But I decided to do a quantitative analysis, and here is what I found.

I used a euchre-playing program of my own design (not perfect, but quite good, and I think satisfactory for the purpose), as well as a program which determines the odds of winning from a given starting score, given the dealing partnership [N/S], first hand dealt to E/W (defenders) and turn card [all other cards randomized], and the odds of the 6 possible outcomes from random future games [4, 2 or 1 pt. scored, by dealing partnership or defenders].

I have found that, with randomly dealt cards, the distribution of outcomes is as follows:

4 pts. to dealing partnership [N/S]: 6.5%

2 pts. to N/S: 14.5%

1 pt. to N/S: 45.7%

1 pt. to non-dealing partnership [E/W]: 18.6%

2 pts. to E/W: 12.2%

4 pts. to E/W: 2.5%

I then established 3 sets of hands dealt to 1st seat, for the initial deal:

1) worst hand:

turn card:

2) average hand:

turn card:

3) below average hand:

turn card:

Next, I looked at 2 possible approaches to playing the hand:

A) normally (i.e., 1st seat passes with a weak hand);

B) 1st seat calls dealer up, effectively donating to prevent the dealing partnership [N/S] from scoring 4 pts.

And finally, I examined 3 different scenarios of initial score:

I: E/W winning 9-6

II: E/W winning 9-7

III: E/W winning 8-3

3 hands X 2 ways of playing X 3 initial scores = 18 separate cases.

Score 9-6, in favor of E/W:

[Just as a point of reference, before any cards are dealt, E/W has an 81.6% chance of winning the game, being ahead 9-6 and not having the deal.]

With the worst hand dealt to E/W, I found the distribution of outcomes to be as follows [note: random cards for all subsequent hands, if necessary]

4 pts. to N/S: 22.09%

2 pts. to N/S: 18.6%

1 pt. to N/S: 52.9%

1 pt. to E/W: 1.9%

2 pts. to E/W: 4.5% [mostly from euchring N/S]

4 pts. to E/W: .01%

If 1st seat doesn't donate (passes), the odds of their partnership winning are 63.7%

If 1st seat does donate, the odds of their partnership winning are 74.1%

**Thus, clearly better to donate in this scenario.**

With the average hand dealt to E/W, I found the distribution of outcomes to be as follows:

4 pts. to N/S: 8.5%

2 pts. to N/S: 13.2%

1 pt. to N/S: 54.7%

1 pt. to E/W: 7.4%

2 pts. to E/W: 15.7% [mostly from euchring N/S]

4 pts. to E/W: .5%

If 1st seat passes, the odds of their partnership winning are 78.4%

If 1st seat does donate, their odds of winning the game are 77.7%

**Thus, pretty much a wash (the difference isn't significant). Not ostensibly better to donate in this case.**

With the below average hand dealt to E/W, I found the distribution of outcomes to be as follows:

4 pts. to N/S: 12.6%

2 pts. to N/S: 13.9%

1 pt. to N/S: 62.4%

1 pt. to E/W: 1.8%

2 pts. to E/W: 9.3% [mostly from euchring N/S]

4 pts. to E/W: 0%

If 1st seat passes, the odds of their partnership winning are 72.8%

If 1st seat does donate, their odds of winning the game are 75.9%

**Thus, slightly better to donate under this scenario (though still quite close).**

Score 9-7, in favor of E/W:

Worst hand dealt to E/W:

If 1st seat doesn't donate (passes), the odds of their partnership winning are 57.4%

If 1st seat does donate, the odds of their partnership winning are 68.2%

Thus, clearly better to donate in this scenario.

Thus, clearly better to donate in this scenario.

Average hand dealt to E/W:

If 1st seat passes, the odds of their partnership winning are 72.3%

If 1st seat does donate, their odds of winning the game are 72.6%

Thus, pretty much a wash (the difference isn't significant). Not ostensibly better to donate in this case.

Thus, pretty much a wash (the difference isn't significant). Not ostensibly better to donate in this case.

Below average hand dealt to E/W:

If 1st seat passes, the odds of their partnership winning are 65.9%

If 1st seat does donate, their odds of winning the game are 70.4%

**Thus, clearly better to donate in this scenario.**

Same results as for the score 9-6; not surprising.

Score 8-3, in favor of E/W:

Baseline chance of winning, all random cards: 89.3%

Worst hand dealt to E/W:

If 1st seat doesn't donate (passes), the odds of their partnership winning are 83.1%

If 1st seat does donate, the odds of their partnership winning are 84.1%

Thus, slightly better to donate in this scenario.

Thus, slightly better to donate in this scenario.

Average hand dealt to E/W:

If 1st seat passes, the odds of their partnership winning are 88.1%

If 1st seat does donate, their odds of winning the game are 86.2%

**Thus, somewhat better NOT to donate in this case.**

Below average hand dealt to E/W:

If 1st seat passes, the odds of their partnership winning are 85.8%

If 1st seat does donate, their odds of winning the game are 84.7%

Thus, slightly better NOT to donate, but perhaps insignificant.

Thus, slightly better NOT to donate, but perhaps insignificant.

CONCLUSIONS:

Donating clearly can be advantageous, but it is perhaps overrated. With a truly mediocre hand, donating does appear to increase the partnership's chances of winning the game, especially when winning 9-6 (or 9-7) and the opponents are dealing. The the advantage quickly attenuates as the strength of the hand increases, or the distance from the final 10 points increases. To claim that 1st seat should donate (with the score 9-6 in their favor) whenever they don't have a loner blocked - even if a bower is turned - seems to be too extreme. The ultimate goal is to win the game, not to prevent a loner.

A caveat about my analysis: I accept that my tables of point distribution may be inaccurate. I would be happy to re-run this analysis with numbers you feel are more appropriate. As for the "odds of winning", that is simple math [calculated by a program, and based on the given point distribution - irrefutable].

I welcome your comments.