## What Are The Odds?

Back in my entry of 9th of October, you may recall I said that “*I once did a statistical analysis of your chance of rolling at least one 18; I’ll have to see if I can find it.*" As it turns out I couldn’t find it—so I redid it from scratch using perl. The following information assumes a standard "4d6, drop lowest" roll, with no special extras like rerolls or point shift.

The **average roll** on 4d6 drop lowest is **12.244**, compared to 10.5 on a straight 3d6. Your most likely rolls on a straight 3d6 are 10 or 11; this is the basis of the human average as well as minimum and maximums. Of course, a straight 3d6 rarely generates you a lot of high ability scores.

The odds of rolling **an eighteen in one roll** are **1.620%**, or just over one in sixty-two. However, a character has six rolls arranged as desired – the chance of rolling **at least one eighteen** are 9.337%, a little better than one in eleven. With straight 3d6, such as rolling up a commoner, your chances of an eighteen would be a mere 0.463% – that’s only one in 216.

So if less than one in ten characters will naturally begin with an eighteen, what can be done to increase your chances of getting one one? One solution is to play a character other than a human for once. A quick calculation reveals that counting in the +2 racial bonus, the chances of getting at least one eighteen or higher are **56.757%** – more than half.

Here are the statistics generated by my perl script, for your perusal.

Rolling every possible combination of 4d6 drop lowest... Made 1296 rolls of 4d6 drop lowest. The average roll is 12.2445987654321. Score Frequency Percentage One or more ----- --------- ---------- ----------- 3 1 0.077% 0.462% 4 4 0.309% 1.838% 5 10 0.772% 4.541% 6 21 1.620% 9.337% 7 38 2.932% 16.352% 8 62 4.784% 25.482% 9 91 7.022% 35.391% 10 122 9.414% 44.744% 11 148 11.420% 51.692% 12 167 12.886% 56.295% 13 172 13.272% 57.443% 14 160 12.346% 54.643% 15 131 10.108% 47.237% 16 94 7.253% 36.350% 17 54 4.167% 22.536% 18 21 1.620% 9.337%

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Statistics Got to love it

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