If you know you have a 2.5% possibility for example to win over losing how much should i bet as percentage of the balance?
Any advice?!
Let me see if I can put this into language that reflects what you're truly asking: "If you know you have a 2.5% greater probability to win a hand, over losing, how much should you bet as a percentage of the bankroll?" Is that what you meant to write? If so:
In a 4.5/6 S17 DAS game, having a 51.25% probability of winning a hand (ties excluded) and, therefore, a 48.75% probability of losing, represents a 2.5% greater probability of winning over losing. To have those percentages, the true count would be approximately +8, and your edge would be around 4.32%. As the correct Kelly wager is edge divided by variance, and variance is about 1.31, the correct percentage of your bank to bet would be about 3.3%. For many players, that's more than a max bet.
Don
Don - thank you for this excellent response and detailed breakdown.
As a follow up I am curious to know if the variance of 1.31 is specific to this type of game/scenario or blackjack in general with basic strategy and deviations at play. If we add LS to the game outlined would that lower the variance and increase the player's edge?
If so, wouldn't that correspond to an even higher percentage of bankroll than the 3.3% to almost 4% as the optimal bet? Lastly, where can I learn more about calculating variance for blackjack?
Last edited by CuriousOne; 05-25-2022 at 08:49 AM.
You're asking the wrong question. To determine Kelly wagers, you don't need to know anything about how many hands you win, lose, or tie. You need only know what your overall advantage is, at any particular true count. Many wagers in BJ pay more than even money (naturals, splits, doubles), and some losing wagers are less than 100% of your bet (insurance, surrender). So, stop talking about winning and losing probability; it isn't what you're looking for.
Don
yesIf we add LS to the game outlined would that lower the variance and increase the player's edge?
Yes, 2 factors. Surrender adds about a 1/3 to win rate. Don I think is including the value of index play - I18 for example - which increases edge per true count the higher the TC becomes - examples - 8v6, 8v5, 99v7 10v10, 10 10v 5 or 6, insurance etc.If so, wouldn't that correspond to an even higher percentage of bankroll than the 3.3% to almost 4% as the optimal bet?
Point - optimal betting of entire bankroll at that point should provide an excellent view of the exit which will include a guided tour.
Freightman - thanks for your reply. It has led me to the last piece of this puzzle found here Variance in Blackjack (wizardofodds.com) this site confirms your data on the variance of Late Surrender -0.03629 or -3.6%
And your point is well taken - if your goal is to maximize your money knowing this will be a one and done casino then this is optimal.
Assuming these variance calculations are correct, combined with previous published player advantage tables (or casino edge) for various games (4.5/6 S17 DAS being -0.428 player advantage at a TC 0)
We can calculate the optimal bet using: Player Advantage / Variance as a percentage of bankroll, outlined by Don above.
Note: please let me know if we are permitted to link to other on line sources or not and I will edit post if necessary.
Last edited by CuriousOne; 05-25-2022 at 02:02 PM.
A quick comment on all of the above. The OP wasn't very clear as to exactly what he meant by 2.5% "possibility to win over losing." I know very well, via hundreds of Chapter 10 charts, what the player edge is at every TC for every number of decks and every rules set. But I took the wording literally, namely that the player would win 2.5% more hands than he would lose. Hence my response. If that isn't what the OP meant, then he should come back and clarify.
Don
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