.480414;
    3: Lose 1 with probability 0.495917.

    EV for this bet is 1.5*0.023669 + 1*0.480414 -1*0.495917 = 0.02. Variance is 1.0292.

    log(EG) = 0.023669*log((B+1.5)/B) + 0.480414*log((B+1)/B) -0.495917*log((B-1)/B) [B represents bankroll]

    Calculate 1st derivative with respect to B. Set derivative = 0, which will solve Kelly bankroll for a 1 unit bet.

    The derivative degenerates to a quadratic equation, where:
    a=-0.04
    b=1.999172
    c=3

    Plugging the above constants into the quadratic equation, B equals 51.437.

    And the Kelly fraction is:

    1/51.437 = 0.01944, which is closely approximated by the shorthand formula for Kelly fraction, EV/Variance = 0.02/1.0292 = 0.01943.

    And EG is:

    1.000194

    With a doubling rate of:

    log(2)/log(1.000194) = 3,566 bets.

    EV/Variance is a good approximation for Kelly fraction when EV is small. When EV gets larger, this will diverge from the actual Kelly fraction. For example, assuming the above game has EV 0.2 (with same likelihood of 1.5x), Kelly equals 0.1955. EV/Variance equals 0.2021.

    Quote Originally Posted by Meistro123 View Post
    I know, that is what I said.
    You seemed to imply that breaking even gambling but spending a lot of money in expenses will somehow not cause your EG to go down. Any reduction in bankroll without a concurrent reduction in bet size(s) will reduce EG, assuming the player was betting at levels to achieve max EG. At the point the player is unable to reduce bet sizes to sustain +EG, the game becomes unplayable and the player must stop. But the player has not gone broke.

  2. #28


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    You seemed to imply that breaking even gambling but spending a lot of money in expenses will somehow not cause your EG to go down.
    What are you talking about? I said flatly that breaking even can cause you to go broke.

  3. #29


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    Quote Originally Posted by Meistro123 View Post
    What are you talking about? I said flatly that breaking even can cause you to go broke.
    Again, the player will not go broke. As I said above, with a continuing diminishing bankroll, the player will reach a point where bets cannot be made to achieve +EG for that game. The player will still have a bankroll, but it will not be sufficient to play that game.

    I hope that is clear.

  4. #30


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    Quote Originally Posted by bigedge View Post
    Simply, risk of ruin should not apply to a serious AP intending to grow his/her bankroll.

    Any system, if able to freely bet a fraction of one's bankroll, will never go broke. This includes full Kelly, fractional Kelly, bet 50% every time, etc. Blackjack is an exception because (a) minimum bets prohibit the ability to freely bet fractionally, and (b) bets may be (frequently) made with a -EG, but are part of a larger +EG system.

    The AP needs to realize when the system ("game") in which they are playing becomes -EG, they need to stop that system and develop another system which yields a +EG. This will happen before any zero bankroll situation. (Actually, AP should give up a +EG game when a better EG opportunity arises)

    The most important calculation for the AP to make is not % risk of ruin, but what is the EG for the system he/she is playing for a given set of assumptions, and maximizing EG thru game choices, reduction of costs to participate, etc.

    Another important calculation is the probability that his/her system may reach a point of -EG due to expenses not part of +EG play, such as frequency of cover bets, costs to participate, minimum bet, etc.
    EV (EG?) is of zero value if you have no money to bet. EV/RoR are mutually dependent metrics that must be planned with both your game and your bankroll in the equation. To do otherwise is foolish.
    Luck is nothing more than probability taken personally!

  5. #31


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    I did not lose my bankroll playing blackjack but i lost my bankroll through expenses , therefore I am not a loser! Just as saying you are the best player in the world but you are not allow to play or you don't have a bankroll. I think being practical and realistic is a key factor .

  6. #32


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    Effect of overhead on risk of ruin is a very real thing and most people mistakenly do not include it in their RoR calculations, and are taking expenses out of the same fund making their RoR/kelly calculations more or less flawed/invalid. I used to like to keep a seperate account for business/living expenses that would last long enough to reach 2-3x NO to this reason.

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