Oh, the Possibilties! (HeadsUP Holdem)

Goal: To determine the possible number of states in a 2-player game of limit texas holdem.

Note: In order to determine the magnitude of states, a finite number of raises must be established, so I have set this limit to match what is typically found with online poker sites (a bet and four raises).

1st Objective:
Calculating the number of betting routes before the flop.

(Remember, the button acts first before the flop, and is acting as the small blind.)

c=check f=fold r=raise

f

c c c c c c c c c
c r r r r r r r r
c f r r r r r r
c f r r r r
c f r r
c f

r r r r r r r r
c f r r r r r r
c f r r r r
c f r r
c f

So, there is one course of action when the button starts off by folding, 9 when he starts of by calling, and 8 more when he starts off by raising, totaling 18 courses of action before the flop. (Yes, I realize that some of the lines make little poker sense: such as reraising, then folding, but all lines must be included to allow for a complete model).

2nd Objective:
Calculating the number of betting routes on each street after the flop.

c
c

c c c c c c c c c c
b b b b b b b b b b
c f r r r r r r r r
c f r r r r r r
c f r r r r
c f r r
c f

b b b b b b b b b b
c f r r r r r r r r
c f r r r r r r
c f r r r r
c f r r
c f

So, there is one course of action when they both check, and ten courses each when the 1st player to act checks or bets totaling 21 courses of action on each street (flop, turn, river).

3rd Objective:
Multiplying the possible hand combinations by the possible betting routes.

There are 1,624,350 (1,326 * 1,225) starting hand combinations possible in a heads up holdem match.
There are 18 different ways the betting could go.
So, there are 29,238,300 ways the preflop action could go.

There are 17,296 { (48*47*46)/6 } different flops in a heads up holdem match (knowing all four hole cards).
There are 21 different ways the betting could go.
So, there are 363,216 ways the flop action could go.

There are 45 different turn cards possible.
There are 21 different ways the betting could go.
So, there are 945 ways the turn action could go.

There are 44 different river cards possible.
There are 21 different ways the betting could go.
So, there are 924 ways the river action could go.

So, when you multiply all the ways the action could go on each street you reach the enormous number of 9,273,013,006,761,504,000 ...or 9.273 quintillion. Is this correct? I’ve read the that the possible number of states is just over one quintillion, am I off by a factor of nine???

Did I make any silly mistakes that account for this?

Thanks in advance to all those who math ability is greater than my own (so, I guess, I’ll be thanking a lot of people).

Rick.