The numbers
Which number is best in white elephant?
Short answer: last. Longer answer: it depends on your house rules, and the rule most families add to make it fair for player #1 overshoots badly. We simulated 200,000 games for each rule set to find out.
Going last is the best seat
With the most common rules (a gift freezes after its third steal, no instant steal-backs), the last player ended up with one of their three favourite gifts 43.8% of the time. Player #1 managed 29.8%. With 12 gifts, pure luck would give you 25%.
The reason is simple: the last player sees every gift opened and can steal any that isn't frozen. Player #1 opens blind, has nothing to steal, and spends the rest of the game being a target.
The final swap overcorrects
Lots of groups give player #1 a last move: once every gift is open, #1 may trade for any unfrozen gift. It's meant to make up for opening blind. With a 3-steal limit it does far more than that: player #1 jumps from the worst seat to the best, ending with a top-three gift 69.3% of the time, nearly three times their luck-only share. Everyone else is slightly worse off for it.
The fix isn't to drop the swap. It's to pair it with a lower steal limit. With one steal per gift plus the final swap, every seat's odds landed between 29.7% and 37.5%. That was the fairest common rule set we tried, and also the fastest.
Every rule set we tried
| House rules (12 players) | #1 top-3 | Last top-3 | Range across seats | Steals / game | Turns / game |
|---|---|---|---|---|---|
| 3 steals, then frozen | 29.8% | 43.8% | 28.8–43.8% | 20 | 32 |
| 3 steals + #1 final swap | 69.3% | 32.1% | 26.6–69.3% | 20 | 32 |
| 2 steals, then frozen | 17% | 48.8% | 17–48.8% | 14 | 26 |
| 1 steal, then frozen | 9.9% | 40.5% | 9.9–40.5% | 8 | 20 |
| 1 steal + #1 final swap | 37.5% | 34% | 29.7–37.5% | 8 | 20 |
| No steal limit* | 17.2% | 100% | 17.2–100% | 36 | 48 |
*With no steal limit we used the "a gift can only be stolen once per turn" rule; without it the game never ends on paper. All rule sets include "no instant steal-back". Pure luck = 25% for every seat.
What this means at your party
- You drew a high number? Patience pays. Watch what gets opened and what people react to.
- You drew #1 and there's no final swap? Open something, then hope it's ordinary. In our games, a gift everybody likes gets stolen; a gift that suits you in particular tends to stay with you.
- You're the host and want it fair? Use one steal per gift plus the final swap. If your crowd loves the chaos of steals, keep three steals and skip the final swap; it's the next fairest and gives you about 20 steals a game.
- Huge group? More players means more steal options for late seats. With 20 players and 3 steals, the last seat still led, but the middle seats flattened out.
How the simulation works
Each of the 12 gifts has a "how good is it" value that everyone mostly agrees on, plus a personal-taste part that differs from person to person (a coffee-lover rates the grinder higher). Players don't know what's inside a wrapped gift. On your turn you steal the best gift you're allowed to take if you like it more than an average wrapped one; otherwise you open. Whoever you stole from goes next and can't take that gift straight back. A gift freezes when it reaches the steal limit. We scored each player on where their final gift ranked among all 12 by their own taste.
It's a model, not a family: real people steal for laughs, protect their spouse's gift and hold grudges. The direction of the results held when we made tastes more alike or more different, and with 8 or 20 players; the exact percentages moved. The code is short and readable: download sim.mjs (run it with Node: node sim.mjs n=12 limit=3 swap=1).
Run your game with these rules
Questions
- What is the best number to get in white elephant?
- The last number. In 200,000 simulated 12-player games with a 3-steal limit, the last player ended with one of their three favourite gifts 44% of the time; pure luck would give 25%. Number 1 was the worst seat at 30% unless the group plays a final swap for #1.
- Is it better to go first or last in white elephant?
- Last, unless player 1 gets a final swap. With the final swap and a 3-steal limit, player 1 became the best seat by a wide margin (69% chance of a top-three gift).
- What are the fairest white elephant rules?
- Of the common rule sets we simulated, one steal per gift plus a final swap for player 1 spread the luck most evenly: every seat landed between 30% and 38%. It also made the shortest game.