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Friday, December 23, 2016

Blackjack vs dealer 10 paid upfront

I was recently paid for my blackjack at the start of the round with the dealer showing a 10. In the European no-peek game, where the dealer takes all her cards except the first one after the players' hands are complete, payments for blackjacks have to wait until the end of the round if the dealer is showing a 10 or an ace - the player blackjack might end up only pushing against the same dealer hand.

As the dealer paid my blackjack it occurred to me to wonder what would happen if she went on to make a blackjack herself: would she remember and ask for the money back? Probably not, and in any event I had whipped all my money out of the betting circle so that my wager wouldn't act as a memory jogger. however, the question didn't arise as the dealer didn't make a blackjack.

So then I thought it would be interesting to calculate the value of player blackjack vs dealer 10 always being paid at the beginning of the round, with the payment standing even if the dealer makes blackjack and the hand should be treated as a push (again, this is only relevant in the no-peek game - in the US peek game the dealer checks for blackjack at the start of the round of play and this situation could never arise).

Player and dealer get a blackjack once in a tad over every 21 hands. There being four 10s per thirteen-rank suit, player blackjack coincides with dealer 10 every (21 X (13 ÷ 4)) = 68.25 hands. With one ace per suit, the dealer will drop an ace on her 10 to tie the player blackjack once every (68.25 × 13) = 887.25 hands. Since the proposal here is that player blackjack is paid at 2:1 rather than pushing, this gives us an addition 1.5 units per 887.25 hands, or an additional 0.169%.

For single deck the number is a fraction over 0.17%.

As such, this single payment error, occurring once in just under 900 hands, rebates fully one third of the house edge, assuming optimal play and a 0.5% hold for the casino.

This serves to reinforce an important gambling truth: with accurate play, blackjack is a low house edge game whose return is highly sensitive to any additional factors that might come into play - see my page on casino mistakes for many other such instances. You won't be an overall winner in the long run playing basic strategy, but you can use it to prepare the ground for turning things in your favour when these little victories occur.

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