Pig Dice Game: When to Hold and When to Roll
You roll a 6. Then a 4. Then a 5. Your turn total climbs to 15. Do you roll again, or do you hold and bank those points? One wrong roll wipes everything. Pig looks simple on the surface. Underneath, it hides a deep mathematical puzzle that researchers have studied for decades. This guide explains the rules, the optimal strategy, and the exact thresholds for when to hold and when to roll.
How to Play Pig Dice
John Scarne invented Pig around 1945 and described it in his book "Scarne on Dice." The rules are among the simplest in all of dice gaming.
You need one die and two players (or more). Players take turns rolling. Each roll adds the face value to your turn total. You can keep rolling as long as you want, accumulating points.
There is one catch. If you roll a 1, you lose all points accumulated during your turn. Your turn total drops to zero. Your turn ends immediately.
At any point before rolling, you can choose to hold. When you hold, you bank your turn total into your permanent score. Your turn ends and the next player rolls.
The first player to reach 100 total points wins the game.
That is the entire rule set. The simplicity is what makes Pig so compelling. Every roll carries a real decision with real consequences.
Pig Dice Game Strategy Tips
Researchers solved Pig using reinforcement learning and value iteration. Todd W. Neller at Gettysburg College published an analysis in 2004 that computed the optimal policy for every game state. The strategy depends on your score, your opponent's score, and your current turn total.
Here are five strategy tips based on the math:
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Hold at 21 or more in the early game. When both players have low scores (below roughly 70), the optimal hold threshold is 21. If your turn total reaches 21 or higher, hold and bank those points. Rolling further increases your risk of hitting a 1 without enough reward to justify it.
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Increase your hold threshold when you are far behind. If your opponent sits at 85 and you are at 40, you cannot afford to play safe. The optimal threshold rises. You need bigger turns to close the gap. Hold at 25 or even 30 in these situations. The math favors aggression when you trail significantly.
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Decrease your hold threshold when you are near 100. If you have 90 points and your turn total hits 10, you reach 100 and win. Hold immediately. Never roll when holding would win you the game. The temptation to pad your score is irrelevant when victory is available.
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Never roll if holding would win. This rule overrides everything else. If your permanent score plus your turn total equals or exceeds 100, hold. Rolling a 1 at that moment is the worst possible outcome. Bank the win.
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Adjust based on your opponent's score, not just your own. The optimal threshold shifts based on both scores. When your opponent is close to 100, you must roll more aggressively to keep pace. When your opponent is far behind, you can hold earlier and protect your lead. Always consider both numbers before deciding.
Gameplay Examples
Imagine you have 55 points and your opponent has 50. Your turn total is 18. The early-game threshold says hold at 21. You are three points away. You roll. You get a 3. Turn total hits 21. You hold and bank 21 points. Your score jumps to 76. That is a strong, optimal turn.
Now picture a different scenario. You have 35 points and your opponent has 88. You are far behind. The standard threshold of 21 will not close this gap fast enough. You roll aggressively. Your turn total reaches 22, then 28, then 31. You roll again. You get a 5. Turn total hits 36. You hold and bank 36 points. Your score moves to 71. You are still behind, but you gave yourself a fighting chance with one big turn.
Consider the endgame. You have 94 points. Your opponent has 89. Your turn total is 5. You need 6 points to win. You roll. You get a 4. Turn total hits 9. Your score would reach 103 if you hold. You hold immediately. Game over. You win.
What if you had rolled again? A 1 would have wiped your turn total. You would stay at 94. Your opponent would get the dice with a chance to reach 100. Holding was the only correct move.
Variations of Pig
Two-Dice Pig uses two dice instead of one. Rolling a 1 on either die ends your turn and wipes your total. Rolling snake eyes (two 1s) sets your permanent score back to zero. This variant increases variance and makes each roll riskier.
Pig Dice Pass lets you pass the dice instead of holding. The next player inherits your turn total. They must roll or hold with your accumulated points on the line. This adds a psychological layer.
Hog uses multiple dice. You choose how many dice to roll each turn. The sum adds to your turn total. If any die shows a 1, you score zero for that turn.
Why People Love Pig
Pig appeals to players who enjoy pure decision-making under uncertainty. The rules take 30 seconds to explain. The strategy takes a lifetime to master. Every roll forces a judgment call between greed and caution.
The game also plays fast. A full game of Pig lasts 5 to 10 minutes. This makes it perfect for quick sessions or warm-up rounds.
Play Pig Dice for Free
Play Pig Dice for free on Clasica Games. For more dice strategy, try Farkle, Bunco, and Liar's Dice. Browse our full dice games collection for more options.
FAQ
What is the optimal hold threshold in Pig? Hold at 21 or more during the early game. Adjust upward when far behind and downward when near 100. Always hold if banking would win the game.
Who invented Pig dice? John Scarne invented Pig around 1945. He described the game in his book "Scarne on Dice."
How do you win at Pig dice? Follow the hold-at-21 policy as your baseline. Adapt your threshold based on both scores. Never roll when holding would reach 100.
What happens when you roll a 1 in Pig? You lose all points accumulated during your current turn. Your permanent score stays unchanged. Your turn ends.
Can Pig be played with more than two players? Yes. Pig works with three or more players. The optimal strategy adjusts based on how many opponents remain.
Conclusion
Pig rewards disciplined decision-making. Hold at 21 in the early game. Push harder when you trail. Hold immediately when you can win. The math is settled. The strategy is proven. Put it into practice and watch your win rate climb. Play Pig Dice now and test your nerve.
References
- Todd W. Neller, "Optimal Pig Strategy Analysis," Gettysburg College, 2004, https://cs.gettysburg.edu/~tneller/games/pig/
- John Scarne, "Scarne on Dice," Crown Publishers, https://archive.org/details/scarneondice0000scar
