Yes. For this to be satisfied for SVB and Fedor playing bar-box 8-ball, they's need to be flipping a coin for each break. That would make the events (games) independent. For two games as independent events you have, from SVB's perspective
P(WW) = 0.5 * 0.5 = 0.25
P(LL) = 0.5 * 0.5 = 0.25
P(WL) = 0.5 * 0.5 = 0.25
P(LW) = 0.5 * 0.5 = 0.25
As a result you have 0-2 a quarter of the time, 2-0 a quarter of the time, and 1-1 half the time
Depends on your definition of A and B. I view them as P(Shane wins given he breaks) and P(Shane wins given he does not break) since those are the only two options in most any race. In winner- or loser-break format the probability of winning a given game is dependent on the previous games. In alternate-breaks, it is not.
Small nitpick, but I suspect you meant to say that loser-breaks would result in almost all 1-1 scores.For winner breaks, alternate breaks, and loser breaks, the games are not independent events for these runout players. For winner breaks and loser breaks you get almost all 0-2 and 2-0 scores. For alternate breaks you get almost all 1-1 scores.
Agreed.I see what you are saying that the probability of winning game 3 doesn't depend on the OUTCOME of game 1, But game 1 and game 3 are correlated here. The likelihood is high you either win both or lose both
Yes, this is exactly my point.
...then handicapping races based on Fargo is very dependent on table size, whereas I was led previously to believe that Fargo is somehow indifferent to table sizes. If I want to handicap a race to any number n then to do so accurately I need to know the table size. Likewise, as we previously discussed, if I want to handicap a race it would also very much depend on what game the players are playing, for example 9b vs 1p.
I am not sure what you are referring to here. But if you find an example, I will happily concede. I am not wedded to any particular analogy or explanation. I want them to be right and helpful. If they are missing one of those, I will abandon them.
I think the breakdown comes from not having a clear definition of how Fargo is useful and how it should be used. Is Fargo indifferent to table sizes and the specific pool game being played? Or is it not?