[Jerrod Ankenman]

[ QUOTE ]
It's possible no optimal strategy exist from
street to street. Let's start the game from
the turn.
Two person fix limit game. Pot is P after the
flop action. Each bet is 1 unit.
You hold TPTK on the turn.
Opponent checks. You bet. Opp check/raises.
Now your options are fold, call, reraise. If
you reraise, opp has options of fold, call, cap.
Now you have fold and call options.

You---fold----call-----RR-----fold-----call
Opp
fold___-1_____M1____P+2_____xx_____xx
call___xx_____xx_____M2_____xx_____xx
cap___xx_____xx_____xx_____-3_____M3

In matrix M1 the new pot size is P+4.
M2 is P+6. M3 is P+8.

Many of the cells are empty. Other cells
lead to another matrix. The river matrices
must be solved to have values to enter
into those cells. Only then can the
indifferences between line strategies be
solved.
Your linear hand strength will change from
the turn to the river dependent on the river
card. So instead of one M1 matrix, there
may be 46 M1 matrices. This matrix may be
unsolvable. Optimal strategy may not exist.

[/ QUOTE ]

For two-player zero-sum games, optimal strategies always exist. To see this, just specify strategies more robustly, including actions with each hand type in each possible sequence (betting action and cards that have come). Then make a matrix of these strategies. Obviously at least one cell must be the minimax, and therefore optimal.

jerrod