Euchre Simulator
I simulated the euchre card game in Python.
It's a cool little simulation, and is easily extensible to other variations of euchre or to user-vs-computer gameplay.
Some people say that euchre is a poor man's bridge, and the results suggest that these people are exactly right. A player bidding randomly would still win 21% of their games. A player bidding and playing randomly would win 10%. These numbers seem absurdly high for a venerable card game. A trained monkey could probably win a world championship with an ounce of luck.
Bidding
After simulating millions of hands of euchre, I modelled the results down to the following strategy which is not too difficult to remember.
1. Calculate your hand's score according to this table.
| (A) Number of Trumps | (B) Trump Cards | (C) Offsuit Cards | (D) Flipped Card Penalty* |
|---|---|---|---|
| 1 = 1 2 = 2 3 = 6 4 = 9 5 = 12 | JRight = 10 JLeft = 8 A = 6 K = 5 Q, T = 4 9, 8, 7 = 3 | A = 4 each K = 1 each | J = -5 A = -2 * Only applies during the first round of bidding and if your opponent is the dealer. |
Your score is (A) + (B) + (C) + (D).
2. If your score is higher than the minimum point threshold for your position, then make the call. Otherwise pass.
| Bidding Round | 1 — Flipped Card | 2 — Open Bidding | ||||||
|---|---|---|---|---|---|---|---|---|
| Position | Left | Opposite | Right | Dealer | Left | Opposite | Right | Dealer |
| Minimum Points for Bid | 26 | n/a | 31 | 16 | 15 | 20 | 15 | 17 |
| Minimum Points for Lone Bid | 30 | 25 | 34 | 25 | 26 | 28 | 26 | 28 |
Although this is an elaborate set of rules, it would win only about 51% of games when the other three players follow a simple trump-counting bidding strategy. How much better could a more sophisticated version be? Eventually it would be nice to use this simulator to generate training data for an ML model of optimal bidding strategy.
Of course, the best strategy also depends on the other players — if your opponents bid more cautiously then you should be more cautious too. The game situation could also be taken into account.
Playing
The simulator uses a rule-based approach for choosing cards. Its first-order approximation is:
- Golden rule
- If you made trumps and the outcome of the hand is still uncertain, keep one trump in your hand as a saver.
- First card in trick
- If your team made trumps, lead your best trump card.
- If your opponents made trumps, lead your best offsuit card.
- Second or third card in trick
- If all your cards would lose, or you think your partner's lead card will win, or you made trumps and are VERY nervous, then throw away your weakest card.
- Otherwise, take the lead in the trick with either your strongest offsuit (if you can follow suit) or your weakest trump.
- Last card in trick
- If your opponents are leading the trick and you can win it and it wouldn't break the golden rule, then play your weakest card that wins the trick.
- Otherwise, throw away your weakest card.
I tried to run experiments where I varied this strategy, but couldn't come up with anything better.
Check out the project here.