maths

Our semi-regular pub quiz ends with the jackpot round - one team competes in a luck-driven “higher/lower” card game to win a jackpot (currently c.£500), and if they lose, some more money is added to the jackpot for the following week. I’d never seen anyone win the jackpot - so was curious to work out what the chances actually are and what the optimal strategy (to the extent that there is strategy beyond the obvious) is.

The cards are dealt without replacing them in the deck, so the probabilities vary during the game, making it trickier to explicitly calculate the probability of winning. But it is relatively simple to estimate using Monte Carlo simulation - running multiple simulated games, counting the wins, and using that to estimate the win probabilities when applying various strategies.

[This post - on archives (and their ultimately inconsequential gaps), the mathematical quirks of unexpected hangings and “The Bottle Imp” by Robert Louis Stevenson - was adapted from a post originally published on LiveJournal on 23 March 2004 and is re-posted here as part of a migration from Livejournal. It has some minor editing, interjections from 2022, and fixing/replacement of broken links - not everywhere has been able to follow Tim Berners-Lee’s 1998-and-still-there advice that Cool URIs don’t change.]

When deciding which home assistant is best, a key test might be “OK Google/Alexa, tell me a maths joke”. (OK, your priorities may vary.) Alexa has a variety. Google has only one, and that is “How do you keep warm in a cold room? You go to the corner, because it’s always 90 degrees.”