I know this blog has been somewhat moribund recently, and I'd like to say I'm taking steps to fix this (Narrator: No such steps are being taken). But every now and then I do think of something to post
I was toying with the idea of a dice game, and came up with an easy but possibly tricky version. It can teach kids about probability and decision make, but at the risk of turning them into degenerate gamblers.
Two player game. Each player has one dice which they roll. At the start of the game they put $1 into the pot. The player with the higher number wins , but ... The loser can pay another $1 for a second roll. If they beat the winners first roll, they win the pot (ie $3) but if they tie or are still lower on the 2nd roll, they lose ($3). If the initial roll is tied, then the players add another $1 to the pot each (bringing the pot to $4 for the next roll). If they player declines the 2nd roll, they automatically lose.
Simple rules I hope, and something that can be easily played (if you have lots of $1 coins).
Where the trickiness lies is in when you should 'buy' the 2nd roll if you lose. If you lose to a 6, then buying a 2nd roll is a waste of time (as ties still lose the 2nd time around). But if you lose to a 2 (because you rolled a 1) then you probably should buy, as you have a 2/3 chance of winning. But the middle numbers become a little bit harder to judge. And secondly, is your decision affected by the size of the pot (eg you've tied 2 rolls in a row, so the pot is now $6 rather than $2).
I fed all this into an AI, just to check the math. It described this as an example of 'option pricing' (ie what should I pay for an expected return) but did not find any examples of this game existing elsewhere (noting it is AI and therefore is probably wrong)
There are also possible variants - One is a gamblers ruin version, where after each tie the pot is doubled (rather than increased by $2). Another is a turn limited game, where you play a fixed number of rounds (say 6 to 10). Does your decision change the closer you get to the finish of the game?
