Expected value of hard 16 vs 10

Hard 16 against a dealer 10 is the hand players most often get wrong, because every option loses and the best one loses only fractionally less. Under six-deck S17 rules, standing on 10+6 has an expected value of −0.540954 per unit and hitting has −0.534676 (Wizard of Odds): hit, and if the table offers late surrender, surrender instead for exactly −0.5.

The published numbers

The Wizard of Odds six-deck, dealer-stands-on-soft-17 expected-value table lists each two-card composition separately. Values are expected profit per unit of initial stake; −0.54 means an average loss of 54p for every £1 bet.

Doubling is listed for completeness: it exactly doubles the loss of hitting once, because you take one card and cannot continue. Nobody doubles a 16.

Surrender is not in the source table because that rule set has no surrender, but its value needs no table: you forfeit half the stake with certainty, so EV = −0.5 regardless of the cards. The Wizard’s surrender page lists 16 against 10 as a surrender in every deck count, total-dependent and composition-dependent alike.

In money terms

On a £10 stake under six-deck S17 rules (10+6 composition):

Hitting rather than standing saves about 6p per £10 hand. That is small, which is why the play feels arbitrary, but it is not zero, and the direction never flips in a shoe game for a two-card 16. Surrender saves another 35p per hand on top, which is why late surrender is one of the few rules that is worth seeking out; the surrender guide lists the other hands.

Why standing loses 54%

When you stand on 16 you cannot beat any completed dealer hand. You win only if the dealer busts, and against a 10 the six-deck S17 dealer busts 23.02% of the time after the peek has ruled out a natural (Wizard of Odds dealer-odds table). So:

EV(stand) ≈ 0.2302 × (+1) + 0.7698 × (−1) = −0.5395.

The published −0.540954 differs by a little over a thousandth because your 10 and 6 are out of the shoe, leaving the dealer marginally less likely to bust. Of the 77% of hands where the dealer does not bust, more than a third end on exactly 20 (36.84%), which is relevant to the hitting side below.

Why hitting loses slightly less

Hitting has two routes to defeat. Using the infinite-deck approximation for the first draw:

1. Bust at once: a 6, 7, 8, 9 or 10-value card, 8 of the 13 ranks, probability 8/13 ≈ 0.615. Loss of 1 unit.
2. Survive: an ace through 5, probability 5/13 ≈ 0.385, leaving 17 to 21. Each outcome is then settled against the dealer’s distribution for a 10 upcard: 17 (12.13%), 18 (12.10%), 19 (12.13%), 20 (36.84%), 21 (3.77%), bust (23.02%).

A player 17 beats only a dealer bust and pushes a 17, so it is still a losing hand. A 20 wins against everything except a 20 (push) and 21. The weighted sum across all five survival totals is what the engine computes, and it comes to a loss of about 0.535 overall. The surviving 38.5% is worth more than it looks because a 20 or 21 wins outright against the dealer’s most common total, while standing can never win those hands.

The structure of the comparison is easy to state: standing gives you a 23% chance of winning; hitting gives you a 38.5% chance of staying alive, and the live hands win often enough that the total comes out ahead by about 0.6% of the stake. The player bust probability article covers the general case.

Two cards versus three or more

The hit-versus-stand gap is so narrow that the composition of the 16 can reverse it. The Wizard of Odds lists one exception that applies across two to eight decks: stand on 16 against a 10 when the 16 is made of three or more cards. The surrender page makes the same distinction, recording 16 against 10 as a surrender “always” in composition-dependent play but noting that composition matters for the hit/stand choice.

The logic is removal. A 16 made of 7+5+4 or 6+6+4 has taken three small cards out of the shoe. The cards that improve a 16 are precisely the small ones (ace to 5), so a shoe that has lost some of them is slightly worse for hitting, and the remaining shoe is proportionally richer in 10s that help the dealer make 20. Even in six decks, where each removed card is only 0.3% of the pack, the effect exceeds the 0.006 margin between hitting and standing. The site’s strategy chart is total-dependent and says hit; the three-card rule is the first exception worth memorising, and the composition-dependent exceptions article lists the others.

Compare the two-card compositions in the published table. Hitting beats standing by 0.0063 for 10+6 but by only 0.0014 for 9+7. With 10+6, both removed cards (a 10 and a 6) are cards that would have busted a hit, and the missing 10 also slightly lowers the dealer’s chance of busting, so hitting gains and standing loses. With 9+7 the removed cards are also bust cards for a hit, but no 10 has left the shoe, so the dealer busts a little more often and standing (−0.536809) improves by more than hitting does. The pattern is consistent: the fewer 10s and the more small cards your 16 has consumed, the closer standing gets.

Card counters and 16 vs 10

The thinness of the margin makes 16 against 10 the most valuable index play in the Hi-Lo system. The Illustrious 18 index for it is 0: stand when the true count is zero or positive, hit when negative. A positive count means the shoe is ten-rich, which raises the dealer’s chance of making 20 and your chance of busting; both push the decision toward standing. The Illustrious 18 article covers the full list.

For a basic-strategy player with no count, the published values settle it: hit a two-card 16 against a 10, stand on a three-card 16, surrender where the rule exists.

Related reading

• Player bust probability when hitting
• Composition-dependent exceptions
• Surrender
• Hard 16 vs 10 hand page