Match play and composition blackjack hands

10 July 2016

By John Grochowski

QUESTION: I used to like it when every casino had a fun book and you could get a little slot play and some match play at the tables, some food discounts, free popcorn or a hot dog – it was fun hunting for the best bargains for a low roller!

The reason I bring it up is that I actually got a couple of match plays last month, and used them on craps at the pass line. The player has to have an edge with the match, right? How big is it?

ANSWER: When you use a match-play coupon and win, you get double winnings for that one play. Bet $5 and a match play on an even-money bet, and if you win, you get $10 in winnings, you keep your $5 bet, and the dealer takes away the coupon. Lose, and you lose $5 and the dealer also takes the coupon.

Without match play, the 1.41% house edge on the pass line in craps means you win 49.295% of the time, and lose 50.705%. Subtract 49.295 from 50.705, and you get 1.41.

So let’s say you wager $5 on the pass line for each of 100,000 come-out rolls. You risk $500,000, and your expectation is that you’ll win 49,295 bets and lose 50,705.

Each time you win using the match-play coupon, you get $10 in winnings, plus you keep your $5 bet. So after 100,000 trials, you have 49,295 x $15, or $739,425. Subtract the $500,000 that represent your wagers, and that means you have a profit of $239,425.

Divide that by $500,000 in wagers, then multiply by 100 to convert to percent, and your edge over the house is 47.885%.

If you had an unlimited supply of match-play coupons and never made a bet without one, you would have a 47.885% edge over the house.


QUESTION: Are basic strategy cards (in blackjack) just for your first two cards, or do they apply to the totals after more cards? That is, if I’m supposed to hit 14 when the dealer has a 9, do I still hit when my 14 is a 7, 6 and ace besides when it’s a 9 and 5, 10 and 4 or 8 and 6?

ANSWER: In most cases, yes, you should follow the same strategy with three or more cards as with two. You still hit 14 against a 9 no matter how many cards make up your 14.

The most common exception comes on double down hands. You’re allowed to double down on only your first two cards, so if you have a three-card 11, you can only hit, not double. On nearly all double-down totals, the best play with three or more cards is to hit. The exception is soft 18, where in a six-deck game in which the dealer hits soft 17, basic strategy calls for doubling down vs. dealer’s 2 through 6. If your soft 18 is three or more cards, you stand instead.

To dig a little deeper, there are some close calls on composition-dependent hands. A card counter would consider the full count, not just the cards in one hand, but a non-counter can make a small gain by standing on 16 vs. 10 if the player’s hand includes a 5 or 4. You’d stand vs. 10 with 5-5-4-2, for example, but hit with 10-6 or 9-7.

Composition-dependent gains are small enough that a recreational player doesn’t need to worry too much about such plays. For most players, it’s enough to make the same basic strategy plays with three or more cards that you would with two.