Odds of Any Card Winning A Euchre Hand

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RedDuke
Posts: 444
Joined: Sun Dec 02, 2018 2:22 am

Odds of Any Card Winning A Euchre Hand

Unread post by RedDuke » Wed Jan 15, 2020 5:18 am

We talk a lot about the odds of any particular hand winning a game of euchre. Richard even attempts to determine this with his BPS. The following numbers come from a computer simulation of 100 games using the following rules:

1. Highest trump that a player has is led.
2. Each player will attempt to play the highest card they have in the led suit in an attempt to win it.
3. If can't follow suit, the player will use the lowest trump they have in an attempt to win it.
4. A player will not play higher than their partner unless there is no other choice.
5. The result of the tricks was saved noting the denomination and suit of the winning card.
6. Hands are totally randomly dealt.

I can't take credit for this simulation. These results come from Perry at EuchreUniverse (https://www.blogger.com/profile/07621971607218955539). They're fascinating though what we see. The results may or may not be what you expect but they can help you better evaluate your hand.

So, here's the odds of any given card winning a trick:

Right bower 100%
Left Bower 76%
Ace of trump 53%
King of trump 45%
Queen of trump 40%
Ten of trump 34%
Nine of trump 32%

Ace of next suit 44%
King of next suit 13%
Queen of next suit 2%
Ten of next suit 1%
Nine of next suit 1%

Ace of green suit 50%
King of green suit 19%
Queen of green suit 6%
Jack of green suit 1%
Ten of green suit 1%
Nine of green suit <1%

This actually shows that non-trump aces aren't really as valuable as we often assume them to be. If they're in the opposite color as trump they have only a 50% winning the trick and if they're in next that drops to 44%. That is roughly in line with what I see in actual gameplay though. Any lesser card is almost worthless in comparison unless its trump (or you know where the ace is). We also see that any trump weaker than the left is only marginally able to be depended on.

This really shows the advantage that the dealer has since they get to go last on the first trick!



irishwolf
Posts: 816
Joined: Tue Apr 24, 2018 9:33 pm

Unread post by irishwolf » Wed Jan 15, 2020 10:03 am

What does not make sense is WHO made the trump suit? Eldest, the dealer, 3rd seat or 2nd seat?

Big difference based on who was the maker? And what round?

cgutowski
Posts: 5
Joined: Wed Aug 21, 2019 8:51 am

Unread post by cgutowski » Wed Jan 15, 2020 10:30 am

I'm a little surprised the green King is at 19%. Seems high.

May be skewed by:
"4. A player will not play higher than their partner unless there is no other choice."

If I have a green 9 and A and my partner leads a green 10, J, Q, I'm definitely playing the A not the 9. Good chance the person to the left has the K and your A is less likely to have a chance to win a hand. This is a common enough play that is probably skewing the green A value down and the green K value up.

irishwolf
Posts: 816
Joined: Tue Apr 24, 2018 9:33 pm

Unread post by irishwolf » Wed Jan 15, 2020 11:48 am

Not sure where you are getting your numbers from. It is a fact that the ace to the suit of the king, will be buried 17%. If I lead a King, my partner will have the ace 27% so that elevates the King winning.
The rest of the simulation is a mystery.

jblowery
Posts: 125
Joined: Tue Dec 11, 2018 10:43 am

Unread post by jblowery » Wed Jan 15, 2020 12:49 pm

That is limited information though when you look at those cards in a vacuum. For example, if I have an uprotected left and I'm 4-suited my chance of taking a trick with it are WAY lower than 50%, much less 76%. Even lower if my opponents made the call. If it is 1st seat then it is lower yet. f I have rt+ left then it goes up to 100%. This is just an extreme example; there are many more. The cards never exist in a vacuum. It always depends upon who calls and what else is in your hand.

RedDuke
Posts: 444
Joined: Sun Dec 02, 2018 2:22 am

Unread post by RedDuke » Thu Jan 23, 2020 5:59 am

irishwolf wrote:
Wed Jan 15, 2020 11:48 am
Not sure where you are getting your numbers from. It is a fact that the ace to the suit of the king, will be buried 17%. If I lead a King, my partner will have the ace 27% so that elevates the King winning.
The rest of the simulation is a mystery.
It was from a simulation of 100 games to 10 points each and as jblowery points out it was done in a vacuum. Expert play will of course change these odds.

irishwolf
Posts: 816
Joined: Tue Apr 24, 2018 9:33 pm

Unread post by irishwolf » Thu Jan 23, 2020 10:33 am

Okay, thanks. Not sure it that useful to me! I know Perry (from Chicago and a good euchre player) but never discussed this with him or have known that it existed. He had a website for about 4 years then disbanded it. There was some pretty good stuff on it.

Tbolt65
Posts: 598
Joined: Sun Jun 16, 2019 9:14 pm
Location: Las Vegas

Unread post by Tbolt65 » Thu Jan 23, 2020 1:00 pm

irishwolf wrote:
Thu Jan 23, 2020 10:33 am
Okay, thanks. Not sure it that useful to me! I know Perry (from Chicago and a good euchre player) but never discussed this with him or have known that it existed. He had a website for about 4 years then disbanded it. There was some pretty good stuff on it.
His blog/website is still there. I was on it sometime last year since I was away from euchre for nearly 9 years and was looking at all the euchre stuff I used to be involved with. Do a search for Perry Romanowski euchre universe.

Tbolt65
Edward

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