Donkey
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What 90,000 games of Donkey tell us
Every family has theories about Donkey (Kazhutha, Bhabhi): “the Ace of Spades is lucky”, “a hand full of Kings is a good hand”, “it's all luck anyway”. We let computer players play 90,000 complete games with the same rules engine that runs this site, and counted what actually happens. Some family wisdom holds up. Some of it is backwards.
1. Is the Ace of Spades lucky?
The player with the A♠ must lead it in the first round. Whether that helps depends almost entirely on how many people are playing:
| Players | Fair share of losses | A♠ holder loses | First round is cut |
|---|---|---|---|
| 3 | 33.3% | 26.5% (lucky) | 0.6% |
| 4 | 25.0% | 21.4% (lucky) | 5.2% |
| 5 | 20.0% | 20.3% (neutral) | 17.6% |
| 6 | 16.7% | 21.8% (unlucky) | 35.8% |
| 8 | 12.5% | 26.4% (very unlucky) | 77.7% |
Why: with 8 players everyone holds only 6 or 7 cards, so it is very likely that someone has no Spades at all. They cut the opening A♠ immediately, and because the Ace is the highest Spade on the table, the A♠ player picks up the whole first pile. That happens in more than three out of four 8-player games. With 3 or 4 players almost everyone still has a Spade, the first round is thrown away cleanly, and the A♠ player has simply got rid of their most dangerous card for free.
This is probably why some families have a house rule that the first round is always thrown away, even if someone cuts. In big games it removes a real disadvantage.
2. High cards are a burden, not a blessing
In most card games Aces and Kings are what you hope for. In Donkey they are what picks up the pile when someone cuts. The more of them you are dealt, the more often you lose:
| Aces + Kings dealt to you | 4 players: you lose | 6 players: you lose |
|---|---|---|
| 0 | 17.3% | 8.6% |
| 1 | 20.6% | 14.3% |
| 2 | 24.8% | 20.6% |
| 3 | 29.6% | 27.8% |
| 4 | 32.7% | 34.6% |
| 5 | 37.8% | (too rare) |
With 6 players, a hand with four Aces and Kings is four times as likely to lose as a hand with none. This is why the first tip in our strategy guide is to get rid of high cards early, while they are still safe.
3. Short suits are your friend
A suit where you hold two cards or fewer runs out quickly, and once it's gone you can cut whenever it is led. In 4-player games:
| Short suits in your starting hand | You lose |
|---|---|
| None (all four suits have 3+ cards) | 34.8% |
| 1 | 26.4% |
| 2 | 19.1% |
| 3 | 8.9% |
A balanced hand feels safe, but it is the hardest to escape from: you are never out of a suit, so you can never cut.
4. One extra card matters
52 cards don't always divide evenly, so some players start with one card more than others. That single card makes a clear difference:
| Players | Shorter hand loses | Longer hand loses |
|---|---|---|
| 3 | 31.3% (17 cards) | 37.3% (18 cards) |
| 5 | 18.1% (10 cards) | 22.9% (11 cards) |
| 6 | 13.9% (8 cards) | 18.1% (9 cards) |
| 8 | 10.9% (6 cards) | 14.1% (7 cards) |
With 4 players everyone gets exactly 13 cards, which makes 4 the fairest table size.
5. Pick-ups happen constantly
Practically none of the 50,000 games between careful players finished without a pick-up. On average:
| Players | Pick-ups per game | Rounds per game | Biggest hand during the game |
|---|---|---|---|
| 3 | 18.9 | 30.7 | 23 cards (up to 41) |
| 4 | 21.4 | 31.6 | 21 cards (up to 41) |
| 5 | 24.3 | 34.1 | 21 cards (up to 42) |
| 6 | 28.0 | 36.9 | 22 cards (up to 42) |
| 8 | 35.5 | 44.9 | 25 cards (up to 45) |
So roughly two out of three rounds end in a pick-up (more in bigger games), and in a typical game someone ends up holding about 20 cards at some point. In the most extreme games one player held 45 of the 52 cards. No lead is ever completely safe.
6. Is it all luck? No.
To measure skill we put one careful player at a table of players who play any allowed card, and then the reverse:
| Table | Fair share | Careful player among random players loses | Random player among careful players loses |
|---|---|---|---|
| 4 players | 25.0% | 14.5% | 40.7% |
| 6 players | 16.7% | 7.0% | 34.9% |
Even a very simple strategy (lead the lowest card of your shortest suit, follow with your lowest card, throw your highest card when you cut) cuts your chance of being the Donkey roughly in half. Playing without thinking makes it 1.5 to 2 times more likely. The cards matter, but how you play them matters more.
7. Some games would never end
In about 1 in 2,000 games, the last two computer players kept passing the same pile back and forth forever, each forced into the same moves. Real people break these loops by changing their play, and the declare rule lets the last two players end a game that is going nowhere.
How we did it
Every game was played by the same rules engine that runs the online game on this site: all 52 cards dealt, A♠ leads, follow suit, clean rounds thrown away, a cut makes the highest card of the led suit pick up, and if that player is already out the next-highest card leads. We simulated 10,000 games each for 3, 4, 5, 6 and 8 players with careful computer players, plus 40,000 mixed games for the skill test, 90,000 games in total. Each game was a first game: no Ace penalties, no requests for cards and no declaring. The games that went round in circles (under 0.1%) were left out.
Computer players are not people. Real players read the table, remember who has cut, and bluff with their faces, so your family's numbers will differ. The direction of every result above, though, matches the advice experienced players give.