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Fix calculation for number of positions in the game (#109)
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zhiqiangxu authored Apr 16, 2024
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Expand Up @@ -133,7 +133,7 @@ The Game Tree is a binary tree of positions. Every claim in the DAG references a
The Game Tree has a split depth and maximum depth, `SPLIT_DEPTH` and `MAX_GAME_DEPTH` respectively, that are both
preset to an FDG implementation. The split depth defines the maximum depth at which claims about
[output roots][g-output-root] can occur, and below it, execution trace bisection occurs. Thus, the Game Tree contains
$2^{d-1}$ positions, where $d$ is the `MAX_GAME_DEPTH` (unless $d=0$, in which case there's only 1 position).
$2^{d+1}-1$ positions, where $d$ is the `MAX_GAME_DEPTH` (unless $d=0$, in which case there's only 1 position).

The full game tree, with a layer of the tree allocated to output bisection, and sub-trees after an arbitrary split
depth, looks like:
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