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Blackjack Solver

Exact blackjack solver using backward induction. Computes mathematically optimal play by solving the full decision tree via dynamic programming — no heuristics, no approximations beyond two standard, documented ones.

Features

  • Exact backward induction — every possible future card sequence and its optimal continuation is evaluated
  • Per-hand solver — optimal action + EV for any hand vs any dealer upcard
  • Overall house edge — probability-weighted enumeration of all possible initial deals
  • Strategy chart generator — color-coded basic strategy with diff highlighting when cards are removed
  • Web dashboard — interactive UI with hand analysis, dealer outcomes, shoe composition, and strategy charts
  • Web Worker — all computation runs in a background thread, UI stays responsive

Supported Rules

Rule Options
Deck count 1–8
Dealer soft 17 Hit (H17) or Stand (S17)
Dealer peek On (American) or Off (European/ENHC)
Double after split Yes / No
BJ payout 3:2 (default), 6:5, or custom
Dead cards Arbitrary card removal from shoe

Accuracy

Verified against the Wizard of Odds house edge calculator (no resplit baseline):

Configuration Published Solver Difference
8-deck H17 peek DAS -0.6993% -0.7018% 0.0025%
6-deck H17 peek DAS -0.6690% -0.6723% 0.0033%
2-deck H17 peek DAS -0.4244% -0.4343% 0.0099%
1-deck S17 peek DAS +0.1531% +0.1362% 0.0169%

All basic strategy decisions match published tables — every hard total, soft total, pair, and boundary case verified.

Known Approximations

Two standard approximations are used, consistent with professional-grade solvers:

  1. Precomputed dealer outcomes — Dealer outcome probabilities are computed once from the initial shoe (after removing visible cards), not recomputed as the player draws. Error: ~0.003% for 8 decks, ~0.017% for 1 deck.

  2. Split hand independence — Both split hands are solved against the same shoe. Cards drawn to one hand don't affect the other hand's shoe composition. Negligible error for 6+ decks.

Not Yet Implemented

Feature House Edge Impact Notes
Late surrender ~0.08% Changes optimal play for 15 vs 10, 16 vs 9/10/A
Resplit (up to 4 hands) ~0.05% Would require recursive split solver
Double restrictions (9-11, 10-11) ~0.09–0.18% Some casinos restrict which totals can double
OBO for no-peek ~0.11% "Original Bet Only" variant where only base bet is lost to dealer BJ

Architecture

blackjack-solver.js        Core solver (backward induction)
solver-worker.js           Web Worker wrapper (routes EV + chart requests)
blackjack-calculator.html  Dashboard UI (hand input, results, strategy chart)
strategy-chart.html        Strategy chart renderer (loaded in iframe)
server.js                  Dev server (port 8000)

Data Flow

Dashboard → postMessage → iframe (strategy-chart.html)
  → Web Worker (solver-worker.js)
    → generateStrategyChart() / solveOverallEV()
      → solve() × N hands (backward induction per hand)
    → returns results
  → iframe renders tables → notifies parent

Usage

node server.js
# Open http://localhost:8000/blackjack-calculator.html

Or run the solver directly:

node blackjack-solver.js

Legacy Files

  • blackjack-odds.js — Original heuristic-based odds calculator (superseded by blackjack-solver.js)
  • blackjack-simulator.js — Monte Carlo simulation engine using the old odds module