Statistics when third seat calls trump in Euchre
In 2019, I wrote about the tactic of leading trump to your partner if they declared trump from third seat. But not everyone plays by this rule! One day I played a game of Euchre at World of Card Games. In one hand, I was left of the dealer and my partner (third seat) declared trump. I did what I thought was accepted practice and led a trump card. My partner instantly told me that was wrong! I'm sure this happens to people from time to time. Has it happened to you? Card games wouldn't be interesting if everyone made the same tactical decisions.
Because I play this way, the bots at World of Card Games are programmed this way too. If a bot is left of the dealer and their partner declares trump, they will almost always lead a trump card. But I programmed them not to lead it if they only have one trump. It seems like the cautious thing to do. You keep your trump and hope to trump a trick with it later.
Then I got a complaint that the bots weren't leading trump to the third seat maker when they had one trump. I decided to "ask the experts" at the Ohio Euchre forums. That led to an excellent discussion. After thinking about it, I reprogrammed the bots to always lead trump in this case if they can, even with only one trump. This change went live on the site in January 2020.
Statistics for leading trump to your partner in Euchre at World of Card Games
After more thought, I decided to run an experiment. I would have the bots play 10,000 hands and only look at the hands where the third seat bot was the maker. Then I would collect statistics to see what happened if first seat always led trump (if possible). Then I would rerun the experiment, but force first seat to never lead trump.
It turns out that there aren't many cases where third seat called trump! It happened in only about 4% of the hands. So these statistics cover 423 hands.
Here's what happened when the bots were programmed to never lead trump to the third seat maker. Instead, I made the bot in first seat lead their highest non-trump card. The table groups the hands by the points the maker's team won.
| Maker's team won | Hands | % of hands |
|---|---|---|
| 0 points | 63 | 15% |
| 1 point | 316 | 75% |
| 2 points | 37 | 9% |
| 4 points | 7 | 2% |
Notice that the maker got euchred in 15% of these hands, 63 out of 423. But in 75% of the hands, they earned a single point. So on average, it seems like a very successful strategy. When third seat calls and first seat leads an off-suit card, their team usually gets 1 point.
In case you're wondering, I also tested what happens if the first seat bot leads their lowest card (to be clear, this was always a non-trump card). The results are a little worse:
| Maker's team won | Hands | % of hands |
|---|---|---|
| 0 points | 76 | 18% |
| 1 point | 299 | 71% |
| 2 points | 41 | 10% |
| 4 points | 7 | 2% |
Next, let's look at what happened when the first seat bots were programmed to always lead their highest card. They led their highest trump if they had any. Otherwise they led their highest non-trump card. Here's the result:
| Maker's team won | Hands | % of hands |
|---|---|---|
| 0 points | 58 | 14% |
| 1 point | 280 | 66% |
| 2 points | 78 | 18% |
| 4 points | 7 | 2% |
It looks like the maker is significantly more likely to earn 2 points when the bot leads a trump card whenever it can. The maker gets 2 points almost twice as often as when first seat avoids leading trump (18% of the time, compared with 9 or 10%).
I also ran the same experiment with the bots leading their lowest trump if they had any. Otherwise they led their highest non-trump card. The results of these two experiments are so similar that I can't say which tactic is better:
| Maker's team won | Hands | % of hands |
|---|---|---|
| 0 points | 58 | 14% |
| 1 point | 277 | 65% |
| 2 points | 81 | 19% |
| 4 points | 7 | 2% |
Discussion
There's an unspoken assumption behind this tactic. It assumes that third seat would never call trump unless they have a very strong hand, with plenty of trump and hopefully some off-suit (non-trump) Aces.
Indeed, the bots are programmed not to call trump from third seat unless they have at least 2 trumps. While collecting the statistics above, I also checked how many trumps third seat had. They never called trump with just 1 trump in their hand. In 76 cases (18% of the hands), they called with just 2 trumps. I didn't check, but I bet they had both the right and left bower in those cases. In 272 hands (64%), they called with 3 trumps. In 74 hands, they called with 4 trumps. And in only 1 case did they call with 5 trumps (I didn't check, but that might have been a hand for going alone).
Does it matter?
In general, this tactic isn't going to be a huge part of your Euchre battle plan. The reason is that third seat rarely calls trump, as the consider phase statistics show. But when you play a lot of Euchre and look at your win/loss ratio, you'll find that small changes in your tactics add up over time. This experiment with the bots convinces me that over time, you'll win more games if you lead trump to your partner when they're the maker.
Resources
See the Euchre glossary for the jargon on this page.
Playing
Statistics
- Who calls trump, from 129,164 hands
- More trump calling statistics
- When third seat calls trump Reading
- A chi-square test of the shuffle
More Euchre