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# Again in english: Problem with probability formula for gaming logic

 P: n/a Hi, Sorry for posting in German before, totally forgot about that when I was pasting this in here from another German newsgroup I was writing to, trying to get help I am programming a simple version of a soccer simulation The logic works like this so far: [GPG] = constant value goals/game every minute the chance for a goal is [GPG]/90. That goals is shot with probability X by Team1, with (1-X) by Team2. Right now X is set at 50% I'd like to build in a teamstrength formula now. I have a few ideas how to do so already, but I'd like to check some probabilities mathematically first but I am afraid my maths in that area isn't good enough really. Maybe someone can help me and write up a formula for me and maybe even explain it a bit: On the basis of the system descibed above, GPG/90 probability for a goal per minute with X% to Team 1 with 1-X% to team 2 - with what probability wins team1, what probability for a draw and what probability for team2 winning. I need a formula for that which depends on GPG and X A first try that I made to approach this problem seems to be faulty somewhere: Probability for Team1 winning while shooting exactly 2 goals: X = probability for Goal by Team1 per minute (here 2,855/90 * 50% = 0,01585) Y = probability for no goal per minute (here 1-(X+Z) = 0,9682778) Z = probability for Goal by Team2 per minute (hier 2,855/90 * (100%-50%) = 0,01585) In 2 of 90 minutes Team1 must shoot a goal => X^2 In 87 of 90 minutes no goal must be shot, because either Team1 will have more than 2 goals or doesn't win => Y^87 In the remaining 1 minute can either fall no goal or one for team 2 as long as the goal count of 2 for team1 doesn't change by them shooting one => (Z+Y)^1 Probability total = X^2 * Y^87 * (Z+Y)^1 That seems so be wrong though since the value makes no sense. Any help is apprechiated and if possible please not just hints but the full formula. This is not for a test or something if you might think that, it's not even for the game itself, it's just something that would really help me trying to balance the logic of the game by calculating a few possible ways of programming it before implementing them. Thanks Aug 4 '05 #1