Calling all number crunchers!!!!

[slamdunkpro]

This discussion came up after a tournament although I would guess it applies to a ring game as well.

Over a six hour tournament with the average # of hands / hour being 30 (180 hands total); 10 players to a table.
If you stayed to the river every hand; based on the random card principal; How many pairs; two pairs; sets; straights; flushes; boats; quads, straight flushes; should one see in a 180 hand session?

This is more academic curiosity than anything else.

[MickeyHoldem]

playing to the river gives you the following chance of making a hand: (mulitplying by 180 gives what you want)
.00031 = str/flush = 0
.0017 = four of a kind = 0
.026 = full house = 5
.030 = flush = 5
.046 = straight = 8
.048 3-of-a-kind = 9
.235 two pairs = 42
.438 pair = 79
.174 high card = 31

I lost a hand by rounding... bad, bad me!

[ornthnooth]

Okay, Instead of actually doing some math, I cheated and put turbo texas hold 'em into no foldem showdown mode with ten players. I multiplied the number of hands seen by 100 (to 180,000) and averaged the results of four random seats after seeing that the numbers were fairly constant and then divided by 1000.

In 180 hands.

Pair 79.05
Two Pair 42.35
Trips 8.67
Straight 8.28
Flush 5.44
Boat 4.69
Quads 0.32
StrFl 0.044
Royal 0.006

I don't know if this data is too helpful. I don't think that the software distinguishes when the made hand is on the board. Also many of these hands are not the best hand upon showdown. I can get those numbers, but that would take more time and would depends on number of players...etc.

Hopes that satisfies your curiosity.

[blank frank]

Of course, if you're looking for a spread, in 180 hands you will probably see:

22-42 high cards
66-92 pairs
31-54 two pairs
4-15 three of a kinds
3-14 straights
1-10 flushes
1-9 full houses
0-2 four of a kinds
0-1 straight flushes

So only about 1 out of 20 nights should a particular one of those ranges broken. However, be careful about taking them all at once. On a given night you have a better than 1 in 3 chance of at least one of those ranges being broken.