How to bet if you know the possibilities before each hand.

[CuriousOne]

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?