Double Exposure: Seeing Everything and Winning Nothing

Updated

Both of the dealer's cards are face up. You know the exact hand you are playing against before you make a single decision. We computed what that information is worth: 9.85 percentage points. Then we computed what it costs you, and the two very nearly cancel.

The short version

The whole game in three lines

This is the rare variant that decomposes cleanly. We ran the same six-deck game four times, changing one rule at a time, and the two effects turn out to be exactly additive — measured in either order they agree to the fourth decimal.

RulesPlayer edgeChange
Both dealer cards up, everything else normal+9.850%
… but blackjack pays 1:1+7.475%−2.374
… and the dealer wins all ties−0.357%−7.832
Seeing both cards +9.85% Blackjack at 1:1 −2.37% Dealer takes all ties −7.83%
The green bar is what the information is worth. The two red bars are the price. They add up to 10.21, and the difference is the house edge.

The tie rule is the expensive one, and it is easy to underestimate. Ties are not rare: against a dealer who has to reach 17, a large slice of your hands finish level. At a normal table those are pushes and cost nothing. Here every one of them is a loss. That single change is worth more than three times the blackjack payout cut.

One tie still goes your way: if you both have a natural, you win. It is the only concession in the rule and it is worth very little, because two naturals at the same table is a rare event.

You will hit a 20

Perfect information does not make the game comfortable. It makes it obvious, and what is obvious is often unpleasant. These are our computed values for a single hand, one bet, six decks:

You holdDealer showsStandHitPlay
1620−1.000−0.790hit
2020−1.000−0.844hit
1718−1.000−0.496hit
1613+0.036−0.451stand

Read the second row again. You are holding twenty, the dealer is holding twenty, and you take a card. Standing is a guaranteed loss because the dealer takes ties, so a one-in-eight shot at an ace is strictly better than certainty. A basic-strategy player who cannot bring themselves to do this is throwing away a large part of the game.

The fourth row is the mirror image. Sixteen is normally the worst hand in blackjack, but against a dealer stuck on 13 you simply stand and let them break. No hesitation, no chart, no count needed — you can see the whole thing.

How we checked it

A variant this unusual is easy to get wrong, so we verified it twice. First we wrote a second, independent implementation of the whole game and ran it against the first: they agree to four decimal places. Then we used the engine to measure something with a known answer — the value of seeing the dealer's hole card in an otherwise ordinary game. It came out at +9.850%, against a long-published figure of roughly 10%.

That second check matters more than the first. Two implementations can share a wrong assumption; a number that lands on an independently known quantity cannot. If you want the same trick applied to a live game rather than a rule, see hole carding.

Published house edges for Double Exposure range from about 0.26% to 1.47%, because the rules vary a great deal from table to table — how many splits, whether doubling is restricted, who wins a tie of naturals. Ours is the figure for the common six-deck set above, with a single split and no resplitting, which is how the game is normally dealt. Read the felt before you assume it applies.

Keep reading

Variants comparedall of them, side by side Hole cardingthe same edge, not given away What a push isand what losing them costs

By Martin Kosek · every number on this site is computed by us, not copied.

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