Psychological jujitsu and pitching rotations

Evan and I once (he may not remember) played a card game called "psychological jujitsu" I had discovered in a book. It works like this:

Both of the players are given one suit of a standard deck of playing cards. A third suit is shuffled and placed face down between the players. (The fourth suit is discarded.) One at a time, the cards in the middle deck are turned over. Each player chooses one of his/her own cards as a bid, and they are revealed simultaneously and discarded. The player with the higher bid wins the card in the middle. The goal is to win the most points, where each card counts its value from 1 to 13.

Psychological jujitsu is not a sport, if that's what you're wondering. But I think it is related to the issue of pitching rotations in general, and playoff starters in particular.

The differences are numerous:

1. each game is worth the same,
2. game outcomes are not deterministic given starter selection,
3. starters can be reused given enough rest.

However, the similarities—the list of which I'll leave as an exercise for the reader—are what struck me as I was pondering the question of why Jim Leyland chose Nate Robertson as the game 1 starter for the Detroit Tigers in their divisional series against the Yankees.

The justification at the time was that Robertson was tough on lefties. The Yankees line-up is certainly loaded therewith. But their list of righties—Jeter, Sheffield, Rodriguez, Posada (switch-hitter)—is no walk in the park. Is it crazy to think that perhaps Leyland was willing to risk losing game 1 to try to increase Detroit's chances of winning the series as a whole? And is that what he did?

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Related:

• What are the chances?