Composition-dependent exceptions to basic strategy

Basic strategy charts, including the one on this site, are total-dependent: they look only at your total and the dealer’s upcard. A composition-dependent strategy also looks at which cards make up the total, and in a handful of hands that changes the answer. The best-known case works in every shoe game: stand on a hard 16 against a 10 when the 16 is made of three or more cards.

Why composition can matter

Every card in your hand is a card that is no longer in the shoe. That matters in two ways. First, it alters what you can draw: a 16 made of 7+5+4 has removed three of the small cards that would improve a 16. Second, it alters what the dealer can draw: holding a 10 means one fewer 10 for a dealer 4 to bust with.

In an infinite deck neither effect exists, which is why infinite-deck tables such as the Wizard of Odds appendix 1 never distinguish compositions. In a single deck a removed card is 1/52 of the pack, roughly 2%, and composition effects are routine. In six decks it is 1/312, about 0.3%, and only decisions that were already a near tie can be flipped.

The Wizard of Odds six-deck S17 table shows the size of the margins involved. Standing on 10+2 against a 4 has EV −0.211115 and hitting −0.210364, a gap of 0.00075 units. For 16 against 10 the gap between hitting 10+6 (−0.534676) and standing (−0.540954) is 0.0063. Decisions this close are the only ones composition can reverse.

Three-card 16 against a 10 (any shoe)

The Wizard of Odds exception list for two to eight decks has a single entry: “Always: Stand on 16 vs 10 with 3 or more cards.” It is the only composition rule that applies to the site’s profile.

The reasoning follows from the EV of hard 16 vs 10: hitting a two-card 16 is better than standing by about 0.006. The cards that save a hit are ace through 5. A multi-card 16 has necessarily been built from small cards (any 16 of three or more cards contains at least one card of 6 or lower, and most contain several), so some of the saving cards are gone and the remaining shoe is relatively richer in 10s, which also helps the dealer finish on 20. Both effects push against hitting, and 0.006 is not much to overcome.

The Wizard’s surrender page confirms the hand’s status in a different way: with late surrender, 16 against 10 is a surrender “always” in composition-dependent play, whatever the cards. Surrender at −0.5 beats both of the alternatives by a wide margin, so composition never reverses it.

12 made of 10+2 against a 4 (single and double deck)

This is the exception most often quoted, and Wikipedia uses it as its example: “a player should normally stand on 12 against a dealer 4, but in a single-deck game should hit a 12 made of a 10 and a 2.” The Wizard of Odds lists the same play for single deck H17 (appendix 3c) and for double deck S17 (appendix 3b): “12 (10+2) vs 4 = Hit”.

Standing on 12 against a 4 relies on the dealer busting, which a six-deck dealer 4 does 39.58% of the time. Each 10 you hold is a 10 the dealer cannot draw, and a dealer 4 busts mainly by drawing to 14, 15 or 16 and then catching a 10. Removing one of sixteen 10s from a single deck measurably reduces the bust rate; removing a 2 removes a card that would have been safe for the dealer anyway. A 12 of 7+5 or 8+4 leaves all the 10s in play and stands as normal. In six decks the removal is too small to flip the decision, so the site’s chart stands on every 12 against a 4.

Other published single- and double-deck exceptions

The Wizard of Odds composition-dependent appendices list many exceptions for one and two decks, most involving multi-card 15s and 16s. The two-card entries, which are the ones a player could plausibly remember:

Several three-card entries follow the same removal logic as the shoe-game 16 rule: in single deck H17, 15 made of 5+5+5 stands against a 10 and 16 made of 6+5+5 stands against a 9, because the small cards needed to improve them are gone. The reverse also appears: 16 made of 10+2+2+2 (single and double deck) or 10+3+3 (double deck) is hit against a 10, because those compositions have removed a 10 rather than only small cards.

Each entry is specific to the deck count and soft-17 rule in its appendix; a single-deck exception does not transfer to a double-deck game, and none of them transfers to six decks except the three-card 16.

What it is worth

The Wizard of Odds appendix 15 compares house edge under total-dependent and composition-dependent basic strategy for the same rules (no surrender, no resplit aces):

Wikipedia quotes the same orders of magnitude: 0.04% in single deck, 0.003% in six. At £10 a hand and 100 hands an hour, the six-deck gain is worth about 3p an hour. In a single-deck game it is worth 39p an hour, still modest but comparable to other rule differences players do chase. The honest summary is that composition-dependent play is a curiosity for shoe players and a small real gain for single-deck players.

How the site handles it

The strategy chart and trainer use a total-dependent six-deck S17 chart. That is the right design: a chart that lists every composition would be unreadable and would buy 0.0031%. Learn the chart, add the three-card 16 against 10 rule, and ignore the rest unless you move to a single-deck table, in which case the deck count article covers what else changes. Card counters replace composition logic with the count, which captures the same removal effects across the whole shoe rather than just the cards in one hand.

Related reading

• Expected value of hard 16 vs 10
• How basic strategy is derived
• Deck count: single vs multi
• Strategy chart