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Exact casino math

Baccarat

Exact third-card logic with standard Player, Banker, and Tie payout references.

Expose the deterministic draw tree and make the commission-adjusted Banker edge easy to inspect.

Rules focusThe rule assumptions and model boundary this page uses for its calculations.
Player and Banker actions are entirely rule-driven once the two-card totals and Player third card are known.
OutputsThe main numbers or result groups this page will produce after you run the analysis.
Wager payout tableHouse edge referencePlayer draw ruleBanker draw rule

Rules

Third-card rules

Baccarat stays deterministic once the two-card totals and the Player third card are known.

Player and Banker actions are entirely rule-driven once the two-card totals and Player third card are known.

  • Naturals on 8 or 9 end the round immediately.
  • Player draws on totals 0 through 5 and stands on 6 or 7.
  • If Player stands, Banker draws on 0 through 5 and stands on 6 or 7.
  • If Player draws, Banker follows the standard third-card table based on Bank total and Player third card.
  • The standard wager probabilities below assume the common commission game and published eight-deck outcome frequencies.

Analyzer

Explain the next baccarat draw decision

The controls and wager reference are compressed so the draw matrix stays in view.

Current branchPlayer drawsPlayer draws on 4.Banker draws against Player third card 6.
Player1:144.62% win / 9.52% pushEV -0.012u | Edge 1.23%
Banker19:2045.86% win / 9.52% pushEV -0.011u | Edge 1.06%
Tie8:19.52% win / 0.00% pushEV -0.144u | Edge 14.36%
Natural stopNoAny two-card 8 or 9 ends the round immediately.
Player ruleDrawPlayer draws on 4.
Banker ruleDrawBanker draws against Player third card 6.
Bank totalPlayer standsP3 0P3 1P3 2P3 3P3 4P3 5P3 6P3 7P3 8P3 9
0DrawDDDDDDDDDD
1DrawDDDDDDDDDD
2DrawDDDDDDDDDD
3DrawDDDDDDDDSD
4DrawSSDDDDDDSS
5DrawSSSSDDDDSS
6StandSSSSSSDDSS
7StandSSSSSSSSSS