# Making sense of combinatorics-based marketing hyperboles

Diablo 3 has 97 billion possible skill/trait builds. Per class.

LessPop_MoreFizz, emphasis is mine.

I used base two logarithm to claim "97 billion" configurations only are roughly 37 binary choices because $\log_2(97\times10^9) \simeq 36.5$, but I would like to know if there are more refined techniques to remove the marketing out of these big numbers and see their true meaning.

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Dear LessPop, I didn't mean to put your name there to accusingly point a finger in your general direction -- it's merely required by the attribution requirements of the chat content license. –  badp Oct 26 '10 at 10:38
And the Rubik's cube has more than "3 billion combinations" :-) –  Robin Chapman Oct 26 '10 at 11:03
(For those who don't know, Robin is referred to a frequently quoted but totally incorrect number. The actual number of positions is about 4.3 x 10^{19}.) –  Qiaochu Yuan Oct 26 '10 at 13:02
(... and roughly 12 times more @ 5.19e20 if you allow complete disassembly of the toy.) –  Willie Wong Oct 26 '10 at 14:10