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.

t31 · you chose option 2 of 2 · worth 1.17× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t33 · you chose option 2 of 2 · worth 1.23× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t35 · you chose option 2 of 2 · worth 1.30× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t49 · you chose option 2 of 2 · worth 1.17× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t51 · you chose option 2 of 2 · worth 1.23× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t61 · you chose option 2 of 2 · worth 1.17× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t63 · you chose option 2 of 2 · worth 1.23× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t65 · you chose option 2 of 2 · worth 1.30× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t75 · you chose option 2 of 2 · worth 1.17× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t77 · you chose option 2 of 2 · worth 1.23× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t79 · you chose option 2 of 2 · worth 1.30× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t81 · you chose option 2 of 2 · worth 1.37× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t83 · you chose option 2 of 2 · worth 1.45× 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 1.17× 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 1.23× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t97 · you chose option 2 of 2 · worth 1.30× 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 2 of 2 · worth 1.37× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t101 · you chose option 2 of 2 · worth 1.45× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t103 · you chose option 2 of 2 · worth 1.54× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t105 · you chose option 2 of 2 · worth 1.64× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t107 · you chose option 2 of 2 · worth 1.76× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t109 · you chose option 2 of 2 · worth 1.89× 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 2.05× 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 2.24× 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 2.46× 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 2.74× 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 3.08× 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 2 of 2 · worth 3.52× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t123 · you chose option 2 of 2 · worth 4.10× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t125 · you chose option 2 of 2 · worth 4.93× 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 1.26× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t32 · you chose option 2 of 2 · worth 1.26× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t34 · you chose option 2 of 2 · worth 1.34× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t36 · you chose option 2 of 2 · worth 1.43× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t48 · you chose option 2 of 3 · worth 1.03× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t50 · you chose option 1 of 2 · worth 1.55× 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 1 of 3 · worth 0.82× 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 3 · worth 0.62× 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 1 of 2 · worth 0.82× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t23 · you chose option 1 of 3 · worth 0.88× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.

t28 · you chose option 2 of 3 · worth 0.66× under optimal play · best free option was 0.79× — no roll here, the choice was yours. Values come from the sealed tree itself.

t33 · you chose option 1 of 3 · worth 1.12× under optimal play · the best option available — no roll here, the choice was yours. Values come from the sealed tree itself.