Broken Uno house rules; or, the importance of systems thinking, rather than ‘reasoning by Lego’

House rules are a staple of card and board games, and Uno is no exception. Recently with friends, we played some games of Uno, observing a common house rule:

House Rule 1. A player who incorrectly calls ‘Uno’ must draw two cards.¹ (Each player must allow the number of cards in their hand to be clearly visible.)

On this occasion, we also applied another common house rule, described in the 2008 Uno rules as part of ‘Seven-O Uno’:

House Rule 2. A player who plays a ‘7’ must trade their hand with another player of their choice.

Finally, we introduced a somewhat quirky house rule, similar to ‘Jump-In Uno’ but without a ‘jump-in’ element:

House Rule 3. A player can play multiple cards of the same number, regardless of colour, at once. (For example, if the top card on the discard pile is a blue 4, a player could play a blue 6, red 6 and green 6 all at once.)

Individually, these house rules are quite reasonable, and each varies the game in some interesting way. However, in combination, these rules prove to be disastrous.

Under this combination of house rules, a sneaky player could, on every single turn, deliberately incorrectly call ‘Uno’, thereby amassing a large number of cards in their hand under House Rule 1. Were this to be the only house rule, this would simply be a terrible strategy – the potential to pick up some useful cards would be vastly outweighed by the number of additional useless cards amassed.

However, under this strategy, it is overwhelmingly likely that the player will draw some number of 7s. In conjunction with House Rule 2, this makes the strategy somewhat more appealing. If House Rules 1 and 2 were to be the only house rules, though, this still would be a poor strategy. Yes, the player could play a 7 and hand their giant hand to another player, but with that would also come a high probability of giving that player another 7 as part of that hand, thereby giving the advantage to that other player instead!

In combination with House Rule 3, though, everything comes together. Using House Rule 3, all of the 7s could be played at the same time, therefore eliminating the possibility of giving another player a 7.

By using these rules in combination, the player can amass a large number of cards (including 7s), wait until the end of the game, play all the 7s at once, and swap their entire hand with someone close to winning, leaving the victim with nothing particularly useful.

On their own, the house rules were harmless enough, and even in some combinations would not have changed the game significantly. But putting all three together introduced a new failure mode that none of them were susceptible to individually. Even though each house rule behaved well on its own, they did not behave well when combined.

This is an example of what Taylor Hornby (DefuseSec) calls ‘reasoning by Lego’, and has serious implications for more than just Uno (in the linked case, cryptography). The analogy is that, if we consider each house rule to be a Lego brick, then just because each brick is individually structurally sound, it does not necessarily mean that when we join the bricks together the overall structure will be sound. We must adopt systems thinking and consider not only the parts in isolation, but also how those parts interact with each other as part of a greater whole.

Footnotes