Snakes and Ladders can be analyzed by converting it to a Markov Chain

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While this analysis of probability within a closed system is interesting, Snakes and Ladders can’t be “solved” because it’s not a puzzle or a game. There are no choices to be made except of course whether to engage with the activity.

It is, however, an excellent tool for training kids to follow rules. It’s similar to Candyland in this regard.


From a pedagogical point of view, it is supposed to teach counting in the same way that
Candyland is intended to teach colors. Indeed in a similar way that Monopoly is supposed to teach Georgist economic theory.


Naw dogg, it’s supposed to teach morality.


I did the same thing, for the same reason, 15 years ago when my kids were little… only I didn’t use a Markov chain, I just wrote a C++ program to play a million games of Chutes and Ladders and log the statistics.


It’s been done:

No #ChaseKBH, I will not play Snakes and Ladders with you. It's just an absorbing Markov chain.

— James Howard (@howardjp) December 18, 2014

Just wait until AlphaZero takes a crack at it.

“Markov’s Absorbing Chain” could totally be a D&D spell.

Right up there with “Baneful Slime Counterattack”.



Yeah i was going to say, Shoots & Ladders has a religious origin that goes pretty far back. One can look at the modern incarnation and say it might be about teaching basic rule sets, the original premise is about instilling moral values. Take what you will from that, though i find it interesting.

Given that the game was created to teach kids how karma works, does this mean his analysis has figured out mathematically the best way to ascend to moksha?


I’m quite proud of the fact that I “cheated” at Candy Land for years against my kids without them ever noticing. (I.e. - I stacked the deck with double-color cards so that THEY would get them, win, and the game would be mercifully shorter.)

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It’s very odd, if not impossible, that 67 (a square at the top of a ladder), should be the least-landed on square. Unless we’re ignoring the effects of ladders in calculating that.

I’d like to see more research. Unfortunately, with the current state of the NSF bureaucracy, it might be months if not years before adequate supercomputer cluster time is available.

Another fine teachable moment.


Queen Frostine, double purple, double purple - Game blessedly ends.


You are very lucky you don’t have the version that comes with a spinner instead of cards.

Goddammit! Does this mean Snakes and Ladders is going to fall to computers? What will our S&L champions do when AI takes over that game as well?

Is nothing sacred?

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