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the budget solve ·
bb_core.js
Watch a race
Sampled paths under the solved wavefront policy, against the value the solver promised.
The solver prices path-time for your budget and returns a wavefront
policy: one kill-below cutoff per time step. Here that policy is applied
to actual sampled paths — a Poisson number of them, stepping
through the same Markov chain the solver planned over. Paths dropping
below the cutoff die (gray); survivors (blue) run to maturity, where the
best of them, or the fallback at zero, is the payoff. Races replay
continuously and the running mean accumulates.
What to look for: the running mean of realized maxima
must converge to the solver's expected maximum, and the running mean of
spent path-time to the solver's expected path-time. Verdicts are issued
only at doubling checkpoints (32, 64, 128, … races), each an
empirical-Bernstein bound for payoffs bounded by the grid edge, with
levels summing to 1%: a correct simulator shows FAILED with probability
at most 1% over the whole session, however long you watch. The z-score is
informational only; it wanders past 2 routinely under continuous
monitoring, and that proves nothing. The policy is generally a mixture of
a few wavefront atoms (the dashed cutoffs, opacity by weight), and each
path independently follows one of them; by Poisson thinning the sampled
cloud then has exactly the mixture's intensity, so the targets are exact,
not approximate.
Paths are sampled from the identical discrete transition kernel the
solver plans over, so the comparison is exact in distribution: any
persistent gap is a bug, not discretization. 50 time steps, 301 state
points.