I working on some charts and I'm hitting a bit of a block. What I'm trying to calculate is the probabilty of hitting to a specific value or greater. I can figure it out when I'm hitting to numbers up to 9 points higher than my starting value but I'm having trouble for number greater than that. For example: The probabilty of hitting until you get to 18 or greater (but not busting) with a starting hand of 12 is 44.57%. This is because the probabilty of hitting 6 points higher than 12 is 11.14% and since there are 4 point values from 18 and 21 inclusive the total is 4 x 11.14% = 44.57%. So far so good. The problems occur when I want to calculate the probaility of hitting to point values that are 10 or greater. For example: The probability of hitting until you get to 17 or greater (but not busting) with a starting hand of 7 is...? Well the probability of hitting 10 points higher is 38.06% and with 5 non-busting point totals (17, 18, 19, 20 & 21)the total probability would work out at 5 x 38.06% = 190.32%!! That of course is impossible. Can somebody point me in the right direction please? Cheers Reachy
Hitting to specific totals You'll have to do a lot of combinations. There are thousands of possible hands you can get after your initial 7, because of the liklihood of having to take second and even third and fourth hits. You might want to use the dealer outcome probabilities to solve this problem. It gives a dealer's probability of hitting to all the pat totals from a starting point of a 7 upcard. The downside of this is it doesn't give the probabilities of hitting to each stiff total.
I don't think there is a better source than The Wizard of Odds to get this type of info. He may have already done this type of calculation. http://wizardofodds.com/ Hopinglarry
