Last hand, Min/Max 100/500 no surrender, BR1 1351 first to act, bet 325 and BR2 1000 chips bet 500. BR1 (me) dealt hard 15, BR2 8 and dealer up card 9. (- How wrong it was in % to double my hard 15?)
Quick No-sim Analysis I think that doubling your 15 is the correct move, unless you have a basic strategy opponent. Vs a basic strategy opponent you already have the high and the low. He has to win while you push or lose. You know that he won't double. In that case, I would hit to 17 or better. However, Wong's table 5 says to stand on 14. Vs a skilled opponent, if you don't double, your opponent will. By doubling yourself first, you give up a lose/push outcome, but you cover the double. I think that covering the double is more valuable. This seems similar to an actual situation that happened to me and which was discussed here: http://www.blackjacktournaments.com/bb/showthread.php?t=7492 In this situation, I had the same outcomes covered and had hard 17, acting first vs dalexy2kbj's 9 vs the dealer's 3. In this case, I knew he was a skilled player and it turned out to be correct for me to double even my hard 17. I'll hold off on any sim results until others have had a chance to weigh in.
Thank you, but I am not sure if that is pretty much the same with your situation, because doubling 9 vs 3 is likely to be a winner while doubling 8 vs 9 is not.. ?
Stand If you stand your opponent beats you if he wins his double down. You can check on Ken’s table for chances of winning that double and it is about 28.5%. If you stand and your opponent plays basic strategy he beats you if he wins and the dealer doesn’t bust. From gronbog’s table “must win, all totals hands” you can see that 8 vs. d’s 9 wins 34%. Since your 8 would bust 24% (hitting to 17) and not bust ¾ of the times then you have to deduct 3/4th and dealer busts (23%) from the total wins. So, 34% minus 17% leaves your opponent with almost 17% wins when the dealer makes a hand. To consider winning the game by doubling your opponent chances have to be lesser than 28.5%, or even smaller if your opponent is not an expert. If you double your opponent will just hit to at least 17 and one point more than your double. By doubling down you giving up your opponent push if you bust - that’s seven out of thirteen double down cards (54%). 8 total using dealer’s strategy vs. d’s 9 pushes 11.5%, and wins 34% of the times. 54%x45.5%= 24.5% There are still five cases of your double 15 left to analyze, totals 16 to 21, each having 1/13 chance. For doubling to be a better play you can give up no more than about 4%. If you hit an Ace than your opponent has all the pushes 11.5% and wins with the dealer non-busted hand (as in the case above stand on 15) 17%. Similarly, with your double total of 17 (except that you have pushes on 18 or better 10%). So, 2/13 times ~27.5% = 4.2% And 24.5%+4.2% is about equal with 28.5% - the best result if you stand and your opponent doubles. There are still cases where your opponent gains on you even if your double is 18 to 20 – but not by much. Without calculating it my guess would be about 1.5%. Doubling 15 and your opponent playing optimally gives him about 30% chance of winning. S. Yama
Thank you, Mr. S. Yama ! Yes, I knew he should (and would) double in the case if I stand and that he will have about 28.5% to win.. what I didn`t know was the rest of the calculation, how much I would leave him if I double.. I only figured out that about 29.3% (when I don`t lose) my double would not hurt me. Certainly it is a very complex calculation, and in 20 seconds I only figured out that has to be a close call. I knew that my opponent will double, but I also guesstimated that my opponent might (incorrectly) still double if I hit Ace or 2 (maybe even 3) on my own double for a total of 16-18, and that would help? Thanks to your analyze, I see that my double was the wrong decision, losing about 1.5% in total EV. This means if I had 14 instead of 15, I should double ?
a close decision The difference between doubling on 14 and 15 is that you will end up with one more stiff and one less bust hand; all the other results stay the same. Since your opponent has about 45.5% chance when you bust and 28.5% chance of gaining on you when your double is a stiff then 1/13 times the difference between the chances (17%) improves your situation by less than 1.5%. It is almost equally good play, whether you stand or double (perhaps a quarter percent better to double) but the exact calcs or sim would be needed. Also the particular deck composition becomes important where Aces and deuces hurt you but cards 3 to 6 help. S. Yama
Thank you. Would be great if Mr. Gronbog can run a quick sim for both these scenarios, and so we can see the exact figures for each case in part. In regards to deck composition, I know it is not quite the same thing with the true count, but might the true count be relevant in this particular case ?
Sim Results As usual, S. Yama's calculations are very close and, as is becoming the norm, my gut instincts were wrong When playing vs a basic strategy opponent, the simulated EVs for BR1 success of each play in the originally posted situation are: Stand: 83.6%, Hit Once 78.06%, Double: 69.53% Playing vs an optimal opponent, we have: Stand: 71.47%, Hit Once 68.57%, Double: 68.27% If you had 14 vs an optimal opponent, the the numbers are: Stand: 71.47%, Double 69.61%, Hit Once 69.00% Note that doubling is now better than hitting when you have 14. The complete strategy for other totals is: hard 5 through 6: hit hard 7 through 12: double hard 13 through 19: stand all soft hands: double 5,5: double all other pairs: split
Thank you very much Mr. Gronbog, this is so valuable ! (and it seems my initial error by doubling was 3.2% which is pretty big - but now, there will be no error)
