The Rule of 4
One of my favorite card games is called “The Mind”. It is an incredibly simple game with cards numbered from 1-100. Without communicating with words or gestures, the players have to lay their cards down in ascending order. Cards are kept concealed so there is no way of knowing what the other players have. The only form of communication you have are facial expressions and delayed action to provide some indication of what card you have to others. A smile and nod or an eager gesture for example would mean that you think you should go next and are ready to lay down your card. A head shake on the other hand would indicate that you don’t think you should go and that you have a very high number. After playing this game several times, I came up with a strategy called “the rule of 4”, which was my attempt at game theory before ever having learned of the subject.
The Rule of 4 is essentially saying that if you have a 1, for example, you can immediately lay down your card because no one could possibly have a lower number than you. It follows that if you have a 2, and no one immediately lays down a 1, you can lay down your card. This is because if anyone did have a card lower than yours, they would immediately know to lay it down because there would be no logical reason for them to wait. Because people with cards 1 or 2 would almost immediately lay down their cards, it follows that if no one does so, a person with card 3 could lay down their card. Because cards 1 and 2 would immediately be laid down if they were in play, a person with card 3 can be confident that no one has a lower card than them, and therefore can confidently lay down their card. A person with card 4 can then reason that anyone with cards 1, 2, and 3 would already have laid down their card, and can with almost complete certainty, know that they have the lowest card. However, past a card of value 4, assumptions can no longer be made nearly as confidently, especially if players are not aware of The Rule of 4. Although the rule may be difficult to understand in this context, it is made immediately clear during game play.
When we first started studying game theory in class, I was reminded of the time I came up with this strategy, as it also involves a delicate balance of players making choices that have different outcomes. Players have the choice to either lay down their card or wait depending on the values of their cards. If player 1 lays down cards more readily than player 2, this can disturb the balance and result in cards being laid down out of order, causing the whole group to lose a life. The entire purpose of the game is assessing your options, (to wait or not to wait), while also assessing the probability of what cards the other players are holding. The game can only be beaten if all players are relatively on the same wavelength regarding how readily they should lay down cards of different values. And this length of delayed action changes each round as more cards are in play (round 1: 1 card each …. Round 12: 12 cards each).
https://arstechnica.com/gaming/2018/08/the-mind-most-polarizing-card-game-of-the-year/