Would You Go Alone.....

[inglewoodjack]

In this situation:

Dealer is my partner; I am in 2nd seat.

Dealer flips up a

This is my hand:



I ordered up, went alone, and got euchred because 1st seat had 3 spades.

Thoughts?

[RedDuke]

It was a risky lone because of the situation you described. You had the top trump (the left) but if either opponent had three trump, you could still get into trouble.

With that said, I might have gone alone there if I was down in the score (say 7-2 or something similar). I'd have to do the math, but I don't think that hand will get set that often unless one opponent has three trump, one of which is the ace. I'm guessing he led a trump too.

How did the hand play out? What was his first lead? If he leads the Ace, then you take it with the left and lead back the king. You'd probably at least get three tricks there.

[Richardb02]

Being euchred on a hand like this is an opportunity to use logic to overcome the emotion of losing (actually the emotion of being a loser)!

I look at the odds of Enemy having 3 trump.
At the table I use a very simplified estimate of probability. There are 4 suits, so each time a card is drawn, there is a 1/4 chance that a particular player gets a trump. So 1/4 x 1/4 x 1/4 is the odds of getting 3 trump with 3 cards. But, player gets 3 chances to draw the 3rd trump, so the formula becomes 1/4 x 1/4 x 3/4 = 3/64 = 4.7%. I will always accept a 5% chance of being euchred.

In fact, I will accept a 33% probability of being euchred, if I have accounted for all possible hands that could result in an euchre. An example of covering all possible euchres, based on this hand, is let's assume that if enemy has 3 trumps between the 2 of them, then we are very likely to be euchred. Logically, the probability has doubled from 4.7% to 9.4%.

A more accurate analysis says that there are 4 trump left and there are 18 cards not seen. So there is a 4/18 probability that a player will obtain a trump. The next card has a 3/17 probability of being a trump. The 3rd card has a 2/16 chance of being a trump. The 4th and 5th cards add 2/16 chances of drawing the 3rd trump. The formula becomes 4/18 x 3/17 x (2/16 + 2/16 + 2/16) = 1.5%. The more accurate analysis reducing the odds from 4.7% to 1.5% makes sense because it accounts for there being less trump each time that a trump is drawn.

My approach to calculating probabilities is simplified. RedDuke please provide us a more detailed calculation of the probabilities.

The take away, when you get euchred, look back at the combination of cards that lead to the euchre. Then use a simplified probability calculation to determine if the probability was in your favor. If the probability was in your favor then forget about the outcome.

You had a 95% probability of getting at least 1 point on this hand. If you decide not to call alone you lose a 32% (my average) of making 4 points. You lose 1.18 points, on average, by settling for a call with your partner! Wes please comment on the EV for this hand.

[inglewoodjack]

It was a risky lone because of the situation you described. You had the top trump (the left) but if either opponent had three trump, you could still get into trouble.

With that said, I might have gone alone there if I was down in the score (say 7-2 or something similar). I'd have to do the math, but I don't think that hand will get set that often unless one opponent has three trump, one of which is the ace. I'm guessing he led a trump too.

How did the hand play out? What was his first lead? If he leads the Ace, then you take it with the left and lead back the king. You'd probably at least get three tricks there.

1st seat lead a heart - everyone followed, I played my .
I led the left to take out a round of trump. First seat played .
Next I led the . 1st seat trumps with .
1st seat leads , taking out my .
1st seat leads diamond. All I have left is . Euchre.

[RedDuke]

At the table I use a very simplified estimate of probability. There are 4 suits, so each time a card is drawn, there is a 1/4 chance that a particular player gets a trump. So 1/4 x 1/4 x 1/4 is the odds of getting 3 trump with 3 cards. But, player gets 3 chances to draw the 3rd trump, so the formula becomes 1/4 x 1/4 x 3/4 = 3/64 = 4.7%. I will always accept a 5% chance of being euchred.

That is extremely simplified. Remember that the trump suit has 7 cards, next has 5, and the green suits have 6 each. So your odds of drawing a trump card are actually more than 1/4.

A euchre deck consists of 6 cards of each suit, for a total of 24 cards. Thus, to determine the probability of getting any single hand in euchre, we need to know how many possible hands there are. That is done using a combination:

24C5 = C(24,5) = 42,504.

So there are 42,504 possible hands.

Now we want to know the probability of one hand having 3 trumps. That's a bit more complex. We have to figure out how many possible combinations there are of 3 trump cards. We can do this again with a combination:

7C3 = C(7,3) = 35

So there are 35 different ways that we can get three trumps. However, there are also two other cards in the hand and they can be anything. So how many ways can you pull 2 cards out of a 21 card deck?

21C2 = C(21,2) = 210

So what we do is multiply them together and then get the probability:

(7C3)(21C2)/24C5 = 0.1729 or 17.3%

So there's a 17% chance that any player in a euchre hand will have three cards of the same suit.

Now, there's a 1/4 chance that those will be trumps. So 0.25*.173 = 0.04325 or about 4.325%. Pretty close to what Richard said above.

1st seat lead a heart - everyone followed, I played my .
I led the left to take out a round of trump. First seat played .
Next I led the . 1st seat trumps with .
1st seat leads , taking out my .
1st seat leads diamond. All I have left is . Euchre.

That's about how I figured it went down. Honestly, you probably played it the best way you could. I probably would have led the A-H on that third trick though since there's a slightly lower chance that green aces will be trumped than next aces but even then it sounds like first seat only had one heart.

[Wes (aka the legend)]

inglewoodjack,

What was the score? Never forget to include that.

[Wes (aka the legend)]

You had a 95% probability of getting at least 1 point on this hand. If you decide not to call alone you lose a 32% (my average) of making 4 points. You lose 1.18 points, on average, by settling for a call with your partner! Wes please comment on the EV for this hand.

I hate to give the same cop-out answer all the time but I'm afraid it is too hard to tell without that hypothetical euchre simulator. That said it wouldn't be hard to create a crude EV model based off our guesses but I don't think it really gets us anywhere.

But for the fun it let's assume if we go alone we get euchred 5% of the time, get 4 points 25% of the time and score a point 70% of the time. And for the sake of simplicity over accuracy lets assume if we don't go alone we never get euchred, we score 2 points 50% of the time and we score 1 point 50% of the time. So what's the better move based on those assumptions.

EV of going alone: (.25 x 4) + (.70) + (.05 x -2) = 1.6

EV of just calling: (.50 x 2) + (.50 x 1) = 1.5

1.6 > 1.5 therefore go alone

Of course we can tweak these numbers anyway we want to get any answer we desire but I do think there is some value to doing EV exercises like that. Sometimes an insight will be gained and sometimes the numbers will spit out a dramatic enough difference to change one's mind on a certain strategy.

Ok with that all said, what would I actually do in this spot even tho I'm not sure what's best? With OP's hand I'm going alone at every score except when my team has 8+.

My overall thinking of this spot:

I feel super strongly that this hand is a MUST go alone at every score except when we have 8+:



The fact that you can't get over-trumped on the first lead is pretty important to me.


OP's hand might be the grey area spot:



But like I said, I'm going for it at every score except when we have 8+


Maybe this hand is where we should play it safe and not go alone at neutral scores:



Again, only that euchre simulator will know.

What I will say is one must be prepared to pull the trigger and go alone at many scores even with this hand:



In fact if you play on that one popular euchre app where going alone always puts you last to act, then that hand is a must go alone at any score except when you have 8+. Ofc we're still assuming we are in seat 2 and the upcard is the Js.

One last hand example to stress how important the score can be in dictating one's decision:

Your team is down 9-6. The dealer upcard is the .

You're in the 2 seat with:

This is a MUST go alone hail mary even with the Right out in the wild.

[Wes (aka the legend)]

With that said, I might have gone alone there if I was down in the score (say 7-2 or something similar).

Down 7-2, I would definitely go alone with OP's hand.

In fact, assuming Js is the upcard and we're in the 2 spot, all (Left + 1)+(Suited Ace)+(Ace) are now activated at that score. So this hand now is a must go alone:



In fact, there are other worst hands in this spot where I'm going alone:



In fact even this hand:



And maybe even this hand:



That last hand may seem ridiculous but you only need 2 cards buried (As & Jc) to have a shot and you have the perfect outside ace combo: 2 green aces and no gap in the suited ace.

[Wes (aka the legend)]

That's about how I figured it went down. Honestly, you probably played it the best way you could. I probably would have led the A-H on that third trick though since there's a slightly lower chance that green aces will be trumped than next aces but even then it sounds like first seat only had one heart.

Hearts was played on the first trick, so he was better off leading the since it was a fresh suit.

[inglewoodjack]

inglewoodjack,

What was the score? Never forget to include that.

No score. Tournament-type play. Playing to maximize points.

[inglewoodjack]

That's about how I figured it went down. Honestly, you probably played it the best way you could. I probably would have led the A-H on that third trick though since there's a slightly lower chance that green aces will be trumped than next aces but even then it sounds like first seat only had one heart.

Hearts was played on the first trick, so he was better off leading the since it was a fresh suit.

Agree - that was my reasoning also.

[Wes (aka the legend)]

inglewoodjack,

What was the score? Never forget to include that.

No score. Tournament-type play. Playing to maximize points.

I play it the same as you, but that doesn't prove it's correct!

[inglewoodjack]

inglewoodjack,

What was the score? Never forget to include that.

No score. Tournament-type play. Playing to maximize points.

I play it the same as you, but that doesn't prove it's correct!

Agreed! And - I would play it again if I had the chance!