PDA

View Full Version : How many combinations of heads up action are there?

ZeeJustin
12-15-2004, 07:49 PM
Let's say the cards don't matter, or perhaps they are already known. How many different ways are there that a heads up hand can be played?

Lets assume it's heads up, player X posts the SB, and player Y posts the BB. The SB is also the button.

1 possible combination would be, X raises, Y folds.
Another combination would be, X calls, Y checks. Y bets the flop, X raises, Y folds.
Etc.

How many of these combinations are there total?

Edit: Assume each player has over 12x BB, and the 4th bet is a cap, like on party.

RocketManJames
12-15-2004, 08:18 PM
Here's a quick stab at this.

Pre-flop:
F
LC, RC, RF
LRC, LRF, RRC, RRF
LRRC, LRRF, RRRC, RRRF
LRRRC, LRRRF

14

Other streets:
CC, BC, BF
CBC, CBF, BRC, BRF
CBRC, CBRF, BRRC, BRRF
CBRRC, CBRRF, BRRRC, BRRRF
CBRRRC, CBRRRF

17

So, I have 14 * 17^3 = 68782.

There's a good chance I am not right, but like I said, a quick stab at this.

-RMJ

MortalWombatDotCom
12-15-2004, 11:54 PM
you can't just multiply your 14 by 17 ^ 3 because any time a betting round ends with a fold, there is only one way for the non-existant rounds to play out.

assuming i correctly counted that 7 of the 14 preflop sequences and 8 of the following sequences end with one player folding, how about
7 + 7 * (8 + 9 * (8 + 9 * 17)) = 10206?

RocketManJames
12-16-2004, 12:37 AM
Doh! I knew I had done something silly. Ha ha. I'm such a moron.

-RMJ