proportions problem

comodin

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Oct 13, 2014
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hi

sorry for my English



Suppose two players Chess Player A and Player B. Each of them has a ranking (RA and RB) ranging from 0..100
We set (is inconsequential the like) a value to range between 0 and 100 that we call "space stalemate" ST [/ b] which marked the "space" within which a hypothetical game between the two players heading end in stalemate.


The result of a hypothetical meeting between the two, assigned a value in% of probability… stalemate would be valued: PT , you win the Player A: PA , and Player B wins: PB

Assumptionsif the twoplayers face offina game:


a) The difference between RA and RB is 0: the game would end in stalemate and there would be no chance of winning the played A or Player B (STRICTLY)

RA = 80; RB =80; ST = 15;
RARB = 80 – 80 = 0
PT100% ; PA% ; PB = 0% ;


b) The difference between RA and RB is less than the value of ST
Ranking higher A than Rank B: Since the difference between the rankings is within space stalemate s ST , the game will most likely runs on stalemate, however will continue having the possibility of A player wins or Player B


RA =80 ; RB =70; ST = 15;
RARB = 80 – 70 = 10 < ST
PT = ¿? % ; PA < PT % ; PA < PB% = 100 – (PT+PA)


c) The difference between Rankin A and Rank B is greater than the value of stalemate Area ST : Not being the difference in rankings in the space stalemate will be more chance to win one of the two players (who have more Ranking)


PlayerBRanking >Player A Ranking

RB[/b ] =80 ; RA =10; ST = 40;
RBRA = 80 – 10 = 70 > ST
PB = ¿? % ; PT < PB % ; PA< PT% = 100 – (PB+PT)



e) The difference between Ranking A and Ranking of B is equal to the value of space stalemate: exist the very possibility of that occurring stalemate to win the Major Ranking

RA =80 ; RB =40; ST = 40;
RARB = 80 – 40 = 40 = ST
PA = ¿? % = PT% ; PB= 100 – (2*PA)

In summary

· If the difference rankings is 0 .. stalemate possibility is of 100%

· If the difference Rankins is LESS than the value of Space stalemate, possibility is then most stalemate and the rest is divided among the winning chances of each player

· If the difference in ranking is EQUAL to the value of Space stalemate chance to win the highest ranking and played that stalemate are given is the same.


· If the difference value is GREATER ranking of stalemate Space no more chance of winning the highest ranking ... played followed by: Possibility stalemate .. Ability less Player Ranking


The question would be: given the rankings of the players RA and RB and the value of spacio tables ST in a hypothetical confrontation which would be likely you will be paid team that PA that won the team B PB to do ode stalemate PT

Thanks for your time
 
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