A small game. An interesting problem.

This is Tim Cao's independent arithmetic-game experiment, inspired by Prime Climb, created by Daniel Finkel and Katherine Cook of Math for Love. It is not an official digital edition, and is not affiliated with or endorsed by the original creators.

Explore the original board game or return to this table.

This table's rules

Two players each start with two pawns on 0. Both must reach 101 exactly to win.
Each turn has two ten-sided dice, numbered 1 to 10. Each die is used once, on either unfinished pawn.
Add, subtract, multiply or divide the pawn's position by the chosen die. Results must be whole numbers between 0 and 101.
Landing on a rival pawn sends it back to 0, immediately. Start and finish are safe; your own pawns may share a space.
A pawn at 101 stays there. If both arrive, the game ends immediately.

This variant deliberately omits prime cards and the original game's doubles bonus. Prime-number marks are a mathematical reference only. The tile board, pieces and interface are original to this adaptation.

Choose your opponent

Random: chooses a legal turn without a strategy.
Greedy: favors moving its pawns closer to 101.
Positional: considers useful factors, proximity and opportunities to bump.
V-Table: uses a precomputed cooperative value table to estimate the strength of a position.
Aggressive: adds a stronger preference for sending rivals back to start.

V-Table is a heuristic in this two-player game, not a guarantee of optimal play. Every opponent now follows the same sequential moves, immediate bumps and finish locking as a human.

The research behind the table

A single pawn has 102 positions. Two interchangeable pawns have 5,253 unordered positions, small enough for a cooperative value table. A full two-player model has roughly 27.6 million position pairs, so this browser version uses the smaller table as a practical estimate.

The figures below are preserved from the original research snapshot. They are historical illustrations, not fresh benchmarks of the current corrected engine; the old tournament rankings have not been revalidated.

Historical research heatmap of expected turns for one pawn — Single-pawn expected turns, original research.

Historical research heatmap of adversarial win probabilities — Adversarial position estimates, original research.

Local play

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