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    Matchup Maths

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    Conelead

    Posts : 156
    Join date : 2010-02-16
    Age : 33
    Location : Acton, MA

    Matchup Maths

    Post  Conelead on Mon Mar 22, 2010 5:12 am

    I just did math for hypothetical matchup odds assuming this is true:

    Game 1: 90/10
    Games 2 and 3: 40/60

    and came up with a matchup win percentage of 46%, which was far lower than I expected. This is making me rethink the methodology behind my testing, assuming my maths is correct.

    Odds of winning games 2 and 3 = 0.16
    Odds of winning game 2 or game 3 = 2 * 0.6 * 0.4 = 0.48
    Odds of losing games 2 and 3 = 0.36

    Odds of winning match = (0.9 * 0.48) + (0.1 * 0.16) = 0.46

    This clashes with my experience greatly. I assume I made a maths mistake, but I can't find it.


    Last edited by Conelead on Mon Mar 22, 2010 3:42 pm; edited 1 time in total
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    Chris

    Posts : 75
    Join date : 2010-02-09
    Location : Somerville

    Re: Matchup Maths

    Post  Chris on Mon Mar 22, 2010 3:32 pm

    You actually need to figure out the probability of
    A. winning the first game and winning the second game. B. winning the first, losing the second and winning the third.
    C. losing the first, winning the second and third.

    And add them together.

    In your example (.9*.4)+(.9*.6*.4)+(.1*.4*.4) = .36+.216+.016 = .792, 59%

    Even though your math is wrong the conclusion that post sideboard games are much more important is absolutely correct.
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    Conelead

    Posts : 156
    Join date : 2010-02-16
    Age : 33
    Location : Acton, MA

    Re: Matchup Maths

    Post  Conelead on Mon Mar 22, 2010 3:41 pm

    That makes much more sense. I flopped the odds of winning/losing games 2 and 3 in my post by mistake, but forgot to include the option of "winning all three games" or, in other words, winning game 1 and 2 and having it stop there. Okay, that jibes much better with my experience. I know that post-sideboarded games are very important, but my testing methodology takes into account what happens when Game 1 is really bad. Normally I see how much sideboard space it takes to get G2 up to 50/50, and decide based on that whether or not it is worth sideboarding any specific cards for that matchup at all. Merfolk vs. Zoo in Legacy is a great example. Game one is abysmal for Merfolk, and it isn't worth the slots in the board. My active decision would be to not board any cards specific to the Zoo matchup, because it is too bad for it to be worth addressing. This situation comes up reasonably frequently in testing, especially for Legacy and Extended, and if my initial math was correct I would have to rethink that methodology. Luckily it is not. I have fixed the typographical error in my post. So, new maths looks like this:

    Game 1: 90/10
    Games 2 and 3: 40/60

    and came up with a matchup win percentage of 46%, which was far lower than I expected. This is making me rethink the methodology behind my testing, assuming my maths is correct.

    Odds of winning games 2 and 3 = 0.16
    Odds of winning game 2 or game 3 = 2 * 0.6 * 0.4 = 0.48
    Odds of losing games 2 and 3 = 0.36

    Odds of winning match = (0.9 * 0.16) + (0.9 * 0.48) + (0.1 * 0.16) = 0.144 + 0.432 + 0.016 = 0.592

    So we have a 59% match-up, which is a little below what I expected, but close enough that it matches reasonably with experience. That is useful information to know, frankly.

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