GNU Backgammon

 JSD's and confidence intervals

 From: Daniel Murphy Address: raisingcain@readyandabel.com Date: 9 January 2005 Subject: JSDs and Confidence intervals Forum: GammOnLine

```If we roll out two plays, and they are separated by X JSDs, what is the
confidence interval? If the confidence interval is Y, how many JSDs are
the plays separated by?
```

 Tom Keith  writes: ```I did a computer simulation tossing 2 coins each 1000 times to see which one came up heads more often, and did this a million times. The chart below shows the results. The first column is the number of JDS's difference between the coins' probability of landing heads. The second column is the fraction of time that the coin biased in favor of heads was also the coin that landed heads more often. The third column shows the probability we'd expect mathematically if the values being compared were normally distributed. P(Order is Correct) ------------------------- JSD's Simulation Mathematical ----- ---------- ------------ 0.0 0.500000 0.500000 0.1 0.544514 0.539828 0.2 0.579752 0.579260 0.3 0.614363 0.617911 0.4 0.648087 0.655422 0.5 0.696493 0.691462 0.6 0.727010 0.725747 0.7 0.755925 0.758036 0.8 0.783103 0.788145 0.9 0.820406 0.815940 1.0 0.842885 0.841345 1.1 0.863430 0.864334 1.2 0.882059 0.884930 1.3 0.906512 0.903200 1.4 0.920593 0.919243 1.5 0.933008 0.933193 1.6 0.943867 0.945201 1.7 0.957498 0.955435 1.8 0.964999 0.964070 1.9 0.971378 0.971283 2.0 0.976759 0.977250 2.1 0.981262 0.982136 2.2 0.986616 0.986097 2.3 0.989402 0.989276 2.4 0.991669 0.991802 2.5 0.993498 0.993790 2.6 0.995579 0.995339 2.7 0.996613 0.996533 2.8 0.997424 0.997445 2.9 0.998055 0.998134 3.0 0.998742 0.998650 3.1 0.999068 0.999032 3.2 0.999314 0.999313 3.3 0.999500 0.999517 3.4 0.999692 0.999663 3.5 0.999780 0.999767 3.6 0.999843 0.999841 3.7 0.999889 0.999892 3.8 0.999923 0.999928 3.9 0.999955 0.999952 4.0 0.999969 0.999968 ```

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