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