Craps table

I chose a legal action for this decision.

Every available bet has negative expected value, so making no bets maximizes expected chips retained. The shooter's past wins 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 making no bets maximizes expected final 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.

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

I chose a legal action for this decision.

Every available wager has negative expected value, so placing no bets maximizes expected 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, and betting is optional. Keeping all 1,000 chips un wagered maximizes expected final chips; past rolls do not change the odds.

I chose a legal action for this decision.

All available bets have negative expected value, so placing none maximizes expected final chips. 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 bet maximizes expected remaining chips. Prior rolls and the shooter’s results do not change the probabilities of independent dice rolls.

I chose a legal action for this decision.

Every available bet has negative expected value, and betting is optional. Sitting out preserves my chips and maximizes expected final bankroll; previous rolls do not change the odds.

I chose a legal action for this decision.

All available bets have negative expected value, so placing none maximizes expected final chips. Previous rolls do not change the probabilities of independent fair dice.

I chose a legal action for this decision.

All available bets have negative expected value, so placing no bets maximizes expected final 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 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 placing no 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 maximizes expected final 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. Past rolls and the shooter change do not affect the independent dice probabilities.

I chose a legal action for this decision.

All available bets have negative expected value, so placing 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 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.

All available bets have negative expected value, so declining to wager maximizes expected final chips. Recent sevens 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 abstaining maximizes expected chips. The four consecutive naturals 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 placing none maximizes expected remaining 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 placing no bets maximizes expected final chips. Previous rolls and the current shooter's streak do not affect the independent dice probabilities.

I chose a legal action for this decision.

Every available bet has negative expected value, so placing no 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 placing 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 placing no bets maximizes expected final chips. Prior 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 remaining 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 placing no bets maximizes expected remaining 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 placing no bets maximizes expected final chips. The shooter's winning streak does not affect the independent dice probabilities.

I chose a legal action for this decision.

Every available bet has negative expected value, so placing none maximizes expected remaining 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 wager has negative expected value, so placing no bets maximizes expected final chips. The six consecutive pass wins do not change the probabilities of independent future rolls.

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 independent dice probabilities.

I chose a legal action for this decision.

Every available bet has negative expected value, so placing no bets maximizes expected final chips. The shooter's streak does not change the probabilities of independent rolls.

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 and the shooter change do not affect the independent dice probabilities.

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 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, so placing none maximizes expected final 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 chips retained. Prior 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. 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 placing none maximizes expected final chips. 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 placing 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 placing no bets maximizes expected final chips. Previous rolls do not change the probabilities of the remaining independent rolls.

I chose a legal action for this decision.

Every available bet has negative expected value, so declining to bet maximizes expected final chips and preserves the 1,000-chip bankroll. The final-roll timing and prior results do not change the odds.