In my April article in the 2+2 magazine (link
) I describe how to determine the correct action on the river when you are bet into heads up. In the first part I give a formula for calculating the EV of the three raise options. I have expanded this into a spreadsheet that allows you to calculate the EV of all possible river strategies for the three situations you face (being in position when villain bets, being in position when villain checks, and being out of position) given your reads on your opponent. You can download it here
Here is a brief description of how it works. The three tabs on the bottom represent the three possible initial situations you could find yourself in at the river.
For the two in position tabs, the first column is space for you to list the possible hands you think your opponent could have - this doesn't affect the formulas it's only so that you can keep track more easily.
In the second column you list the weighted number of combinations available for that hand. You calculate this by first determining how many possible ways your opponent could have that hand given the board and your hole cards, and then multiplying by the probability that you think your opponent would play this particular hand as it's played out so far. For instance, based on the action preflop, and on the flop and turn if you think your opponent would always play the corresponding hand in this manner simply put the number of possible ways she could have that hand given the board and your cards. If you think that half the time she would play this hand as it was played and half the time she would do something else (remember this is only considering action up until your first action on the river) then multiply this number of combinations by 1/2.
In the third column put a 1 if you are ahead of this hand and 0 if you are behind. Finally, try to determine what they would do with this hand if you were to raise as much as possible (I'm assuming for this spreadsheet that betting is capped at a bet and 3 raises as is standard online). For each of the options in the next several columns, put the percentage of the time that you think that they will do that. So if, for example, you think that they will always call with this hand put a 1 in the call column. If you think that they will 3 bet and fold to a cap half the time and the other half will 3 bet and call put a .5 in each of these columns.
Finally, put the pot size (in big bets) in the red cell under pot size. The pot size is the size of the pot at the time of your first action on the river, so if you are in position and your opponent bet the pot size includes her bet. Once you have filled this out for all possible hands, the EV for all the possible options available to you will appear in the yellow area.
For the out of position tab the process is very similar. The only difference is that now you should specify what your opponent will do with her given hand if you bet out and then raise at every opportunity and if you check and then raise at every opportunity.
The faster, though less careful way to use the spreadsheet is instead of listing all the hands you put them on simply put the percentage of the time that you are ahead in the first cell below "combos" and the percentage of the time that you are behind one cell below that. Put a 1 in the cell below "ahead?" to indicate that those are the times you are ahead. Then, for each of the possible lines your opponet could take you put how often you think they would do that when they are ahead and behind.
Here's an example. Suppose I think I'm ahead 3/4 of the time given the action up until the river. My opponent bets into me. I think that if he has me beat and I raise he will 3 bet and call and if I'm ahead half the time he will 3 bet and fold and the other half he will simply call. If not there, I would click "In position, bet into" on the bottom. Then put .75 in cell B2 and .25 in cell B3. I would put a 1 in cell C2. In cells E2 and F2 I would put .5. In cell G3 I would put 1. After putting in the pot size (say 10), you can see that the EV of folding is zero (no formulas needed there), EV of calling is 7.25, EV of raising and folding to a three bet is 2.875, EV of raising and calling a three bet is 7.875, and the EV of capping is 7.625. Since the largest is 7.875 your best move in this situation would be to raise planning on calling if the villain 3 bets.
If you have any questions feel free to ask them here.