♠ Single Dummy Bridge Solver ♥ ?

♠ Single Dummy Bridge Solver

A Monte Carlo simulation engine that evaluates bridge positions from a single-dummy perspective — you see your hand and dummy, but not the opponents' cards.

v1.0 · 18 Feb 2026 · Author: Gideon Tan and AI

What can I use this for?

• Batch session review — Log into BBO and fetch all your hands from a session by date. Every hand where you were declarer or defender is evaluated trick-by-trick with full two-phase belief analysis, producing per-hand scores (0–100) with grade breakdowns. Results stream in as each hand completes, with elapsed time and ETA. You can look up any player's hands (not just your own) and stop the batch at any time. Click "Load" on any hand to open it in the full solver with bidding constraints pre-applied. The session summary shows your average score, grade distribution, and worst hands for targeted improvement.
• Full hand evaluation — Import a .lin file from BBO and get a trick-by-trick score (0–100) of your card play. Each non-forced decision is graded from Optimal to Blunder, with the cost quantified as lost make probability. Two-phase belief weighting accounts for what a thoughtful player would know from the play so far, showing both weighted and unweighted results so you can see how much information the play revealed. Posterior deltas show exactly how each decision point shifted card placement probabilities from the prior.
• Best play at a decision point — Play through to any position, then run the solver to see which card maximises your expected tricks.
• Opening lead analysis — Set up your hand and the contract, skip the play-through, and solve from trick 1 to evaluate each lead.
• Defensive decisions — Sit as a defender, enter dummy's cards once revealed, and find the optimal defence at any point.
• Infer from the play — Run Belief Analysis to see what the play so far reveals about unseen hands: likely HCP ranges, suit lengths, and specific card placements.
• Compare two cards — Click any two cards in the solver results to see a side-by-side comparison with sample deals showing when each card wins or loses tricks.
• BBO post-mortem — Import a .lin file from BBO, replay trick by trick, and check whether your play (or the opponents') was optimal at each decision. Use "Play to my turn" for fast navigation.
• Bidding-informed play — Encode what the auction reveals via constraints (e.g. East opened 1NT → HCP 15–17, balanced) and see how that changes the optimal line.
• Safety play vs. max tricks — The solver shows the full trick distribution for each card, not just the average. Spot when one line averages higher but risks going down, while another guarantees the contract.
• Restricted choice / card reading — After an honor drops, run Belief Analysis to quantify the posterior. Was ♠Q from QJ doubleton or a singleton? The marginals answer directly.
• Partnership defence discussion — Both defenders can review a hand: "should we have switched to hearts at trick 3?" Play through the alternative, compare solver output, and export to PDF to share with your partner.
• Suit combination analysis — Set up just the relevant suit across your hand and dummy, leave the rest unconstrained, and find the optimal way to play a specific holding. E.g. AJ943 opposite K72 — finesse or play for the drop?

Core functionality

• Monte Carlo deal generation — Randomly distributes unseen cards across opponents, respecting constraints (bidding, showouts, user-specified HCP/shape).
• Double-dummy solver — Each generated deal is solved to optimal play using DDS (Bo Haglund's engine), giving the trick count for every possible card.
• Two-phase belief architecture — Phase 1 generates belief deals scored for consistency with observed play, producing posterior marginals (card probabilities, HCP distributions, suit lengths). Phase 2 generates independent solver deals weighted by the posterior via importance sampling. This cleanly separates "what do we know?" from "what should we play?"
• Hand evaluation engine — Walks every non-forced decision in a completed hand, running full two-phase belief + solver analysis at each point. Grades each decision (optimal/good/inaccuracy/mistake/blunder) based on the gap between the played card and the best available. Produces an overall 0–100 score with configurable parameters: belief deals, sub-deals, solver deals, trick range, and skill level.
• Batch session engine — Fetches hand records from BBO via authenticated login, parses LIN data for all hands, infers bidding constraints automatically, and evaluates each hand with the full two-phase engine. Runs in a background thread with incremental result streaming — each completed hand is immediately available in the UI while subsequent hands continue processing. Supports cancellation, elapsed/remaining time estimation, and loading any result into the full solver for deeper analysis.
• Posterior marginals with deltas — Belief-weighted deals produce probabilistic estimates: P(East has ♠A) = 82%, HCP 10–14, etc. In hand evaluation, deltas from the unweighted prior show exactly how the play shifted beliefs (e.g. ♦K 50% → 65% (+15%)). These soft-weight the solver rather than excluding deals outright.
• Card comparison & play-through — Click any two cards in the results to see a side-by-side comparison across the deal set. Then open the play-through modal to step through sample deals card by card, seeing exactly why one play outperforms another in specific layouts.
• Auction inference — Automatically infers constraints from the bidding sequence (opening bids, responses, overcalls) and applies them as prior constraints for deal generation. In batch mode, these are applied per-hand automatically.
• Constraint system — Visual builder for HCP, suit lengths, specific cards, and shape patterns. Supports all four hands.
• BBO .lin import — Import hand records from BBO with full auction display, player names, and automated play-through. Constraints can be added via the visual builder to encode bidding information.
• Share hand — Copy a link that restores the full board state — hands, played cards, constraints, trick count, and LIN import data — so others can pick up exactly where you left off, including running hand evaluation.
• PDF export — Print the full analysis to a shareable PDF including the board layout, solver results, card comparisons, sample deals, and hand evaluation results with posterior beliefs per decision.

How it works

The solver generates a large number of random deals consistent with what you know (your hand, dummy, played cards, constraints). Each deal is solved double-dummy to find the optimal trick count for every legal card. Results are aggregated across all deals — the recommended play is the one that maximises expected tricks across the distribution of possible opponent holdings.

When Belief Analysis is enabled, the engine uses a two-phase architecture. Phase 1 generates belief deals and scores each for consistency with the observed play — a deal where the opponents' actions match what actually happened gets a higher weight. These weights produce posterior marginals: probability distributions over card placements, HCP, and suit lengths for each unseen hand. Phase 2 generates a fresh, independent set of solver deals and weights them against the posterior via importance sampling. This separation avoids overfitting while allowing the play history to inform the analysis.

Hand Evaluation applies this two-phase process at every non-forced decision point in a completed hand. At each point, Phase 1 runs with the play history up to that moment, so beliefs evolve as more information becomes available — early decisions have weak beliefs (little history), while later decisions have strong beliefs (rich history). The delta display shows exactly how much the play shifted each probability from the prior.

The skill parameter (0–100%) controls how optimal you assume the other players are. At 100%, any suboptimal play is treated as very unlikely. At lower values, the engine is more forgiving of imperfect play.