From: Sander Land Date: 2008-01-05T22:45:50+09:00 Subject: Re: [QUIZ] Studying Blackjack (#151) On Jan 5, 2008 12:25 PM, Denis Hennessy wrote: > Here's my results so far. I don't completely trust them yet since I'm > not sure I understand the blackjack rules properly (I'm assuming the > dealer has to use an ace as 11 unless they bust). I think that's correct. > > /dh > > $ ./blackjack.rb > Odds for each dealer outcome based on initial upcard (2 deck game) > 17 18 19 20 21 BUST > A 12.58% 12.82% 12.75% 12.85% 36.07% 12.93% > 2 13.93% 13.33% 13.07% 12.39% 11.92% 35.36% > 3 13.27% 13.06% 12.45% 12.18% 11.53% 37.50% > 4 13.07% 12.02% 12.10% 11.63% 11.31% 39.88% > 5 12.10% 12.28% 11.73% 10.90% 10.73% 42.25% > 6 16.62% 10.62% 10.67% 10.12% 9.75% 42.21% > 7 37.05% 13.82% 7.80% 7.88% 7.34% 26.11% > 8 12.97% 36.12% 12.90% 6.89% 6.96% 24.16% > 9 12.09% 11.20% 35.41% 12.11% 6.10% 23.09% > 10 11.29% 11.22% 11.30% 33.56% 11.31% 21.32% > J 11.29% 11.22% 11.30% 33.56% 11.31% 21.32% > Q 11.29% 11.22% 11.30% 33.56% 11.31% 21.32% > K 11.29% 11.22% 11.30% 33.56% 11.31% 21.32% Those last four lines are identical. Are you calculating the probabilities and not simulating, or do you just output the last run four times? Here are my results, 2 decks and 1_000_000 deals each. $ ruby1.9 blackjack.rb upcard: 2 17 18 19 20 21 bust 13.9% 13.4% 13.1% 12.4% 11.9% 35.3% upcard: 3 17 18 19 20 21 bust 13.3% 13.1% 12.5% 12.2% 11.5% 37.4% upcard: 4 17 18 19 20 21 bust 13.1% 12.0% 12.1% 11.7% 11.3% 39.8% upcard: 5 17 18 19 20 21 bust 12.1% 12.3% 11.7% 10.9% 10.7% 42.1% upcard: 6 17 18 19 20 21 bust 16.6% 10.7% 10.7% 10.1% 9.8 % 42.1% upcard: 7 17 18 19 20 21 bust 36.8% 13.9% 7.9 % 8.0 % 7.3 % 26.1% upcard: 8 17 18 19 20 21 bust 13.0% 36.0% 12.9% 6.9 % 7.0 % 24.3% upcard: 9 17 18 19 20 21 bust 12.1% 11.2% 35.3% 12.2% 6.1 % 23.1% upcard: 10 17 18 19 20 21 bust 11.3% 11.2% 11.3% 33.6% 11.3% 21.3% upcard: 11 17 18 19 20 21 bust 12.6% 12.8% 12.7% 12.9% 36.0% 13.0%