Hit or stand?
Pick your hand and what the dealer is showing. You’ll get the correct play — and, just as importantly, the exact math behind why it’s correct.
Dealer Stands on Soft 17, DAS, pays 3:2
Your hand is too weak to stand on — the risk of busting is worth it.
Hard 16 against a dealer 10.
Expected value per unit staked, playing correctly. Half of all spots in blackjack are negative before you do anything — the game is decided by how much you give back on the bad ones.
Show the math behind it
EV is per unit bet: stand/hit are relative to your original wager, double/split reflect the extra money put at risk (so a double or split EV lower than stand can still be the right call if it wasn’t an option at all).
Reading an expected value
Every figure on this page is expected return per unit staked. A hand at -50% gives back half your bet on average over a great many repetitions of that exact situation; a hand at +20% returns your bet and a fifth again. They are averages over the long run, not predictions about the next card.
The sign is the part worth internalising, because it is bleaker than most people expect. Plenty of hands are negative under every available action — there is no play that makes a hard 16 against a ten profitable, only a play that loses least. Basic strategy is not a way to win at blackjack. It is a way to lose at the slowest possible rate, and the house edge that remains after playing perfectly is the price of admission.
Why the second-best action matters
A strategy chart gives you one letter per cell and hides the thing that decides how much any of it matters: how far ahead that letter actually is. Those gaps run from almost nothing to more than your entire stake, and the difference is not academic — it is the difference between a mistake that costs you a rounding error and one that costs you the hand.
The tightest on the whole chart is Hard 16 against 10, where the correct play wins by 0.06% of your bet. There are 31 spots on the chart where the decision is that close or where the house rules change the answer outright, and they are set out on the hands worth arguing about.
Everywhere else — the other 319 spots — the margin is wide enough that there is nothing to discuss. That asymmetry is worth carrying to a table: the hands that generate arguments are, almost without exception, the hands where the argument is worth less than 2% of a bet.
What this engine assumes
These are exact figures from a recursive expected-value engine, not a copied chart and not a simulation — every dealer outcome is enumerated rather than sampled. The model treats the shoe as infinite, so each rank stays equally likely no matter what has already been dealt. That is the standard assumption behind every basic-strategy chart, and it is what makes the figures stable enough to publish.
It is also the model’s one real limitation: it does not count cards. In a real shoe the true numbers drift from these as cards are removed, which is the entire basis of counting. Nothing here tells you anything about that. The methodology page sets out the engine and where it simplifies.