How We Compute the Odds
Every win percentage and expected value on this site comes from one engine that we wrote. It doesn't simulate millions of hands and report an average — it solves the math exactly, from the actual cards left in the shoe. Here's precisely how, including the assumptions and the few standard approximations we make.
We compute the dealer's exact outcome distribution by recursion over the remaining shoe (conditioned on the US peek rule), then evaluate the expected value of standing, hitting, doubling, and splitting against it — no simulation, no lookup tables.
The dealer's outcome distribution
The heart of the engine is the dealer's exact probability of finishing at 17, 18, 19, 20, 21, or busting, given their up-card. We compute it with a memoized recursion over the dealer's hand state — total and whether it's "soft" (an ace counted as 11). At each step the dealer's draw probabilities come from the actual composition of the remaining shoe (plus the unseen hole card added back), so the numbers shift correctly as cards leave the deck. The dealer stands or draws by the table rule (hit until 17, and hitting soft 17 when that rule is on).
Crucially, the distribution is conditioned on the US peek rule: when the up-card is an ace or a ten, the dealer has already checked the hole card for blackjack, so we exclude the blackjack case and renormalize. This is why our dealer-bust numbers (a 6 busts 43.9%, an ace only ~20%) match the standard published figures for a peeked game.
Your expected value for each play
With the dealer distribution in hand, we evaluate every legal action as an expected value per dollar of your original bet:
- Stand — your total compared against the dealer distribution: win, push, or lose.
- Hit — draw one card from the shoe composition, then play the resulting hand optimally (the engine recursively chooses the better of hitting again or standing), so hit's value reflects correct continuation, not a single draw.
- Double — exactly one card, forced stand, at twice the stake (the EV is stated per original bet, which is why doubling can differ from hitting even at the same win rate).
- Split — valued as two independent post-split hands, with double-after-split allowed and split aces receiving one card each.
The book play we show is simply the action with the highest expected value among those legal for the hand — which is exactly what basic strategy is.
The default game
Unless you change the settings, every number assumes the most common US shoe game: 6 decks, dealer hits soft 17, blackjack pays 3:2, double on any two cards, double after split, split to four hands, split aces get one card, no surrender. The trainer's settings let you change decks (1–8), the soft-17 rule (H17/S17), and the payout (3:2 / 6:5), and the chart, odds, and dealer all follow your choice.
The approximations — stated honestly
Two standard simplifications keep the engine exact enough to trust and fast enough to run live:
- Fixed-proportion draws. Within a single EV calculation, draw probabilities use the current shoe proportions without removing each drawn card mid-computation. For a 6-deck shoe the error is negligible (a fraction of a hundredth of a percent), and it keeps every number instant.
- Split valuation. A split is valued as two times one optimally-played post-split hand, with double-after-split, but without modeling re-splits. This is the standard approximation used across basic-strategy analysis; it can differ from a full re-split model by a tiny margin on a few pair hands.
How we know it's right
The engine is validated against long-established published results. A few checkpoints: insurance returns exactly −7.69% (3 × P(ten) − 1); the dealer busts 43.9% showing a 6 in an H17 game; doubling 11 vs 6 returns about +66.5¢ per dollar; and 16 vs 10 is the near-coin-flip everyone argues about, at roughly −54¢ played out. These aren't numbers we looked up — they're what the engine produces, and they line up with the literature. If you ever find one that doesn't, tell us.