Toads and Frogs how hot is this position?
Toads (Left) move one square to the right, or jump a single frog into the empty square beyond it. Frogs (Right) do the same to the left. Nobody is captured; whoever cannot move loses. The side panel shows the exact game value of the position in Conway's sense, and its thermograph: the mean is who is ahead and by how much, the temperature is what it is worth to move first. With hints on, every move you may make is marked ✓ (keeps the win) or ✗ (hands it over).
value of the position
thermograph
Tax every move by t. The left wall is what the Toads get by moving first, the right wall what the Frogs get; they meet at the temperature, and the mast above them is the mean.
How the values are computed
A position is a game {Toads' options | Frogs' options}. Before valuing it, the engine applies Erickson's rules: a run of pieces from a TT to an FF can never move and splits the strip in two; a toad with no frog ahead of it is worth exactly the empty squares in front of it, and so is a finished frog; and a position whose only moves are jumps into single gaps is 0. What is left is valued from its options and reduced to canonical form (dominated options deleted, reversible ones bypassed), so equal games get the same id. The thermograph is built from the options' walls, and its mean adds up over sums.
Checked against the literature
The repository recomputes the published tables of Erickson (New Toads and Frogs Results, 1996) and Thanatipanonda (Further Hopping with Toads and Frogs, 2008), their closed forms and conjectures, and checks every value on every strip up to 12 squares against a plain win/lose search and against the same game valued without any simplification rule.