← SXTHow it works

The mathematics behind every decision.

Sextillion computes only from public information. The dealer's hidden card is never inspected by the live engine.

Hidden vs. public information

The dealer's hole card is dealt face down. The engine treats it as unknown and averages over every card it could plausibly be, in proportion to the shoe. If the dealer shows an Ace or a Ten, they peek. If they do not have blackjack, that non-reveal is itself information: some possibilities have been ruled out. "Nothing was revealed, but something was learned."

Sampling without replacement

Blackjack is not roulette. Every card that appears is one less card that can appear again. When a ten shows up, tens become less likely for the rest of the shoe. All probabilities update accordingly.

Conditional probability

Every number the Lens displays is conditioned on the visible cards, the dealer's upcard, and the remaining shoe. Change any one of those and the numbers change with them.

Dealer outcome branches

The dealer's hand is a small tree of possible draws. The Lens compresses that tree into a distribution over final totals: bust, 17, 18, 19, 20, 21. Each branch is weighted by the probability of that card sequence.

Expected value

For each action, the engine computes the average outcome across all possible futures. The action with the highest expected value is the strongest long-term choice. It is not a promise about any single hand.

Variance

A 20% event still happens one time in five. An 80% event still fails one time in five. Sextillion shows the mathematics; the cards decide the rest.

Decision quality vs. outcome

A strong decision can lose. A weak decision can win. Sextillion measures decisions against the model, and outcomes as their own record. They are never combined.

Estimation vs. calibration

Estimation accuracy compares one guess to the engine's calculated model right now. Empirical calibration compares many guesses to what subsequently occurred. Both are useful. They are not the same.

Expected points (educational)

  • Normal win: +1
  • Normal loss: -1
  • Push: 0
  • Blackjack: +1.5
  • Doubled win: +2
  • Doubled loss: -2

Educational units, not money.

Counterfactual reasoning

A counterfactual compares alternatives from the same information state. The alternative is a distribution, not a guaranteed path. Actual future cards must not be used to judge an earlier decision.

Expected value compares long-term point outcomes. Higher win probability and higher expected value are not always the same. Volatility describes the spread of possible outcomes; it is not a synonym for disadvantage.

Action A

+0.20

Win 55% · Push 5% · Loss 40% · σ ≈ 0.97

Action B

+0.10

Win 60% · Push 0% · Loss 40% · σ ≈ 0.98

A has the higher expected value, but B has the higher win probability. Suppose the realised outcome was a loss. Did the result change which decision was mathematically stronger? No. The realised result was one branch from the earlier distribution.

Compare distributions, not destinies