Analysis of heads or tails strategies for pub quizzes
- Number of coins
- Team size, number of teams
-
random
-
individual strategies
- choose least popular
- choose based on room_split(option) / P(option success); (same as above for a one coin game)
-
team strategies
- even split across options (e.g. for a two coin game, 25% HH, 25% TT, 50% HT)
- match room splits (e.g. for a one coin game, if room is a 20% H, 80% T split, try to match this as closely as possible within the team)
- inverse room splits (e.g. for the same room split as above, team splits as closely as possible to 80% H, 20% T)
I considered working in the psychology aspect (e.g. accounting for Gambler's fallacy, or a hot-hand bias). If we make the assumption that we can "choose last", then any strategy which is based on the room's split should perform equivalently to any strategy which accounts for these psychological biases. That is because the only thing which is impacted by these biases is the room split itself.
Analysed the impact of the following factors for a single coin game of heads of tails with team play:
- team size
- team strategy
- random
- 50/50 split
- all same every round
- all same in a specific round, and revert to random or 50/50 in other rounds
Team size had the greatest effect. Adding a person to your team provided a far greater impact than any of the strategies tested.
Anlayses a two coin, non-team play game. Introduces a strategy which is depedent on the other player's answers, and finds that the optimal strategy is to select the least popular choice.
In general if less than 25% of the players are opting for two heads then opt for two heads, if less than 25% of the players are opting for two tails then opt for two tails and if less than 50% of the players are opting for one head and one tail then opt for one head and one tail. Mike Fletcher, 2018
To get started with this project, create a python 3.12 environment and run pip install -r requirements.txt from the project's root directory.