Last edited by aceside; 05-16-2021 at 09:15 AM.
The tricky part is the bet size. To use the above numbers I posted, we have: For one hand, bet size=1; for two-hand, total bet size=1+1=2. Is the total EV=+0.5%+0.5%? Or the total EV is just +0.5%? We players know very well that playing two hands does not give two times blackjack salary. This has been bothering me.
EV is the same. Bet size is not multiplied by 2. With two hands, each bet is around 75% of a one hand bet, depending on circumstances.
Last edited by Norm; 05-16-2021 at 08:11 AM.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
Consider positive EV only, and use only this bet pattern: one unit when one-hand, 0.75 unit when two-hand, and 0.36 unit when 6-hand.
For one-hand play, variance=1.3 and EV=+0.5%;
For two hands play, total variance=[2X1.3+2X(2-1)X0.48]X0.75^2=2.0 and total EV=+0.5%;
For six hands play, total variance=[6X1.3+6X(6-1)X0.48]X0.36^2=2.9 and total EV=+0.5%.
Based on this calculation, one round of six-hand gives this expected amount 6X0.36X0.5%=2.2X0.5%, 2.2 times of the one-hand. Suppose the six hands are from different people, then each player only makes 2.2X0.5%/6=0.37X0.5%, a little more than one third of the solo playing. Is this correct?
No. The change in variance and EV only affects the players playing multiple hands and only their hands. Why would other players change their bets because you are playing multiple hands? Their variance and EV is unchanged by what you do.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
For the total variance part, I just use this formula I copy from the Wizard. If the variance of one hand is v, the covariance is c, and the number of hands played at once is n, then the total variance is n×v + n×(n-1)×c. Of course, this assumes the bet size is one unit flat for each hand.
For the total EV when playing two hands, there is no such a formula to use, and this is also what I am asking Norm for. It is mostly determined by the specific blackjack rules and the deck number, but instantaneously determined by the true count, so I just assume a reasonable EV of +0.5%.
Of course I post here to learn. This forum has cleared some of my doubts; for example, I mistakenly thought that the play deviation indices change with the dealing depth in a 8-deck shoe, but this has been proved wrong. So far, I can barely beat some games, but only when playing solo. If I play with two or more other players, I cannot beat these games anymore. What is the math behind multiple-player tables?
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