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Game Probability Modeling

  1. Jun 25, 2014 #1
    I wanted to model a particular game and determine the probability for each team to win. I have no idea how to do the determination of probability part, but here's the game broken down:

    There are 3 types of players, T's, D's and I's.

    The amount of each type of player is as follows:
    1/8 D
    2/8 T
    5/8 I
    (game is only played in multiples of 8)

    All of the T's, D's and I's are placed in a list, every turn 2 distinct players from the list are chosen randomly and interact according to the following:

    T--fights I, fights D, peace T
    D--kills I, peace D, fights T
    I--fights I, dies D, fights T

    "fights" - a coin flip determines which player goes back into the list for the next round
    "peace" - both players go back into the list for the next round
    "kills" - the player who is killing has a 100% chance to remove the other player from the list and return for the next round
    "dies" - the player who is dying has a 100% chance to be removed from the list
    The game ends when either:
    -only T's remain (T win)
    -all T's are removed from the list (T lose)

    Where should I start in terms of getting the probability breakdown for whether T's win or lose?
     
  2. jcsd
  3. Jun 25, 2014 #2

    mfb

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    2016 Award

    Staff: Mentor

    There are two methods to do this:

    - make a large tree diagram, keeping track of all options (e.g. after one round: [0 D 2 T 5 I or 1 D 1 T 5 I or 1 D 2 T 4 I]). This gives exact values, but takes a while both manually and with computer assistance.
    - simulate 10000 (or more) games and just see how often T wins. This does not give an exact result, but if you have some programming knowledge it could be faster.
     
  4. Jun 25, 2014 #3
    I did the second, I'm a bit disappointed there isn't a more clever mathy way to go about things. :frown:
     
  5. Jun 25, 2014 #4

    mfb

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    Staff: Mentor

    There is a possible simplification: as there is just one D, "D peace D" never happens. Every selection of {D,I} leads to a death of one of them. T does not distinguish between the groups, so you can reduce the analysis to two groups: T and non-T.
    That should have a reasonable tree diagram and it is much easier to evaluate, as you just have to consider four cases each time (T T, T non-T and T wins, T non-T and non-T wins, non-T non-T). Should be possible with pen and paper.
     
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