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 dealer's hole card is dealt face up. No guessing, no upcard tables.
- That knowledge is worth +9.85% to you. We computed it.
- You pay 2.37% because blackjack drops to even money.
- You pay 7.83% because the dealer wins every tie.
- Net house edge: about 0.36%.
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.
| Rules | Player edge | Change |
|---|---|---|
| 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 |
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 hold | Dealer shows | Stand | Hit | Play |
|---|---|---|---|---|
| 16 | 20 | −1.000 | −0.790 | hit |
| 20 | 20 | −1.000 | −0.844 | hit |
| 17 | 18 | −1.000 | −0.496 | hit |
| 16 | 13 | +0.036 | −0.451 | stand |
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.
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By Martin Kosek · every number on this site is computed by us, not copied.
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