Now that I've got my program to work I forgot why I wrote it in the first place!!! What I want to know is how to use the data that it's generating. Here is an example (I don't have the program in front of me so this is from memory): I want to know what my probability of winning when the dealer has a 2, my opponent has 17 and I have hard 5 and I hit to at least 18 (I am BR2 acting last, a single bet win by me would beat a push or loss from BR1). I have a 51.8% chance of being successful hitting to 18+ and I have a 14ish% chance of hitting to 18, no more no less. To calculate my chance of success the formula would be: Prob=R x (prob of Dealer 17 or 18) + R x (prob of Dealer 17, 18 & 19) + R x (prob of Dealer 17, 18, 19 & 20) + R x (prob of Dealer 17, 18, 19, 20 + 21) Prob=R x (13.97%+13.44%) + R x (13.97%+13.44%+13.00%) + R x (13.97%+13.44%+13.00%+12.40%) + R x (13.97%+13.44%+13.00%+12.40%+11.84%) Now the question is what should R be? Initially I thought it should be the 14ish% figure but now I wonder whether it should be 51.8%/4=12.95%. Since 51.8% is the probability of hitting to 18, 19, 20 or 21 would it be correct to divide it by 4 to get the probabilities of hitting those totals individually? Cheers Reachy
Unfortunately, there's no shortcut here. The probabilities for hitting to different totals varies. For example, if you start with a hard 8 and plan to hit until you get to 17 or higher, you're more likely to end up at 18 than the other totals, because of the big influence of the ten-valued cards. So, to solve your problem, you have to work out all the possibilities: Your strategy starting with hard 5 is to hit to hard or soft 18 or better. (That's strategy "h18s18" in the notation from my next All-In article). You'll need to calculate probabilities for each outcome: p(18), p(19), p(20), p(21), p(Bust). You also need the dealer probabilities d(17) through d(21) and d(Bust). Then your chance of success is: p(18) * (d(17)+d(18)) + p(19) * (d(17)+d(18)+d(19)) + p(20) * (d(17)+d(18)+d(19)+d(20)) + p(21) * (d(17)+...+d(21)) Note that this calculation assumes you have three ways to win: You win/Opponent loses You win/Opponent pushes You push/Opponent loses If the push/loss outcome is no good, the calculation is slightly different. The first line would be "p(18) * d(17)" for example.
stop at 18 I thought the problem with calculating P(19), p(20), p(21), etc when you objective is to reach 18 or more is that p(19) would mean hitting if you got 18, p(20) would mean hitting is you got 18 or 19, and so on. Those actions would violate the initial strategy of hitting to at least 18 and then standing. Am I missing the point? Cheers Reachy
Almost there Reachy, your program will already be doing the necessary work. However, rather than just build up a single grand total of the probability of success, you need to maintain separate probabilities for each total you can reach. E.g., when you've found a hand, if its total is 20 and its probabaility is P, then you can say p(20) = p(20) + P You could continue to mantain the grand total, or generate it when needed by summing the subtotals. Oddly enough, I've just been adding this refinement to my own version.
Check it! Made the changes to my program as instructed. This is my output for hitting hard 5 to H18S18: Code: Total - 50.0400129% 17 - 0% 18 - 13.2015056% 19 - 12.7463395% 20 - 12.2911734% 21 - 11.8009944% Does that look any good? Cheers Simon
Those are perfect Reachy. Nice work! If you'd like to check any other strategies for hard 5, here are a few: h17s17: (Stiff: 0.00%, 17: 12.23%, 18: 12.23%, 19: 11.77%, 20: 11.31%, 21: 10.82%, Bust: 41.64%) h18s18: (Stiff: 0.00%, 17: 0.00%, 18: 13.20%, 19: 12.75%, 20: 12.29%, 21: 11.80%, Bust: 49.96%) h19s19: (Stiff: 0.00%, 17: 0.00%, 18: 0.00%, 19: 13.85%, 20: 13.39%, 21: 12.90%, Bust: 59.86%) h20s20: (Stiff: 0.00%, 17: 0.00%, 18: 0.00%, 19: 0.00%, 20: 14.56%, 21: 14.07%, Bust: 71.36%) h21s21: (Stiff: 0.00%, 17: 0.00%, 18: 0.00%, 19: 0.00%, 20: 0.00%, 21: 15.33%, Bust: 84.67%) And, in case you'd like to try one where your soft goal is different from your hard goal, how about this one: h18s19: (Stiff: 0.00%, 17: 0.00%, 18: 12.40%, 19: 12.89%, 20: 12.44%, 21: 11.95%, Bust: 50.32%) This strategy would hit a soft 18, but stand on a hard 18.
Ken beat me to it Code: Prob OK: 50.0400443% Prob 18 : 13.2015135% Hard: 11.9725649% Soft: 1.22894857% Prob 19 : 12.7463473% Hard: 11.5173988% Soft: 1.22894857% Prob 20 : 12.2911812% Hard: 11.016716 % Soft: 1.27446518% Prob 21 : 11.8010023% Hard: 10.4810205% Soft: 1.31998179%
It's alive!!! Amazingly my program comes up with the same answers as you Ken. That must make me a genius ! Now, to hit to different hard and soft totals will require further programming I suspect... Cheers Reachy
Showboating Bloody show off! Now you're splitting your outcomes into hard and soft totals!!!! I suppose you were learning 2 oriental languages at the same time? Cheers Dr Reachy, Head of Blackjack Programming, Reachsoft Corp.
More showboating h18s19: Code: Prob OK: 49.6845721% Prob 18 : 12.4036366% Hard: 12.4036366% Soft: 0 % Prob 19 : 12.8938156% Hard: 11.5703325% Soft: 1.32348307% Prob 20 : 12.4386494% Hard: 11.0696497% Soft: 1.36899968% Prob 21 : 11.9484705% Hard: 10.5339542% Soft: 1.4145163 % I've also got it set up to allow for a specific number of decks or deck composition, and an actual hand rather than a notional total. What is really lacking at the moment is a user interface. I have to change the program and recompile every time I want to try out a new test case.
славно вас для того чтобы заметить or agradable de usted notar or aardig van op te merken u Just don't ask ME to compute anything!
This is easy!!!! A quick change to my program and I can now do different hard and soft totals!!!!! I'm getting good at this But just in case can you check these numbers? Hit 7 to Hard 18 Soft 19: Total - 46.027577% 17 - 0% 18 - 11.620638% 19 - 11.6207017% 20 - 11.6207017% 21 - 11.1655356% Hit 4 Hard 17 Soft 19 Total - 60.0088302% 17 - 12.3888681% 18 - 11.8609831% 19 - 12.4215095% 20 - 11.9313306% 21 - 11.4061389% Cheers Reachy
I concur, Dr Reachy Code: Prob OK: 46.0276457% Prob 18 : 11.620703 % Hard: 11.620703 % Soft: 0 % Prob 19 : 11.620703 % Hard: 11.028987 % Soft: 0.591715976% Prob 20 : 11.620703 % Hard: 10.437271 % Soft: 1.18343195% Prob 21 : 11.1655368% Hard: 9.98210488% Soft: 1.18343195% Code: Prob OK: 60.0117615% Prob 17 : 12.3880315% Hard: 12.3880315% Soft: 0 % Prob 18 : 11.8601466% Hard: 11.8601466% Soft: 0 % Prob 19 : 12.4230443% Hard: 10.9522382% Soft: 1.47080607% Prob 20 : 11.9328654% Hard: 10.4165427% Soft: 1.51632269% Prob 21 : 11.4076737% Hard: 9.84233313% Soft: 1.56534058%
