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Exact casino math

Blackjack

A rule-parameterized EV engine with recursive action search, cached dealer probabilities, and split-aware memoization.

Precompute common rule tables offline and keep a slower exact composition-dependent mode for advanced users.

Rules focusThe rule assumptions and model boundary this page uses for its calculations.
Deck count, soft 17, DAS, RSA, surrender, penetration, and split caps need to be explicit inputs.
OutputsThe main numbers or result groups this page will produce after you run the analysis.
Best actionEV by actionDealer distributionRule sensitivity
Positive Hi-Lo counts assume more low cards are already gone. Negative counts assume more tens and aces were removed.

Rules

Count-aware blackjack

This page now favors fast hand entry and a practical Hi-Lo estimate over manually listing exposed cards.

  • Player and dealer card entry is value-based, so suits are abstracted away for blackjack decisions.
  • Finite shoes can be approximated from a Hi-Lo running count instead of enumerating exposed cards.
  • A shoe value of 0 switches to an infinite or unknown composition model.

Analyzer

Solve a blackjack hand

Pick the hand values, set the shoe estimate, and compare the EV of every legal action.

Player cardsChoose the two blackjack values in your hand. Face cards are collapsed into 10 and suits are ignored.
2 selected, up to 2
Dealer upcardPick the dealer's visible blackjack value.
1 selected

The running count is converted into an approximate set of removed low or high cards for a faster composition estimate.

Enter two player values, a dealer upcard value, and an optional shoe estimate to solve the hand.