Does Playing Two Hands at Blackjack Smooth Out the Payouts?

While playing blackjack, a guy playing two separate hands commented that he does better that way since he will usually win at least one — it smooths out the payouts and protects his bankroll. I think playing two hands would accentuate the streaks (a hot dealer would beat you twice — or a hot player may win twice), but in the long run, it probably won’t make a difference, other than you're playing a negative-expectation game, so you would lose your bankroll at twice the speed. Am I correct? Also, your link to the results of the steakhouse poll.

[Editor's Note: Blackjack author, publisher, player, Hall of Fame member, and humorist Arnold Snyder graciously tackled this one for us.]

Your gut instinct is good. If you're playing a negative-expectation game, betting twice the amount will be twice as costly to your bankroll in the long run.

In a sense, however, the guy you met who was playing two hands to “smooth out the payouts” is also correct. If you were to graph his results, he would show a smoother downhill slide as a result of the simultaneous win/loss hands. So he's observing an actual phenomenon as a result of playing simultaneous hands. He will more smoothly lose twice as much money per hour!

For a player with a positive expectation on a game, multiple hands increases the hourly win rate. Card counters sometimes play simultaneous hands to smooth out fluctuations. But the counter must also lower his per-hand bet size to avoid over-betting his bankroll. Some of the better card-counting guides provide bet-sizing charts for playing multiple hands.

For recreational players who are bucking a house edge, the only way to lower your hourly loss rate is to bet less per hour.

And here's the link to the results of the steakhouse poll conducted a couple of weeks ago.

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Comments

Pat Higgins Sep-05-2019

Pat H

Kinda like hedge betting at craps.  A don't pass and a do pass bet at the same time simply doubles the negative expectation.  Or Making a $5 pass line bet and "insuring" it with an any 7 $1 bet to "protect" your pass line on the come out roll.  Again 2 negative expectation bets so you will lose more in the long run. Snyder is right on.  Play smart.

Stewart Ethier Sep-05-2019

Variance

I'm not convinced that betting one unit on each of two hands "smooths out the fluctuations," compared to betting one unit on one hand.  Smoothing out the fluctuations is equivalent to reducing the variance, and this is something we can compute.  

The variance of two one-unit hands (same table) is 2(1.26)+0.50 = 3.02 (see Griffin, Appendix 9E)
The variance of two one-unit hands (different tables) is 2(1.26) = 2.52
The variance of one two-unit hand is 4(1.26) = 5.04
All three cases have the same expected loss.

The variance of one one-unit hand is 1.26
Here the expected loss is only half as much, and the variance is minimized, among the possibilities considered.

Stewart Ethier Sep-05-2019

correction

Just for. the record, there is a small error in the first variance calculation of my previous comment.  It should be 2(1.26)+2(0.50) = 3.52.  The conclusion remains the same.

Question of the Day - 05 September 2019

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