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When a team has 3 tricks and the other scores a trick, you can throw in all the cards because you know the team of 3 tricks will get one point only. There is no sense playing out the final trick. I have played both ways and do not have a preference as long as everybody is consistent.
What's the best way to determine the "speed" at which the game is played?
When I used to play a lot of Euchre the side that didn't call trump would often toss in their cards after taking one trick conceding the rest of the tricks to the caller.
Sometimes all it would take is to show the left bower after the right had been played on the first trick.
Each group has to decide what they are comfortable with, but I think the more you play the faster you will get.
Edit: I just realized I misread the question and answered a way more complicated case than what you asked. In the case where you literally already have three tricks and the other team has one, definitely throw it in. My answer below is for the more complicated case where you know what the final score will be without having played enough tricks to actually decide it
It depends on the group, and it can get complicated. You can be in a situation where you each have one point and you know that you can win two of the next three (without knowing which two), and in my normal group that plays all the time showing your hand is generally fine, since everyone else can figure out pretty fast how you were guaranteed to win. In a new group I've only played with maybe three times I did that and there was mass confusion and I ended up spending about a minute explaining why I was guaranteed to win, which is much longer than it would've taken to just play the hand (and probably just annoyed people)
As long as it's a friendly game and it's obvious to everyone why it's a win I would do it; if you think you'll need to explain it I would probably just play the hand out anyway, unless you're trying to teach someone how to tell that a hand is won
I agree with others that the speed of play and the acceptance/willingness to throw in cards increases with the more you play and the more comfortable you become with the game and your partner/opponents.
I usually play the way you describe in your question. We play out all the tricks until the remaining cards no longer have mathematical significance. Sometimes, if I am playing an intense game with beginners or suspected cheaters, I want to see all the tricks played one-by-one so that I can make sure no one gets an unfair advantage by reneging.
