Robust Kelly with Bayesian credible-bound shrinkage, walk-the-book pricing, and Monte Carlo bankroll simulation. The cascade below shows you exactly why the recommended size isn't bigger.
Naive Kelly: f = (p_win − m) / (1 − m) where m is the displayed price and p_win your point estimate.
Robust shrink: we don't trust your point estimate. We treat your belief as Beta(p̂·n + 1, (1−p̂)·n + 1) with n from the confidence radio, then take the (1−CL)/2 tail as p_conservative. Kelly is recomputed at this lower bound. Robust-optimization choice over the credible set, not posterior-mean shrinkage (Bayesian Kelly with log utility doesn't shrink).
Walk the book: your stake doesn't fill at top of book. We solve for the fixed point S* = bankroll · (p_cons − m_eff(S*)) / (1 − m_eff(S*)) with a damped iteration. m_eff is the volume-weighted fill price walking through the input depth.
Fractional Kelly: finally multiplied by your chosen fraction (¼ Kelly common — halves variance, only modestly reduces growth).
KL divergence: p·log₂(p/m) + (1−p)·log₂((1−p)/(1−m)). The asymptotic Kelly growth rate of full-Kelly betting at fair odds. "Bits of disagreement with the market."