Archive for squid

Xing glass bridges [or not]

Posted in Books, Kids, pictures, R, Statistics with tags , , , , , , , on November 10, 2021 by xi'an

A riddle from the Riddler surfing on Squid Games. Evaluating the number of survivors (out of 16 players) able to X the glass bridge, when said bridge is made of 18 consecutive steps, each involving a choice between a tempered and a non-tempered glass square. Stepping on a non-tempered square means death, while all following players are aware of the paths of the earlier ones. Each player thus moves at least one step further than the previous and unlucky player. The total number of steps used by the players is therefore a Negative Binomial Neg(16,½) variate truncated at 19 (if counting attempts rather than failures), with the probability of reaching 19 being .999. When counting the number of survivors, a direct simulation gives an estimate very close to 7:

   mean(apply(apply(matrix(rgeom(16*1e6,.5)+1,nc=16),1,cumsum)>18,2,sum))

but the expectation is not exactly 7! Indeed, this value is a sum of probabilities that the cumulated sums of Geometric variates are larger than 18, which has no closed form as far as I can see

   sum(1-pnbinom(size=1:16,q=17:2,prob=.5)

but whose value is 7.000076. In the Korean TV series, there are only three survivors, which would have had a .048 probability of occurring. (Not accounting for the fact that one player was temporarily able to figure out which square was right and that two players fell through at the same time.)

Looking later at on-line discussions, I found that the question was quite popular, with a whole spectrum of answers… Including a wrong Binomial B(18, ½) modelling that does not account for the fact that all 16 (incredibly unlucky) players could have died before the last steps.

And reading the solution on The Riddler a week later, I was sorry to see this representation of the distribution of survivors, as if it was a continuous distribution!

squid games

Posted in Books, pictures with tags , , , , , , , , , , on October 30, 2021 by xi'an

Following my son’s prodding, I watched the Korean series Squid Games a few weeks ago, before it became a worldwide phenomenon, as illustrated by the French national public radio, France Inter, hosting a talk show with a philosopher and a psychiatrist on the layers of the game! And the French Ministry of Education warning primary and secondary school headmasters of the dangers of copycats in the playgrounds… My overall impression was one of originality with comparison with other K drama series I had watched, even though the realistic early scenes of a deeply indebted and failed father reminded me of several of them, not to mention the beginning of Parasite. The switch to the game playground was much less convincing, with the military organisation of the guards rather caricaturesque, growing worse with the appearance of the fromt row (?) evilmaster, and hitting ludicrous levels with the depraved male clients from all over the World. It seems to me that the series was trying to mix too many layers in its motivations, from the Korean debt culture, to organ trafficking, to keeping family structures, which made the result unconclusive and unsatisfactory. It sounded too artificial to be really dystopic. And knowing most of the characters were going to die (sorry for the spoiler!) did not help in relating to them. But overall I fail to see why this easy twist of children games is such a danger for humanity. Or carrying any deep message to the World. After all, The Most Dangerous Game did not change the course of history!

slow food all’italiani

Posted in pictures, Running, Statistics, Travel, Wines with tags , , , , , , , on September 3, 2017 by xi'an

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