How We Calculate the Numbers on This Site
Updated
Every percentage on this site is computed, not copied. The strategy charts and every house edge figure come from expected-value calculations over all the ways a round can play out. This page explains how, so anyone can redo the work, and so the limits of that work are visible.
- Our own solver computes the expected value of every play, for every hand and every rule set.
- Two independent checks: against published charts, and against known house edge figures.
- We publish our known limits, including where the model is approximate.
- Where a decision is genuinely a coin flip, we say so instead of pretending otherwise.
- When we find an error in our own work, we fix it and write it down. There is a log below.
How the chart is computed
For every combination of your hand and the dealer's upcard, the solver computes the expected value of each available action: stand, hit, double, split, surrender. The highest one wins the cell.
The input is the exact composition of the shoe after removing your cards and the dealer's upcard. The dealer's draws are computed with full depletion, meaning each card drawn is removed from the shoe before the next probability is worked out.
Hands are tracked as a total plus the number of aces still counted as eleven. A single soft-or-hard flag is not enough, because it gives the wrong answer on hands holding more than one ace.
How we know it is right
Two checks, and they catch different things.
Against a published chart. The chart generator refuses to run unless the solver exactly reproduces the reference table for eight decks, S17, DAS, and late surrender.
Against known house edge figures. The overall edge is computed independently and compared with published values. Differences between rule sets matter most here, because they do not depend on any residual bias in the model.
| Rule change | Our calculation | Published |
|---|---|---|
| Dealer hits soft 17 (H17) | +0.214% | +0.22% |
| No double after split | +0.120% | +0.14% |
| Late surrender | −0.082% | −0.08% |
| Dealer does not peek (ENHC) | +0.110% | +0.11% |
| Blackjack pays 6:5 instead of 3:2 | +1.357% | +1.36% (eight decks) |
| Six decks instead of eight | −0.029% | −0.03% |
Where the model stops being exact
Honestly stated, because a number without its error bars is half a number.
No resplitting. The model does not resplit an already split hand. That biases it about 0.05% above published absolute house edge figures. It does not affect which action wins a cell, which is why the table above compares differences rather than absolute values.
Dealer distribution held fixed after the player's second draw. From the second card the player takes, the dealer's outcome distribution stops being re-derived. A double, which draws exactly one card, is therefore computed exactly.
Which numbers we computed ourselves
- Every cell of every strategy chart, across 80 rule combinations. See basic strategy.
- The dealer's full outcome distribution for all ten upcards, conditioned on the peek. See dealer rules.
- What each common mistake costs, from insurance to fear of busting. See which mistakes cost the most.
- Side bet odds for Perfect Pairs and 21+3, counted combinatorially for every deck count and paytable.
- Insurance and even money, including the exact break-even point.
- Baccarat house edge for Banker, Player, tie, and the pair bets.
The one set of figures we cite rather than compute is the betting correlation and playing efficiency of counting systems, on the best counting system. Deriving those requires effect-of-removal data for a full game, and the page says plainly that they come from the literature.
What we build on
The method behind basic strategy comes from the work that established and developed it:
- Edward O. Thorp, Beat the Dealer (1962), the first mathematical proof that blackjack can be beaten.
- Peter Griffin, The Theory of Blackjack, the machinery for computing expected value and the effects of removing cards.
- Don Schlesinger, Blackjack Attack, the source of the Illustrious 18 and Fab 4 indexes.
- Stanford Wong, Professional Blackjack, for comparisons between counting systems.
- Wizard of Odds, whose reference charts and house edge figures we check our own output against.
What we do when we find an error
We fix it and we write it down here. Two so far.
August 2026, hard 12. The strategy tables told you to hit a hard 12 against a dealer 4. The correct play is to stand, in every deck count and under both soft 17 rules, by a margin of 0.004 to 0.015 of a bet. Single-deck tables also had it wrong against a 6.
The interesting part is why the checks missed it. The generator validated the solver against a published chart for eight decks only, so the eight-deck tables were right and 48 of the other 80 were not. A check that covers one configuration proves one configuration. We have since re-derived the full six-deck chart cell by cell against an independent calculation: 236 cells, no remaining differences, and we intend to extend that to every deck count.
Earlier, soft 17 in the chart. While moving to a European chart it turned out three cells carried values for a dealer who hits soft 17, while the page stated the opposite. We corrected the chart and rewrote every text that had been derived from it.
We do not claim anywhere on this site that you can make money counting cards. We say that the edge is thin, that penetration usually decides whether it exists at all, and that against a random number generator online it does not exist in any form.
Keep reading
By Martin Kosek · every number on this site is computed by us, not copied.
← Back to the live counter