Introduction
Chase the ace is a simple card game that I was taught when I was younger from my dad. Recently on holiday I was playing with some friends and for a few games it was always the dealer that was put out of the game first. We’d noticed this before and has dubbed it “The curse of the dealer”. I was curious to see if the curse had any basis or if it was just chance.
The rules
For those of you not familiar with Chase the Ace it is the simplest card game I know. Each player is dealt a card (the more players the better!). Play starts to the left of the dealer with each player deciding whether to keep his current card or to force the player on their left to swap with them. When play reaches the dealer they can choose to swap with the deck. After every player has had their turn the person (or persons) with the lowest card (Aces are low) is knocked out of the game. The next round starts again without the losing players until a player remains (or all players are knocked out).
Testing the curse
I created a simple python script to play a bunch of hands with 10 players and keep track of which player or players were knocked out first (the source of which can be found on GitHub.
The strategy played is pretty simple (so it may affect the outcome) and uses the following rules:
- If a player swaps with us and we end up with a higher card then we always keep that card (since we are guaranteed to stay in).
- If we have a card higher than a 7 keep it.
- Otherwise swap.
Using 10 players for 10,000,000 hands gave the following results:
| Position | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Total |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Loses | 791547 | 1037209 | 1146774 | 1206951 | 1252666 | 1280194 | 1305464 | 1322220 | 1328504 | 1325231 | 11996760 |
| % Loses | 6.60 | 8.65 | 9.56 | 10.06 | 10.44 | 10.67 | 10.88 | 11.02 | 11.07 | 11.04 |
Conclusion
We can see that the dealer is indeed at a disadvantage and, in fact your odds of losing decreases as you get closer to early positions. I suspect that this is due to bad cards “bubbling up” through the positions. If you have a high card and are in later position you have a higher chance of losing it. I may revisit this code at some point and see if this code can be reused to generate an optional strategy.
Edit: Someone has pointed out that, in fact, it’s the second to last player that loses slightly more. I’m rerunning this with more games to see if this is chance or not - there may be a point where all players are equally disadvantaged.