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Can You Play With A Worse PR Than Your Opponent?

Posted By: Rich Munitz
Date: Wednesday, 2 March 2011, at 5:19 p.m.

In Response To: Can You Play With A Worse PR Than Your Opponent? (Paul Weaver)

The deal only favors the weaker player if the two players play with low PRs.

It is the difference in PR (which maps to Elo difference) that determines the chance of winning. However it is the absolute PRs that determine the odds being given on the wager. The higher the two PRs with the same PR difference, the closer to a 1:1 wager it becomes.

Lets say the two players have a 50 Elo skill difference. That equates to about a 53.8%/46.2% outcome or the stronger player is a 1.165:1 favorite. Using 33 Elo ~= 1.0 PR, that also equates to an approximately 1.5 PR skill difference. So when does a 1.5PR advantage produce less than a 1.165:1 wager?

1.5 / .165 = 9.1

So if the 50 Elo stronger player plays with a PR of more than about 9.1 while the weaker player plays with a PR of more than about 10.6, the stronger player becomes the favorite in the wager.

A strategy to intentionally make errors to complicate the position is advisable as long as the stronger player can expect the weaker player to make almost as much errors to compensate, since if each player's PR goes up by the same amount it reduces the odds being paid by the stronger player even if it doesn't change his winning chances.

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