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Here's what I don't get. I've played a lot of Hearts for many years - thousands of games I'm sure. The number of times I've played a low heart, and the trick has gone 2H, 3H, 4H, 5H seems way out of probable reality. But the number of times I've seen all four players play the any of the same value card (e.g. 6C, 6D, 6H, 6S) is once. Why is the probability of 2H, 3H, 4H, 5H any lower than any 4 same value cards? In my naiveté it seems that in both cases, the probability calls for 4 players to have a specific card at the same time. Can anyone explain it to me like a 4 year old?

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xkcd.com/1364 –  TimLymington Jun 30 at 22:23
The fact that you see 2H, 3H, 4H, 5H seems surprising. If the player stuck with the 5 is trying not to accumulate hearts, I'd expect that player to slap down the largest heart card he has. If he's trying to shoot the moon, then the 5 makes sense. –  Ellesedil Jul 1 at 0:42
Sorry for not being clearer - the cards most times do not appear in that order but more likely 5H, 4H, 3H, 2H or some other combination started by the 4H or 5H. Thanks for your comments –  Ricksx Jul 8 at 16:00

1 Answer 1

The reason H2,H3,H4,H5 is more likely than H6,S6,C6,D6 is simply the rules of the game. If a heart is led, it is mandatory to play a heart if possible, so most tricks contain four of the same suit, and a trick with one of each suit is extremely rare. When you add in the requirement for all four to be of the same rank, your second example is vanishingly improbable. This boils down to the fact that a card game is not a random selection of available cards (except when my partner is choosing an opening lead, of course).

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There's also the game theory argument that people want to avoid hearts and will be playing their lowest to try and avoid the points, whereas in a situation where they can discard a card off suit, it's much more likely that they might try and discard an off-suite card of high rank. I wouldn't be surprised if all 10s or all Jacks came out in one trick, but other values seem much more unlikely. –  Hao Ye Jul 1 at 0:32

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