[well]

Indeed, my solution contained an error.
[ QUOTE ]
Player A
[0,1/12] : raise
[1/12,3/4] : check
[3/4,1] : raise, when called

[0,2/3] : fold
[2/3,1] : call, when raised

Player B
[0,19/36] : raise
[19/36,7/12] : check
[7/12,2/3] : call, fold when raised
[2/3,3/4] : call, call when raised
[3/4,1] : raise

With this, the value of the game for player B is 17/72

[/ QUOTE ]

For the honest raise I actually found [5/6,1] (just as in the other posted solution).
And of course, instead of check it should read fold by player B...

So I like it I got it right, but what I am interested in,
is how others found this solution. I only read some beginners examples on the net,
and tried to work my own way to solutions to other problems.

To find this solution, I first thought what would be the order of
actions for both players when going from 0 to 1.

For A would this be {bet_fold,check_fold,check_call,raise_call},
and for B {fold,raise,call_fold,call_call,raise}
(The first two of B could be swapped, but probably wouldn't make a difference,
and surely swapped will not be better.)

For the strategies (of A, then B) I used
alpha = {a,b,c} and
beta={w,x,y,z},
where the variables play as the "next action"-points.

Now I need to express player B's EV.
But it wildly depends on the order of the values of a,..,z.
For instance y could be between a and b or between c and 1.

So I wrote a program (in Matlab) that tried every set of positions of the variables of alpha in beta.
With this restriction, the payoff-matrix is easily computed, and solutions can be sought by
solving grad(EV)=0-vector.
In order for such a solution (if found) to be (co-)optimal, I figured that the following
criteria would be suffictient:

- 0<a<b<c<1 and
- 0<w<x<y<z<1.

The programme came with the solution posted.

My question is:
- is this anything like you (Craig and Jerrod) solved it?
- are my criteria indeed correct and sufficient?

Thanks in advance,

Next Time.