Pig: rules & the “hold at 20” strategy

Pig is the simplest push-your-luck game there is. You roll a single die over and over, adding each result to a running turn total — but roll a 1 and the whole turn is wiped and passed to the next player. The tension is entirely in one decision, repeated: roll again for more, or bank what you have and keep it safe? First player to 100 wins.

The die and how you roll

You need one six-sided die and a way to keep score. Play passes clockwise. On your turn you roll the die as many times as you like:

• Roll a 2, 3, 4, 5 or 6 — add it to your turn total and choose whether to roll again or stop.
• Roll a 1 — your turn total for this turn is lost entirely, and the die passes on.
• Choose to hold at any point — your turn total is added to your permanent score, and play passes on.

That is the whole game. The first player to reach 100 points or more wins. It is a superb travel and classroom game precisely because the rules fit on a beer mat but the strategy rewards real thought.

Scoring & a single turn

Every roll offers the same gamble. Five of the six faces help you; one ruins you. Look at the expected value of a single extra roll when your turn total so far is t:

So the expected change from one more roll is (5/6 × 4) − (1/6 × t) = 3.33 − t/6. That figure is positive — rolling adds points on average — right up until t reaches 20, where it hits zero, and turns negative beyond it. In plain terms: while your turn total is below 20, another roll is worth it; once you have 20 or more banked in the turn, the expected gain no longer covers the risk.

Strategy & the odds

That single calculation gives the game’s most famous heuristic: “hold at 20”. Keep rolling until your turn total is at least 20, then stop and bank. Following it maximises the average number of points you score per turn, and for a beginner it is close to unbeatable as a default.

But “hold at 20” maximises expected points, and winning Pig is not quite the same problem — you are racing an opponent to 100, not padding an average. The genuinely optimal policy, worked out by value iteration (famously by Neller and Presser), mostly agrees with holding around 20, but it deviates near the endgame:

• When you are far behind and the leader is near 100, push well past 20 — even to 30 or more — because a safe 20 will not catch them. You need variance.
• When you can win this turn, keep rolling until you reach 100 regardless of the 20 rule — there is no tomorrow to protect.
• When you are close to 100 and comfortably ahead, hold earlier than 20 to lock the lead and force your opponent to gamble.

The through-line: “hold at 20” is your baseline, but scoreboard position should stretch or shrink that number. Play the race, not just the turn.

Common mistakes

• Greeding past 20 out of habit. Every roll beyond 20 loses expected value. If you are not deliberately chasing because you are behind, bank it.
• Holding at 20 when you are losing badly. A cautious 20 will not close a big gap late on — when behind, you must take on more risk, not less.
• Ignoring the finish line. If a roll can take you to 100, keep going; protecting a turn total you will never need is pointless.
• Playing everyone the same. Your threshold should move with the score. Against a runaway leader, hold-at-20 quietly guarantees you lose.
• Confusing Pig with two-dice variants. In “Big Pig” or two-dice versions, snake-eyes and doubles change the maths — the 20 threshold is specific to the one-die game.

Want to feel the push-your-luck rhythm? Roll a single physics die in your browser and try a few turns holding strictly at 20 — then try creeping past it and watch how often a 1 punishes you.

Keep reading: for push-your-luck with six dice and far bigger swings, try Farkle.