Two Hands

[Mr. Ed]

If I bet $100 on one hand, how much can I bet on each of two hands and get the same Standard Deviation? $75? $70? $65?

[DSchles]

If I bet $100 on one hand, how much can I bet on each of two hands and get the same Standard Deviation? $75? $70? $65?

$73. But it's not the same overall s.d. or variance. They are greater than the one-hand s.d. and variance. But, then, so is the expectation, such that it is the overall risk of ruin that stays the same.
Don

[highrollerjw]

If I bet $100 on one hand, how much can I bet on each of two hands and get the same Standard Deviation? $75? $70? $65?

Without being bang on, 1.5x your bet, spread evenly between 2 hands for an immaterial increase to your ROR. Your variance will increase, though.

[Mr. Ed]

Don - thank you for the clarification considering increased EV for the two hands of $73, which offsets the increased Standard deviation to produce the same ROR.

But I have a different question. If you are on a team of two players with a combined bankroll, each at a different table, would you each bet $73 - the same as an individual playing two hands at the same table? My guess is no, since two hands at the same table has the higher variance (since my two hands are not independent at all - they might face the same dealer BJ and both lose together!)

And one last question - should you vary the 73% bet by True Count? At 0, EV is negative, implying a lower percentage, at +5 EV is much higher, implying a higher percentage.

p.s. Yes, I realize that no one is making a $72 vs a $74 bet, but the math always confused me since two hands at the same table are NOT independent and we cannot use the “square root of n” rule to calculate standard deviation for two hands.

[DSchles]

But I have a different question. If you are on a team of two players with a combined bankroll, each at a different table, would you each bet $73 - the same as an individual playing two hands at the same table? My guess is no, since two hands at the same table has the higher variance (since my two hands are not independent at all - they might face the same dealer BJ and both lose together!)

Correct. It's the covariance between two blackjack hands (both being played against the same dealer upcard) that causes the reduction from the single-hand bet. That disappears if you're at separate tables, so you each make the optimal one-hand bet as if each of you owned the entire bankroll.

And one last question - should you vary the 73% bet by True Count? At 0, EV is negative, implying a lower percentage, at +5 EV is much higher, implying a higher percentage.

Short answer: no. At least, not by enough to matter. The variances do, in fact, increase a little as the TC increases. You can see that by running your eye down any of the chapter 10 charts (they're standard deviations, but no matter). So, the bet sizes will increase, of course, but the general rule of about 75% of the one-hand bet doesn't change.

p.s. Yes, I realize that no one is making a $72 vs a $74 bet, but the math always confused me since two hands at the same table are NOT independent and we cannot use the “square root of n” rule to calculate standard deviation for two hands.

The variances, at least, can be calculated according to the equation in the footnote on page 20.

Don