Craps table

I chose a legal action for this decision.

Every available bet has negative expected value, so abstaining maximizes expected chips. The shooter's previous wins do not change the probabilities of independent dice rolls.

I chose a legal action for this decision.

Every available wager has negative expected value, so placing no bets maximizes expected chips retained. Prior rolls and the shooter's streak do not change the probabilities of independent dice rolls.

I chose a legal action for this decision.

Every available bet has negative expected value, so abstaining maximizes expected chips. The shooter's winning streak does not change the probabilities of independent dice rolls.

I chose a legal action for this decision.

Every available bet has negative expected value, so abstaining maximizes expected chips. Previous rolls and the shooter's streak do not change the probabilities of independent dice rolls.

I chose a legal action for this decision.

All available bets have negative expected value, so making no new bets maximizes expected chips retained. Previous rolls do not change the odds of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so making no new bets maximizes expected chips. Previous rolls and the shooter's streak do not change the probabilities of the next roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so placing no bets maximizes expected chips retained. Past rolls and the shooter's winning streak do not change the next roll's probabilities.

I chose a legal action for this decision.

All available bets have negative expected value, so making no bets maximizes expected chips retained. The shooter's streak does not change the probabilities of independent dice rolls.

I chose a legal action for this decision.

Every available bet has negative expected value, so declining to wager maximizes expected chips retained. Previous rolls do not change the probabilities of future independent rolls.

I chose a legal action for this decision.

Every available bet has negative expected value, so placing no bets maximizes expected chips retained. Past rolls and the shooter's streak do not change the probabilities of the next roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so declining to bet maximizes expected chips. Previous rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so abstaining maximizes expected chips. Previous rolls do not affect the probabilities of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, and no bet is required. Sitting out preserves my chips; previous rolls do not change the probabilities of the next roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so making no bets maximizes expected final chips. Previous rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so making no new bets maximizes expected chips retained. Previous rolls do not change the probabilities of the next roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so placing no bets preserves chips and maximizes expected session wealth. Previous rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so making no new bets maximizes expected final chips. Past rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so placing no bets best preserves my chips and maximizes expected ending bankroll. Past rolls do not change the probabilities of the next roll.

I chose a legal action for this decision.

All available bets have negative expected value, so making no new bets maximizes expected final chips. Previous rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so sitting out maximizes expected chips. Previous rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

All available bets have negative expected value, so declining to wager maximizes expected chips. Prior rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so making no new bets maximizes expected chips retained. Previous rolls do not change the probabilities of this independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so making no new bets maximizes expected chips. Previous rolls do not change the probabilities of this independent roll.

I chose a legal action for this decision.

All available bets have negative expected value, so making no new bets maximizes expected chips. Past rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

All available bets have negative expected value, so making no bets maximizes expected chips retained. Previous rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so placing no bets best preserves my chips. Previous rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

All available bets have negative expected value, so leaving my chips unbet maximizes expected session wealth. Previous rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so placing no bets maximizes expected final chips. Prior rolls and the shooter’s streak do not change the independent dice probabilities.

I chose a legal action for this decision.

Every available bet has negative expected value, so making no bets maximizes expected final chips. Previous rolls and shooter streaks do not change the probabilities of independent dice rolls.

I chose a legal action for this decision.

Every available bet has negative expected value, so placing no bets maximizes expected chips retained. Recent wins do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

All available bets have negative expected value, so making no new bets maximizes expected chips retained. Previous rolls and the shooter's streak do not change the odds.

I chose a legal action for this decision.

Every available bet has negative expected value, so making no new bets maximizes expected chips retained. Previous rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so declining to bet maximizes expected chips. Previous rolls do not change the odds of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so making no new bets maximizes expected chips. Prior rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so placing no bets maximizes expected final chips. Previous rolls and the shooter's streak do not change the probabilities.

I chose a legal action for this decision.

Every available bet has negative expected value, so placing no bets maximizes expected chips retained. Past rolls and shooter streaks do not change the odds of independent dice rolls.

I chose a legal action for this decision.

All available wagers have negative expected value, so placing no bets maximizes expected chips. Previous rolls and the current shooter's streak do not change the probabilities.

I chose a legal action for this decision.

All available bets have negative expected value, so making no new bets maximizes expected final chips. Previous rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

All available bets have negative expected value, so placing no bets maximizes expected final chips. Recent rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so making no bet maximizes expected final chips. The final-roll timing and previous results do not change the odds.