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by raydog » Mon Jan 16, 2023 10:49 am
"Score matters, nothing else. At opps on 9, I call diamonds and lead my Kd. At all other scores neither my dreaming nor any greed will get the best of me. I pass. The most I am likely risking is one point."
This is an interesting concept. Here is a more detailed breakdown of what my simulator found as the probability distribution of different point outcomes:
1) call D, lead KD:
win 2 pts: 4.7%
win 1 pt: 46.0%
lose 2 pts: 49.3%
So you can expect to score at least a point 1/2 the time, and the blended EV is -0.43
2) pass:
win 4 pts: 0.7%
win 2 pts: 10.0%
win 1 pt: 9.8%
lose 1 pt: 53.7%
lose 2 pts: 20.7%
lose 4 pts: 5.1%
So indeed, the "most likely scenario" is that you lose 1 pt. But the blended EV is -0.83
One could say that losing 1 pt approximately half the time (passing scenario) is better than losing 2 pts approximately half the time (bidding scenario). That is a factual statement, and concurs with the results I found with my simulator. But it hides or neglects very ugly statics for the other half of the hands.
When bidding, the other half of the hands earn either 1 or 2 pts for your team (just a single point 90% of the time). The expected result is about +1.1
When passing, the other half of the hands earn your team a point or more just 44% of the time, but you lose 2 or 4 pts. 56% of the time. The expected result is -0.63 pts!
So for the favorable half of the hands, you lose just 1 pt rather than 2 pts. (a difference of 1 in your favor). But for the unfavorable half of the hands, you lose 0.63 pts rather than winning 1.1 pts (a difference of 1.73 against you).
So overall, it looks much better to bid D.
But is there a score scenario where it would be better to pass? One that jumps to mind is when the opponents have 8 pts. In that case, bidding D will result in a euchre 49.3% of the time - game over. But if I pass, I only lose 2+ pts 25.8% of the time. And I get the next deal (very favorable).
I have created a program which can calculate the "odds of winning the game", given the current score, the probable point distribution for the current hand, and the "random hand" point distribution probabilities for future hands [it takes into account the fact that neither team will bid alone with 8 or 9 pts]. So I tested a few scenarios.
Your team winning 9-8:
bid: win game 50.7% of the time (obvious)
pass: win game 56.5% of the time (the opponents win the game outright on the current hand just 25.8% of the time, and you have a 67.1% chance of securing a point as dealer on the next hand, so this makes sense)
Score tied 8-8:
bid: win game 38.3% of the time
pass: win game 37.7% of the time
There are a few more paths to victory (or loss) here, which is why using a program helps. It's close, but slightly better to take advantage of the overall point benefit of bidding.
Your team losing 7-8:
bid: win game 28.9% of the time
pass: win game 23.9% of the time
The further you are from victory, the more important it is to accumulate maximum points (on average) in the current hand. So gotta bid here.
Conclusion:
In my opinion, score CAN matter, but is rarely the most important consideration. With this particular hand, the EV story says that you should bid D, but there is one very particular score (winning 9-8) where it is better to pass.
Thank you, justme, for instigating this new line of investigation.
and you're in 1st seat holding
