3-flush in omaha

[2ndGoat]

The game is OMaha or Omaha8, doesn't matter.

On the river the board is H H H S C

What are the odds that a random 4-card hand has 2 hearts?
What are the odds that against 2/3/4/5 random hands, none have a flush?

2nd

[elitegimp]

1st question:

There are 5 known cards, so you are dealing 4 card hands out of a deck of 47, with 10 hearts left in that deck.

There are 47 choose 4 = 178365 ways to deal 4 cards
Of those, (10 choose 2)*(37 choose 2) = 29970 have 2 hearts
Also, (10 choose 3)*37 = 4440 have 3 hearts (still a flush), and (10 choose 4) = 210 have 4 hearts.

So there are 29970+4440+210 = 34630 ways to deal a flush, out of 178365 ways to deal a hand. 34620/178365 = 0.1941, or 19.4%. (16.8% of the total hands have exactly 2 hearts).

I'll let someone else answer number 2.

edit: a lot of wrong numbers [img]/images/graemlins/crazy.gif[/img]

[2ndGoat]

lol thanks for the correction, I would have probably believed you to the grave.