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BGonline.org Forums
PR bet
Posted By: maxim
Date: Thursday, 29 November 2018, at 7:28 a.m.
Up to now, two players A and B played heads up many money games and their PRs taken from their XG profiles with those games are PR(A, profile) and PR(B, profile) respectively.
(As a reminder, PR in XG is not a simple average, it is calculated with 1000 decisions half life, so it weighs recent decisions higher than old decisions.)
Today, players A and B decided to play several games (session) and bet who can play better than their regular profile PR. The goal is to encourage themselves to progress faster long term.
After each session: Player A will pay player B: payoff(A) = $N * ln( PR(A, session) / PR(A, profile) ), which is negative (A gets the money from B) if PR(A, session) < PR(A, profile), or positive if PR(A, session) > PR(A, profile) Same for player B. So, there are two mutual payoffs. $N is some constant, the same for both players.
ln (logarithm) function is used to bring the lognormal PR distribution [0, infinity] to normal [- infinity, + infinity] range.
In order to guard against extremely low PR(A, session), it is assumed not to be lower than PR(A, profile) / 5, otherwise the payoff will shoot into -infinity
In order to guard against players playing extremely bad during a particular session for whatever reason (short session, distracted), the total mutual payoff is capped with some reasonable amount of money.
After each session PR(A, profile) and PR(B, profile) are naturally updated in XG with the results of the session.
Questions:
1. Does this “beat your own PR” bet seem fair?
2. Does this bet seem fair long term, if the players repeat it many times over a long period of time?
3. If the players levels are very different, PR(A, profile) / PR(B, profile) ~= 2, what would you suggest to change in the payoff to signify that it is harder for player B to improve over time compared to player A? Or this concern is already addressed in using ln ?
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