Assume that player A has 70% chance to win any single match and player B has a 65% chance to win any single match.
What are the % chance that player A will win the match between player A and B?
What are the % chance that player B will win the match between player A and B?
Anyone know a general math to do the above?
My feeling is that the ratio would be 0.7 × 0.35 to 0.65 × 0.3 or 49:39; 55.7% for A, 44.3% for B.
That is, it sounds like a binomial tree problem.
Another problem, the last one:
If player A has a 75% chance of scoring 1 goal and 25% chance of scoring 2 goals
And player B has a 55% chance of scoring 1 goal and 45% chance of scoring 2 goals:
What are the odds of the score 1-1
What are the chance of the score 1-2
What are the chances of 2-1
What are the chances 2-2
I thought it would be for the 1-1 instance , .75*.5 + .55 * .5 = 65%
And I thought 1-2 would be .75 * .55 + .45 * .5 = 60%
but the math doesnt seem right because that is already overt 100% There’s something I’m missing in the math.
Actually I think I just figured it out.
The combined chances of 1-1 and 1-2 is 75%, therefore, 1-1 is 41.25% while 1-2 is 33.75%
And the odds of 2-1 and 2-2, combined is 25%… therefore 2-1 is 13.75% and 2-2 is 11.25%
What u think, is that right?
How would you do that tree given 3 ways:
For any game, player A wins 60%, Loses 20% and Draws 20%
For any game, player B Wins 30%, Loses 25%, Draws 45%
What are the probability player A will win, lose or draw if playing player B.
What are athe probability player B will win, lose or draw if playing player A.
Assuming the goal-scoring is statistically independent, this is clearly a binomial tree problem:
P(1–1) = 75% × 55% = 41.25%
P(1–2) = 75% × 45% = 33.75%
P(2–1) = 25% × 55% = 13.75%
P(2–2) = 25% × 45% = 11.25%
This sounds like a trinomial tree problem:
P(A wins & B loses) = (60% × 25%) / ((60% × 25%) + (20% × 45%) + (20% × 30%)) = 50%
P(A draws & B draws) = (20% × 45%) / ((60% × 25%) + (20% × 45%) + (20% × 30%)) = 30%
P(A loses & B wins) = (20% × 30%) / ((60% × 25%) + (20% × 45%) + (20% × 30%)) = 20%
Nice one! This explanation was a lot better than the original binomial with the 49:39! lol.
I just hope that it’s correct!