Carry the Two Mathematics & Gambling Episode 3: Even More Casino Games
Mar 26, 2026
David Taylor, mathematician and author who studies the probability of gambling. He breaks down craps rules and point-phase odds. He compares pass and don't-pass bets and explains free odds and house edge. He covers blackjack strategy and card counting limits. He contrasts poker’s skill dynamics, starting hands, bluffing frequency, and how rake changes incentives.
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Craps Has Two Distinct Probability Phases
- Craps mixes a simple initial win/lose roll with a conditional point phase that changes the probabilities mid-game.
- First roll wins on 7 or 11 (~22%), loses on 2,3,12 (~11%), then point rolls shift win chances (overall pass win ≈49.3%).
Use Pass Bets Plus Maximum Free Odds
- To minimize house edge in craps, bet pass or don't pass and take the maximum free odds allowed.
- Casinos require an initial pass bet to place free-odds and cap odds to a multiple (2x,5x,10x, or more).
Free Odds Remove House Edge But Are Restricted
- Free odds bets in craps carry no house edge but are only available after the point is established.
- Casinos limit these bets to protect expected value, creating a strategic layer tied to betting culture and table psychology.
