When should Carpenter pitch?

This is a follow-up to my earlier post about Leyland using Verlander tonight. Unlike the Tigers, who have to maximize the probability that they will win the next three games, the Cardinals need to minimize that probability. During the regular season, you want the expected value of all the games to be maximized, not the product of the probabilities. That's not the case now.

Just for kicks, what if the probabilities of the Tigers winning the following match-ups was as listed:
Verlander v. Weaver: 50%
Rogers v. Carpenter: 50%
Robertson v. Reyes: 50%
The expected number of wins for each team would be 1.5 if all three games were played, with the likelihood of the Tigers winning all three being 12.5% (1 in 8).

Well, what if the probabilities were as follows:
Rogers v. Weaver: 90%
Verlander v. Carpenter: 20%
Robertson v. Reyes: 50%
The expected number of wins for the Tigers would be 1.6 (1.4 for the Cards), but the likelihood of the Tigers winning all three would drop to 9%.

During the regular season, you'd love to sacrifice one game in a 3 or 4 game set in order to win the rest of them. If you have a 100% chance of winning 3 games and a 0% chance in the other, you'll pile up a lot of wins. But you have no chance of winning all of them (not that it's likely you'll win 162 in a row anyway).

What does any of this have to do with when Carpenter pitches? Well, the best chance the Cards have - if the series goes back to Detroit - is probably matching Carpenter up in game 7 (if it's necessary) against Robertson. Kenny Rogers hasn't allowed a run in three post-season starts. Chris Carpenter isn't as good a pitcher on the road as he is at home, so I'd favor Rogers in game 6. But, Robertson hasn't been as hot as Rogers, so the Cardinals best shot would be trying for a miraculous performance from Reyes in game 6 - and not exposing him to the pressure of game 7 of the World Series - and using Carpenter as the fall back option in game 7.

I'd say Carpenter against Rogers is probably 30% and Reyes v. Robertson in game 7 is a little less. So, the chances that they'd win one of those games is about 50%. However, Reyes has some shot, maybe 10% against Rogers, and Carpenter is probably about 60% against Robertson. That would give them a 64% shot at winning, much better odds than if they match ace v. ace in game 6.