Never deal unless you believe you are not going to win.....
You should NEVER believe you cannot win!
Wat? that's crazy.
Its simple math combined with your assesment of skill and chipstacks. And the bigger the money, the more you should be willing to take a deal, assuming it is a fair one.
3 examples.
1) $11 rush tourney. We got down to 4 left and all had 8 or 9 BB. we could ICM chop and everyone gets around 2d place money $260ish. If we played it out, it was around $180 more to the winner and 4th place was probably $130 less.
Unless I think I have a huge edge at push/folding here it's crazy not to chop. In reality, I think there were 2 better and two worse players, but this was going to be a crapshoot. So I locked in the 2d place money. Of course I believed I could win. I also believed I could come in 4th just as easily.
2) $3 rebuy on stars. I got HU and we were at identical stacks 100bb deep and had been playing 8 hours. 2d was I think $4900 and first $6500 or so. Now in this case that's a sizable swing in dollars. I also know that HU isn't the best part of my game, and that it could take a LONG time to play at 100bb deep. opponent offered to even chop the money - he didn't want to play anymore. In the end we split it at 5500 each and played for 500 to the winner. If I felt like I had a huge efge here then I might well refuse the chop at the beginning. But in this case I'm probably even or behind skill wise. So taking the deal and playing out for the 500 makes the most sense... and is a smart variance hedge.