Re-folding the submitted stream — root_t = keccak256(root_(t−1), t, …) over each round's (stake, game), each decision's choice, and each reveal — must reproduce the root you signed, pinning the exact sequence to your signature.

t39 · you chose option 1 of 2 · worth 0.46× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t46 · you chose option 1 of 2 · worth 0.88× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t53 · you chose option 2 of 2 · worth 0.69× under optimal play · best free option was 0.71× — no roll here, the choice was yours. Values come from the sealed tree itself.

t55 · you chose option 2 of 2 · worth 0.64× under optimal play · best free option was 0.71× — no roll here, the choice was yours. Values come from the sealed tree itself.

t57 · you chose option 1 of 2 · worth 1.12× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t69 · you chose option 1 of 2 · worth 0.96× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t76 · you chose option 2 of 2 · worth 0.68× under optimal play · best free option was 0.83× — no roll here, the choice was yours. Values come from the sealed tree itself.

t83 · you chose option 1 of 2 · worth 1.67× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t99 · you chose option 1 of 2 · worth 1.66× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t10 · you chose option 2 of 2 · worth 1.47× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t12 · you chose option 2 of 2 · worth 1.70× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t14 · you chose option 2 of 2 · worth 1.99× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t16 · you chose option 2 of 2 · worth 2.34× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t18 · you chose option 2 of 2 · worth 2.78× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t20 · you chose option 2 of 2 · worth 3.33× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t22 · you chose option 1 of 2 · worth 4.05× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t93 · you chose option 2 of 2 · worth 1.47× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t95 · you chose option 2 of 2 · worth 1.70× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t111 · you chose option 2 of 2 · worth 1.47× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t113 · you chose option 2 of 2 · worth 1.70× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t115 · you chose option 2 of 2 · worth 1.99× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t117 · you chose option 2 of 2 · worth 2.34× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t119 · you chose option 2 of 2 · worth 2.78× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t121 · you chose option 1 of 2 · worth 3.33× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t130 · you chose option 2 of 2 · worth 1.47× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t132 · you chose option 2 of 2 · worth 1.70× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t134 · you chose option 2 of 2 · worth 1.99× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t136 · you chose option 2 of 2 · worth 2.34× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t138 · you chose option 2 of 2 · worth 2.78× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t140 · you chose option 2 of 2 · worth 3.33× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t142 · you chose option 2 of 2 · worth 4.05× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t144 · you chose option 2 of 2 · worth 4.98× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t146 · you chose option 2 of 2 · worth 6.22× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.