Card Game Euchre Strategy - by Example

by Marya @ World of Card Games

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Statistics when third seat calls trump

January 2 2020

Table of Contents

Lead trump to your partner in Euchre

Last year, I wrote about the tactic of leading trump to your partner if they declared trump from 3rd seat. However, not everyone plays by this rule! Just this week, I played a game of Euchre at World of Card Games. In one hand, I was left of the dealer, and my partner (3rd seat) declared trump. I did what I thought was accepted practice, and led with 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, then they will almost always lead with a trump card. However, I programmed them so that if they only have one trump, they would not lead it. It seems like the cautious thing to do - keep your trump, and hope to trump a trick with it later.

However, I recently received a complaint that the bots were not leading trump to the 3rd seat maker when they had one trump. I decided to "ask the experts" about this. And now there's an excellent discussion at Ohio Euchre forums about this topic. After thinking about this, I decided to reprogram the bots so that they would always lead trump in this scenario if they could, even if they had only one trump card. This change was applied to the site in January of 2020.

Statistics for leading trump to your partner in Euchre at World of Card Games

Upon further consideration, I decided to run an experiment. I would have the bots play 10,000 games. I would only look at hands where the 3rd seat bot was the maker. Then I would collect statistics to see what happened if 1st seat always led with trump (if possible). Then I would rerun the experiment, but force 1st seat to never lead trump.

It turns out that there aren't very many cases where 3rd seat called trump! This happened in only about 4% of the hands. Hence, we're looking at statistics for 423 hands.

Here is what happened when the bots were programmed to never lead trump to the 3rd seat maker. Instead, I forced the bot in 1st seat to lead with their highest non-trump card. In the following list, the number of hands are "bucketed" according to the total points awarded to the maker's team:

Notice that the maker got euchred in 15% of such hands - 63 out of 423 of them. But in 75% of those hands, they earned a single point. So on average, it seems like a very successful strategy. That is, when 3rd seat calls, and 1st seat leads an off suit card, their team usually gets 1 point.

If you are wondering, I also tested what happens if the 1st seat bot led with their lowest card (to be clear, this was always a non-trump card). The results are a little bit worse:

Next let's look at what happened when the 1st seat bots were programmed to always lead their highest card. This means that they led with their highest trump if they have any, or otherwise led with their highest non-trump card if they had no trumps. Here's the result for this scenario:

It appears that the maker is significantly more likely to earn 2 points when the bot leads with a trump card, when possible. They will get 2 points almost twice as often as when they avoid leading trump (18% vs 9 or 10% of the time).

I also ran the identical experiment so that the bots would lead with their lowest trump card if they had any, or with their highest non-trump card otherwise. These two experiments have such similar results that I don't think we can judge which is a better tactic:

Discussion

There's an unspoken assumption when taking this tactic. It is assumed that 3rd seat would never order trump unless they have a very strong hand: plenty of trump, and hopefully some off-suit (non-trump) aces.

Indeed, the bots are programmed not to call trump from 3rd seat unless they have at least 2 or more trump cards. When collecting the statistics above, I also checked to see how many trump 3rd seat had. They never called trump with just 1 trump card in their hands. In 76 cases (18% of the hands), they called trump with just 2 trump cards. I didn't check, but I'm betting they had both the right and left bower in those cases. In 272 hands (64%), they called trump with 3 trump cards. In 74 hands, they called trump with 4 trump cards. And in only 1 case did they call trump with 5 trump cards (I didn't check, but that might have been a case for going alone).

Does it matter?

In general, this tactic is not going to be a huge part of your Euchre battle plan. The reason is that 3rd seat rarely calls trump (click this link to see statistical evidence). However, when you play a lot of Euchre, and you look at your win/loss ratio, you're going to find that the effects of small changes in your tactics will add up over time. This experiment with the bots convinces me that over time, you will win more games if you lead trump to your partner when they're the maker.

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