From: "Eric I." Date: 2008-01-06T14:05:02+09:00 Subject: Re: Studying Blackjack (#151) After going the randomized simulations route, I was inspired by the precise results you achieved by looking at all permutations. So I decided to try using that technique myself. Here's what I got: upcard bust 17 18 19 20 21 natural ------ ------- ------- ------- ------- ------- ------- ------- 2 | 35.33% 13.94% 13.33% 13.07% 12.40% 11.93% 0.00% 3 | 37.48% 13.28% 13.07% 12.46% 12.18% 11.54% 0.00% 4 | 39.85% 13.07% 12.02% 12.10% 11.64% 11.31% 0.00% 5 | 42.25% 12.10% 12.28% 11.73% 10.90% 10.73% 0.00% 6 | 42.21% 16.62% 10.62% 10.67% 10.12% 9.75% 0.00% 7 | 26.11% 37.05% 13.82% 7.80% 7.88% 7.34% 0.00% 8 | 24.16% 12.97% 36.12% 12.90% 6.89% 6.96% 0.00% 9 | 23.09% 12.09% 11.20% 35.41% 12.11% 6.10% 0.00% 10 | 21.32% 11.29% 11.22% 11.30% 33.56% 3.55% 7.77% ace | 11.59% 12.85% 13.09% 13.02% 13.12% 5.28% 31.07% Although very close, my results do differ slightly from yours. For example you determine that when an ace is the upcard, there's a 36.07% chance of getting 21 exactly. I get 36.35% (31.07% natural + 5.28% "unnatural"). On the other hand we both get a 21.32% chance of busting when the upcard is a 10 or facecard. It'll be interesting to see why that's the case when we post our code solutions. Eric ==== Are you interested in on-site Ruby training that's been highly reviewed by former students? http://LearnRuby.com