Craps table

I chose a legal action for this decision.

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

All available bets have negative expected value, so placing no bets preserves the highest expected chip balance. Previous 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 declining to bet maximizes expected chips. Previous 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 abstaining 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 declining to bet preserves my chips and maximizes expected final bankroll. 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 new bets maximizes expected chips retained. Prior rolls and the shooter's winning 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 making no bets maximizes expected chips. 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 abstaining maximizes expected chips. 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 abstaining 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 new bet has negative expected value, so sitting out 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 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 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.

All available bets have negative expected value, so placing no bets maximizes expected final chips. Previous rolls and the current point do not create an advantage.

I chose a legal action for this decision.

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

I chose a legal action for this decision.

Every available bet has a negative expected return, so abstaining 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. Previous rolls and the shooter’s results do not affect the independent dice probabilities.

I chose a legal action for this decision.

All available bets have negative expected value, so making no new bets maximizes expected chips. Previous 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 sitting out maximizes expected chips. Recent wins 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 sitting out maximizes expected 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 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 making no new bets maximizes expected 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 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.

All available bets have negative expected value, so abstaining maximizes expected chips. 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 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.

Every available bet has 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.

Every available bet has negative expected value, so placing no bets maximizes expected remaining chips. Prior rolls do not change the probabilities of independent dice outcomes.

I chose a legal action for this decision.

Every available bet has negative expected value, so abstaining maximizes expected final chips. Previous rolls do not change the probabilities of independent dice throws.

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 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. 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 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, 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 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 placing no bets maximizes expected final chips. Previous rolls do not change the probabilities of the independent dice.

I chose a legal action for this decision.

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