Crazy Eights — Why the Game Ends
Simulate Crazy Eights and see that the wild eights are not what stops it stalling — recycling the discard is, and the eights just shorten it.
The eights are not what makes the game end
The obvious guess is that the wild eights are what saves Crazy Eights from stalling — there is always something you can play. Simulating 3,000 games at each setting says otherwise:
| Recycle the discard? | Wild ranks | Games that finished |
|---|---|---|
| yes | nothing | 100.0% |
| yes | 8 | 100.0% |
| no | nothing | 65.1% |
| no | 8 | 74.6% |
With the discard recycled, every game finished — with eights wild, and equally with nothing wild at all. Turn the recycling off and a third of games strand with an empty stock. The rule that makes Crazy Eights terminate is “draw until you can play, and recycle the discard when the stock runs dry”. The eights are worth about eleven points of finish rate; the recycling is worth thirty-seven.
What the eights actually do is make the game shorter
| Wild ranks | Mean length | |
|---|---|---|
| nothing | 45.8 turns | |
| 8 | 36.3 turns | |
| 8, J | 28.8 turns | |
| 8, J, Q | 23.2 turns |
Every extra wild rank takes roughly a fifth off, and three of them nearly halve the game. Which is a better reason to keep the eights than the one usually given: a game with no wild cards still ends, it just goes on half as long again.
One caution on reading the numbers above. The games that finish without the recycling rule look shorter still, around 23 turns, but that is survivor bias — the third that never finish are exactly the long ones, and they are not in the average. Turn the recycling off in the simulator and it will tell you the stall rate alongside, so the two are never quoted apart.
How to use
- Pick the number of players and which ranks are wild.
- Turn the recycling rule off to see how often a game strands.
- Simulate two thousand games and read the finish rate.
- Compare the mean length with and without wild cards.
Frequently asked questions
Does a game of Crazy Eights always end?
With the usual rule that the discard pile is recycled into the stock when it runs out, yes — every one of three thousand simulated games finished, with eights wild and equally with nothing wild at all. Without that rule about a third of games strand with an empty stock.
Are the wild eights what stops the game stalling?
No, and that is the surprise. Without recycling, eights lift the finish rate from about 65 per cent to about 75 — roughly eleven points. Recycling the discard lifts it from 65 to 100, which is thirty-seven. The eights help; the recycling settles it.
What do the wild cards actually do?
They shorten the game. With nothing wild the mean is about 46 turns, with eights about 36, with eights and jacks about 29, and with three wild ranks about 23. Every extra wild rank takes roughly a fifth off, and three of them nearly halve it.
Why do games look shorter without the recycling rule?
Survivor bias. The games that never finish are exactly the long ones, and they are not in the average, so the survivors look quick. The simulator always reports the stall rate alongside the mean so the two are never quoted apart.
What are the rules of Crazy Eights?
Play a card matching the rank or the suit of the top of the pile. An eight is wild and lets you call any suit. If you cannot play you draw until you can. First player to empty their hand wins.
What happens when the stock runs out?
Under the usual rule the discard pile is turned over, shuffled and becomes the new stock, leaving the top card in place. Some tables instead end the round there, which is the variant that leaves a third of games unfinished.
Does the number of players change how long it takes?
Yes, and you can measure it here. More players means more cards dealt out and more hands to empty, so games run longer in turns even though each individual hand is smaller.
Does this send anything anywhere?
No. The simulation runs entirely in your browser and nothing is stored or uploaded.
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