December 30th, 2009 by Chris

Cooties took a bit more effort to model in Excel than HHCO because the game has distinct states. The objective is to collect all the body parts of your Cootie bug which include: 1 Body, 1 Head, 1 Mouth, 1 Pair of eyes((A single molded piece)), 1 Headgear[1] and 6 Legs. However, you must collect the Body followed by the Head before any other parts may be collected. Each part is selected based on the throw of a standard 6-sided die. If you successfully add a part to your bug, you get to roll again in the same turn. I didn’t model this, but rather did the statistics based on number of rolls required.

The average number of rolls required to complete the bug, based on 100 Monte Carlo runs, is 44 rolls. I’d estimate a tolerance of about +/- 5 rolls. Any individual player is not likely to reach this number, however, since any one lucky player at the table will end the game considerably earlier.

There is about a 20% chance of victory by 28 rolls for any single player. For four players, the game is over 60% of the time by this point. By 40 rolls, about 45% of players will have won meaning our table of 4 will have completed over 91% of the time. I did have one ‘simulation’ exceed my modeling table with no victory after 100 rolls. The next highest was 77 rolls, but the density increased significantly below that.

Now if we can just get Nate to settle down enough to roll when it’s his turn we might actually get through a game in under 30 minutes.

  1. In the modern version this includes antenna, a hat or a bow. []

6 Responses to “Cooties!

  1. Stephen Says:

    Gosh I hated this game. And I don’t care WHAT the Full Monte stats say, 44 rolls is a pipe dream!!

    Although, now that my daughter can beat me soundly at 80% of the Nintendo Wii games we play, cooties is starting to regain some appeal….

  2. Chris Says:

    Hee hee! Actually, when I think about how long the stinking game seems to last, the 44 rolls seems about right. Figure on 5-10 seconds per turn for adults, 30-60 seconds per turn for kids under 5 (with repetitive “It’s your turn” and “Roll the die” and “Give me the die” and “No it’s not your turn yet” and “Take another leg”.) So with 44 spins and 40-70 seconds per round that’s a good 30-60 minutes. Ouch.

  3. Mike L Says:

    For the sake of your sanity, you could dip into your supply of spare dice and have all players take their turns simultaneously. it probably won’t shave much time, but should at least remove the repetative “give me the die” element. Of course, you know you want to simulate the probability of a tie game now…

  4. Chris Says:

    Curse your compelling comment.

    For 100k Monte Carlo runs (not using Excel anymore), I got an average number of rolls of just over 48. The probability of tie in a 2, 3 and 4 player game respectively is approximately: 0.020, 0.058 and 0.111.

  5. Mike L Says:

    Are those the probabilities of a two-way tie only in the three and four player games, or totals for all possible ties (including three-way and four-way ties)?

  6. Chris Says:

    All possible ties. I used OR logic to combine each possible combination of two players, so if three or four players were tied, it would still satisfy the logic.