Craps table

I chose a legal action for this decision.

Every available bet has negative expected value, so making no bets maximizes expected session chips. The shooter's prior wins do not change the probabilities of independent rolls.

I chose a legal action for this decision.

Every available bet has negative expected value, so sitting out maximizes expected chips. Previous wins do not affect the probabilities of this independent roll.

I chose a legal action for this decision.

Every available bet has negative expected value, so sitting out 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 declining to wager maximizes expected remaining chips. Past rolls and the shooter's streak 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. The shooter's streak does not change the probabilities of 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. Previous rolls and the shooter's streak do not change the next roll's 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 the shooter's streak do not change the odds of independent dice rolls.

I chose a legal action for this decision.

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

I chose a legal action for this decision.

Every available bet has negative expected value, so placing no bets maximizes expected final chips. Being the shooter and recent roll outcomes do not change 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 and the shooter’s identity do not change the odds.

I chose a legal action for this decision.

Every available bet has negative expected value, so placing no bets maximizes expected chips. Previous rolls and the current shooter do not change 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 remaining chips. Previous rolls do not change the odds of independent fair dice.

I chose a legal action for this decision.

All available bets have negative expected value, and betting is optional. Keeping my chips off the table maximizes expected final bankroll.

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 the next independent roll.

I chose a legal action for this decision.

All available bets have negative expected value, so abstaining 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, and betting is optional. Sitting out preserves my chips and maximizes expected final bankroll.

I chose a legal action for this decision.

Every available wager has negative expected value, so making no bets maximizes expected final chips. Past rolls and shooter changes do not alter 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 the next independent roll.

I chose a legal action for this decision.

All available bets have negative expected value, and betting is optional. Keeping my chips uncommitted maximizes expected final bankroll; past rolls do not change the odds.

I chose a legal action for this decision.

Every available bet has negative expected value, so making 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 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 bets 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 the next independent roll.

I chose a legal action for this decision.

All available bets have negative expected value, so declining to bet preserves the highest expected chip total. 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. Previous rolls do not change the probabilities of the next independent roll.

I chose a legal action for this decision.

Every available wager has negative expected value, so placing no bets maximizes expected final chips. Past 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 final chips. Recent 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 final chips. Recent wins do not change the probabilities of independent 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 current 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 none 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 and the current shooter's streak do not change the independent dice probabilities.

I chose a legal action for this decision.

All available bets have negative expected value, so placing none maximizes expected final chips. Recent rolls and the shooter’s streak do not change the odds of independent fair dice.

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.

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

I chose a legal action for this decision.

Every available wager has negative expected value, so placing no bets maximizes expected final 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 abstaining maximizes expected final chips and preserves the 1,000-chip bankroll. The final-roll timing and previous results do not create an advantage.