Original analysis you can inspect.
Original, reproducible casino-math studies with stated assumptions, formulas, limitations and practical interpretations.
Published studies
A natural paying 6:5 instead of 3:2 removes 0.30 units on every player natural—about 1.39 percentage points under a standard frequency model.
StudyWhat UTH Strategy Mistakes CostUltimate Texas Hold’em mistakes are priced by the extra wager and the conditional difference between actions, not by whether the hand eventually wins.
StudyWhich Blackjack Rules Matter Most?A ranked rule guide showing why natural payout, soft-17 treatment, doubling, surrender, deck count and hole-card procedure must be evaluated as a complete package.
StudyVideo Poker Pay Tables ComparedA one-line payout change can alter return and strategy. Compare the full pay table, coin level and strategy—not the game name.
StudyWhy Side Bets Feel Better Than Their MathSide bets combine low hit rates, skewed jackpots and fast repetition. The result can be a memorable win alongside a high long-run cost.
StudyCasino Comps vs Expected LossEstimate the usable value of rewards and compare it with theoretical gambling cost using the same amount of action.
Research, learning and flagship libraries
Research standard
Every study identifies the wager, rules, strategy and denominator. Exact enumeration is preferred where practical; simulations must state trial count and uncertainty. Screening estimates are labeled and never presented as an exact complete-game result.
How to use this library
Use this page to choose the research question you need. Each linked study states its own rules, denominator, assumptions and limitations.
Denominator traps
See why two accurate percentages can still be misleading.
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