Background

One of my son’s favorite games he received for Christmas this year is UNO Attack. If you are not familiar with the rules, you can get up to speed here. In short, the rules are no different than usual UNO except when you cannot play, instead of taking a card, you press a button on an UNO card shooting contraption. Most of the time you get no cards, but some of the time it will “attack” with 1 or more cards. Tons of fun.

The Problem

While all four of us in my family love to play this game (ages 3, 5, 34, and redacted), my 5 year old son does not like to lose (who does really?).

I asked him, out of four games, how many he should expect to win. His answer of “1” showed his intuitive understanding of expected value. When I asked him if it anyone should be surprised if they didn’t win 1 out of 4. His answer of “no” shows that he even has an intuitive understanding of variance. Proud Dad.

The Solution

So we did an exercise in probability. What is the probability that he would lose “x” amount of games given each player had a 25% chance of winning.

Game	1	2	3	4	5	6	7	8	9	10
Prob	0.750	0.562	0.422	0.316	0.237	0.178	0.133	0.100	0.075	0.056

No so unlikely that he (or any of us) would lose 4 in a row… It did little to console him. Especially when his 3 year old sister won 1 of those games. It didn’t seem to bother him that mom won the other 3….

The Fun

In my efforts to make this more real to him, I created this shiny app. If nothing else, he like watching the colors move.