[Cs5500] Reputation formula

[Yue Liu]

Hi everyone,

I made the following claim for the formula of reputation points exchanged in
each move:

If winR >= losR,         // winner's Reputation >= loser's Reputation
exchangeR = losR*(baseR - (winR - losR)%);
Else,
exchangeR = losR*(baseR + (losR - winR)%);

If exchangeR < 0, return exchangeR = 0;
Else, return exchangeR;

winR = winR + exchangeR;
losR = losR - exchangeR;

;; Note:
;; exchangeR is the reputation points exchanged in a move.
;; winR is the winner's current reputation points.
;; losR is the loser's current reputation points.
;; baseR is the the maximum acceptable differences between two players'
reputation.
;;   baseR can also be interpreted as the permillage of reputation points
should be exchanged if both player have same reputation.

Examples:
Case 1:
If both Alice and Bob have 100 reputation, and the baseR is 100.
If Alice is the winner, then exchangeR = 100 * (100 - (100 - 100))/1000 =
10.
Alice's reputation will be 110 and Bob's will be 90.

Case 2:
If Alice's reputation is 110 and Bob's reputation is 90, and the baseR is
100.
If Alice is the winner, then exchangeR = 90 * (100 - (110 - 90))/1000 = 7.2.
So, Alice's reputation will be 117.2 and Bob's will be 82.8.

Case 3:
If Alice's reputation is 117.2 and Bob's is 82.8, and the baseR is 100.
If Bob is the winner, then exchangeR = 117.2 * (100 + (117.2 - 82.8))/1000 =
15.75.
So, Alice's reputation will be 101.45 and Bob's will be 98.55.
Case 4:
If Alice's reputation is 160 and Bob's reputation is 10, and the baseR is
100.
If Alice is the winner, then exchangeR = 10 * (100 - (160 - 10))/1000 < 0,
so the exchangeR will be 0.
So, Alice's reputation still is 160 and Bob's is 10. In this case, Alice
will not benefit from the successful refutation,
because we want to encourage Alice to play against smarter avatars,
other than keeping beat the low level avatars to get a higher reputation.

Best,
Yue
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