Mar 02 2009
3-5-7 Poker: The 7 Card Hand
Now that we’ve looked at the 3 card hand and the 5 card hand, let’s take a look at the 7 card hand. With 7 out of 52 cards, there are 133,784,560 possible hands. Of those, 4,324 are Royal flushes; 37, 260 are straight flushes; 224,848 are four of a kinds; 3,473,184 are full houses; 4,047,644 are flushes; 6,180,020 are straights; 6,461,620 are three of a kinds; 20,598,408 are two paying pairs (10s or higher).
Now let’s turn those into percentages. You have less than 1% chance each of getting a royal, a straight flush, or a four of a kind; about a 2.5% chance of getting a full house; 3% chance of getting a flush; 4.5% for a straight, just under 4% for a three of a kind; just over 15% of getting a paying two pair; and about a 69% chance of getting nothing. If you hit the less than 1 in 3 hands that pays, what will you get paid?
Royal-100
Straight Flush-20
4 of a Kind-7
Full House-5
Flush-4
Straight-3
Three of a Kind-2
Two Pairs (10s high or better)-1.
Overall, the 7 card hand gives the house just over a 3.25% edge.
