two hands

I play SD/H17/DA2/NDaS/NLS with fair to good pen.

I typically will spread 1-6 by playing one unit on one hand and then 2 or 3 units on two hands. Recently I was reading from Gamemaster's blackjack school chapter 19... and something has caught my attention:

Since I would, whenever appropriate, play 2 hands, I'd need a table for the optimum bets for those situations. The rule here is that 56% of the advantage times the bankroll is the optimum bet for each of two hands. In other words, if it's correct for me to bet $25 on one hand, I would be over betting if I bet $25 on each of two hands at the same true count. Because of covariance (the relationship of two hands to one another), the optimum bet must be reduced.

I have never heard this argument before. Immediately I thought 'well that would mean if a ploppy is playing one hand next to me while I am playing one hand and the true count is +3... that since we are playing '2 hands' that it would be wrong to bet 3 units, and should instead bet less (as should he)'. Am I making sense?

I panicked when I felt I had been making errors all these years, but I am willing to correct my ways if someone can clarify this for me...

Thanks in advance...

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The idea for two hands is this: when you bet N units, on some percentage of the hands you are going to double/split or even both, which means that if you simply flat-bet for an hour, your average bet is going to be higher than the bet you made.

The GameMaster betting schedule info covers this and points out that where you want to bet $100 based on your advantage times your total bankroll (kelly bet) that you _really_ want to bet .76 times the above to stay within the kelly criterion. If you don't factor in the above, you will be slightly over-betting, which increases your ROR by some amount.

Now, when you spread to two hands, things change a bit because the two hands have covariance, they are playied against the same dealer hand. As a result, two times 4 betting units is not really a spread of 1-8. I don't have the info handy, but he covered this pretty nicely.

Of course, you can always over-bet so long as you have the advantage and come out a winner in the long-run. In fact, the more you over-bet, the more your long-term profit. Unfortnately, the more you over-bet, the more your variance, so the kelly bankroll is not enough, or else your ROR will be way higher than the Kelly bankroll idea would suggest...