Puzzle: find the worst situation at the River

[primrose]

It's easy to come up with cases where you're guaranteed to have the strongest hand on the River, but what about having the weakest hand? This is a question I've asked myself once for some reason, and I think it makes for a nice puzzle.

Precise specification: choose 5 community cards and 2 whole cards such that the number N of other possible combinations of whole cards that beat you (beat, not tie!) is as high as possible. Note that there are 45*44/2 = 990 other possible hands, so 0 <= N <= 990.

Solution:

Spoiler

You can get a perfect N = 990 by having whole cards with a board of . You have 3 high and only one 3 is left, which means that any other hand has at least 4 high. Alternatively, you can exchange the roles of 3s and 2s, and of course the suits don't matter. Other than that, I believe the solution is unique.

 

[R.Melnyk77]

.... and anyway, there will always be a donkey who will spoil all our calculations

 

[john_entony]

Wow, I looked at the spoiler instantly. Too bad, as I wanted to spend a few hours calculating the worst possible variant of the river. But really, you put too much importance on the cards. I play by my rival and calculate not the best or worst cards combination, but the possibilities to win.

 

[shanest]

imagine that runout in a real game versus 45. crazy