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Fix typos #9

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4 changes: 2 additions & 2 deletions downloads/notebooks/ChutesAndLadders.ipynb
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Expand Up @@ -1087,9 +1087,9 @@
"\n",
"This vector can tell us what the best first roll is: as my daughter has intuited, starting out by rolling a 1 and climbing the first ladder is best: it decreases your expected time to completion by five moves. The worst first roll is a 2: this actually increases your expected time to completion by 0.5 turns, on average: rolling a 2 to start is akin to moving *away* from the goal.\n",
"\n",
"By the time you get to the 99th square, your espected time to completion is 6 moves, because you have a 1/6 chance of rolling the 1 required to win. Two squares back, on the 97th square, your expected time to completion goes up to 11 moves, because of the chute present on the 98th square.\n",
"By the time you get to the 99th square, your expected time to completion is 6 moves, because you have a 1/6 chance of rolling the 1 required to win. Two squares back, on the 97th square, your expected time to completion goes up to 11 moves, because of the chute present on the 98th square.\n",
"\n",
"The fundamental matrix lets you quantititatively explore a number of other properties of the game; for example, we could adjust the matrix to make square 80 an absorber as well, and ask how probable we are to complete the game there versus landing on square 100 directly. Or we could compute quantities such as the variance of the number of visits and number of steps above.\n",
"The fundamental matrix lets you quantitatively explore a number of other properties of the game; for example, we could adjust the matrix to make square 80 an absorber as well, and ask how probable we are to complete the game there versus landing on square 100 directly. Or we could compute quantities such as the variance of the number of visits and number of steps above.\n",
"For more discussion of applications of the fundamental matrix of an absorbing Markov chain, see the [wikipedia article](https://en.wikipedia.org/wiki/Absorbing_Markov_chain).\n",
"A nice undergraduate-level introduction to these concepts can be found in Chapter 11 of Grinstead and Snell's “Introduction to Probability” (pdf available [here](http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter11.pdf))."
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