Doubling 11 versus a 10

4 October 2018

By John Grochowski

QUESTION: Why should I double down on 11 when the dealer has a 10 up? It seems to me the dealer is trending to a really good hand, with a 20 likely and possibly a blackjack. This seems like spitting into the wind.

ANSWER: At nearly all U. S. tables, the dealer will check for blackjack before players make any hit/stand/split/double decisions. If the dealer has blackjack, that stops the hand and you never get a chance to make your second bet.

That leaves 12 other card denominations, four of which are 10 values, with which the dealer doesn't have blackjack and you have a decision to make. Only a third of those cards immediately give the dealer a 20.

If the down card is 7, 8 or 9, the dealer has a lesser standing hand, and if its 2, 3, 4, 5 or 6, the dealer must take a second hit and could bust.

When all that is taken into account, your average profit per hand is larger if double than if you stand. Exact figures vary slightly depending on the composition of the hand. If you stand in a six-deck game, average profits are 11.86 cents per dollar wagered if you have 6-5, 11.79 with 7-4, 17.79 with 8-3, or 11.70 with 9-2. If you double, average profits are 17.85 cents per dollar of your original wager if you have 6-5, 17.84 with 7-4, 17.69 with 8-3 or 17.39 with 9-2.

Your average profit decreases a bit as your higher card increases because the presence of the higher card in your hand means it's not available for a draw. When you have a 9, a card that could turn 11 into 20 is already out of play.

When you double down, you risk losing double your original bet, but you win double your bet more often, giving you a higher average profit when you double on 11 vs. 10.


QUESTION: I'm having a hard time believing that choices make a difference in pick'em bonuses. There's a programmed payback percentage, right? How can they do that if they don't know how much the bonus is going to pay?

ANSWER: The amount of any one bonus is unknown, but the odds of the game will drive it toward a known average.

To make up a simple example, imagine a bonus round in which you're presented with five choices. A, B, C, D and E. Each time the bonus is played, you could win 10, 20, 50, 75 or 500 credits. Which letter hides which prize amount is randomly generated each time the bonus is played, and which you win depends on your choice.

On any given play, you could win any of the bonuses. You could be disappointed with the 10-credit prize, thrilled with the 500-credit bonanza or get something in between.

Over thousands of plays and thousands of blind choices, each prize will be picked about the same number of times. In our hypothetical example, the average pay per bonus will be 115 credits, and that average result can be folded into calculations for the expected payback percentage.

Many pick'em rounds have more choices. The classic Jackpot Party has dozens of gift boxes gyrating as they hide credits or Poopers. Some have multiple levels in which a lucky pick takes you to another bonus. The math gets more complex, but the programmer still can count on the odds of the game leading to an average result on the bonuses, and that can be used in calculating the overall payback percentage.