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Best of John Grochowski
A Shuffle Through the Gaming Mailbag14 March 2002
A. Here's hoping your friendship is strong enough to survive some rocky times ahead, because all the things you mention favor the house.
In eight complete decks, there should be 32 Aces and 128 10-values, not the 28 Aces and 110 10-values you found. The shortage of Aces and 10-values favors the house because it decreases the frequency of blackjacks. Since players are paid 3-2 on blackjacks and the house is not, anything that lowers the frequency of blackjacks pads the house advantage.
The shortage of 10 values also favors the house because it makes it less likely the player will get a desirable draw in many double-down situations. If you double on 10 or 11, you want the full complement of 10s in the deck.
The added low cards favor the house because the dealer always draws when holding 12 through 16, while players sometimes stand on those hands. The added low cards makes it more likely the dealer will make a 17 or better when drawing to those iffy hands. The shortage of 10s also feeds into that by making it less likely the dealer will bust on those draws.
Eight-deck blackjack is a tough game anyway. I avoid eight-deck games at casinos, and I wouldn't play it at someone's house. With the added disadvantage of the deck composition you report, it's really a stinker of a game.
As a home game, blackjack is far from ideal anyway because there is a house edge built into the game. If you're going to play blackjack at someone's house, I'd recommend using new decks of cards each time, fanned out before you play so that everyone can see that all the cards are there. I'd also suggest taking turns acting as the dealer, so that no one player has the house edge all the time. Finally, to minimize the house edge, use a single deck of cards and have the dealer stand on all 17s, including soft 17. That's very close to an even game, with a basic strategy player having a 0.01 percent edge on the house.
A. I understand where you're coming from. In one time through a single deck, no more than four blackjacks can be dealt because that will have exhausted the available Aces. But one time through the deck doesn't begin to scratch the possible hands in blackjack.
Can we have Ace-8, Ace-7, Ace-6, Ace-5 and Ace-4 in a single time through one deck. No, because we don't have enough Aces. But in repeated play, all those hands will occur, and we need to account for them calculating odds and the house edge.
Likewise, we need to consider each Ace with each possible 10-value as a separate possibility. The Ace of hearts with any of the 16 10-value cards in a deck account for 16 possible blackjacks. Same with the Aces of clubs, spades and diamonds, bringing the total to 64 possible two-card 21s.
There are 1,326 possible two-card hands using a 52-card deck. If we know that 64 of those hands are two-card 21s, we then can calculate that an average of one in 20.7 hands will be a two-card 21 that brings a 3-2 payoff. If we see the two-card 21 possibilities as only four hands instead of 64, we'll be far, far off target when we compute the frequency of two-card 21s and their effect on the house edge.
It's also important to know there are 64 possible two-card 21s when we encounter specialized rules such as the one that gave blackjack its name. Early in the game's history, two-card 21s paid 3-1 if one card was the Ace of spades and the other the Jack of spades.
To calculate the effect that has on the house edge, you have to know that the specific condition of Ace-Jack of spades will occur only once per 64 blackjacks, not the 1 in 4 that your way of looking at the problem would suggest.
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Best of John Grochowski