Why does a FargoRate 100 point difference not exactly equal 2-1 in games?

iusedtoberich

iusedtoberich

AzB Silver Member
Silver Member
Is the 2-1 game score for a 100 point spread an approximation? I always thought it was the whole basis for the system and "exact". Also, why do the odds change based on the match length? See 3 screenshots below.

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Because it's 2:1 for a single game. As the races get longer the chances get closer to even that either player will hit their respective number first for any 2:1 ratio.

If it weren't essentially 50/50 for a 600 player to reach their 2x number before a 500 player reaches x, then the true odds would not be 2:1. That is the "even" matchup.
 
Think of the 2-to-1 race. For the stronger player to win he must win the first 2 games. The chance of doing that is 2/3 X 2/3 which is 4/9, a little shy of half. As the race gets longer, as you show, the difference gets smaller.
 
mikepage said:
Think of the 2-to-1 race. For the stronger player to win he must win the first 2 games. The chance of doing that is 2/3 X 2/3 which is 4/9, a little shy of half. As the race gets longer, as you show, the difference gets smaller.
Click to expand...
So the reason is because it's a "race", and one player will get to the goal first? If, for a hypothetical example, the players were allowed to "tie" at their score, regardless of who got there first, would the calculator then show the 2-to-1 set score was exactly 50/50 odds?
 
iusedtoberich said:
So the reason is because it's a "race", and one player will get to the goal first? If, for a hypothetical example, the players were allowed to "tie" at their score, regardless of who got there first, would the calculator then show the 2-to-1 set score was exactly 50/50 odds?
Click to expand...
I think not quite but almost. Suppose Fedor and Kristina are 100 points apart. That means Fedor has a 2/3 chance of winning each game and Kristina a 1/3 chance. If they play 81 games, Fedor is expected to won 54 and Kristina 27.

Now suppose we look at those 81 games as 27 groups of 3

We expect FFF to occur 8 times (2/3 X 2/3 X 2/3 = 8/27)

So here are all the possibilities and the number of times they are expected to occur out of 27
FFF 8
FFK 4
FKF 4
FKK 2
KKK 1
KFF 4
KFK 2
KKF 2

The first two lines totaling 12/27 are the times Fedor wins the race to 2 (That's the 4/9 I mentioned). The other 15/27 times, Kristina wins one of the first two games and so wins the handicapped race. But if you add up all the games it is 2-to-1
 
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