Sure, it depends, and there is more than one implication to consider. I will try to sort some of them. The case Reachy wrote about, and a few members of bjts made great comments on, is very interesting. The case seems simple enough - there were only three players involved and they all made max bets and the question was of singular matter whether to hit or to double down. But at the same time it is almost too complex for a full analysis. We need to consider quite a few conditional reasoning, optimal play and mathematics being only part of it. The case (so we are on the same page): Two people advancing. BR3 bets first, ....... max bet –500, ... brl 1,300, ... hand- total hard 14 BR2 bets second, ... max bet -500, ... brl 1,400, ... hand – A,5 BR1 bets last, ....... max bet -500, ... brl 1,500, ... hand total hard 11 Dealer showing a 9. Is the best play for BR3 to hit or to double down? The point Joep was trying to make (and for sure he will let us hear it if he meant something else) was that when you need to gain to your opponent(s), and when your opponent(s) has a nonbusting hand it is often a better play to hit to a pat hand than to double down. The reason for it is that whenever you end up with doubled hands total of less than seventeen you will be locked out. In addition to this your opponent(s) can have a correlating result even if your double down result in an excellent hand. This sound good, but it is such generalization that I can as easily find cases substantiating it as cases not corroborating with this generalization. One way of looking at this is to weigh benefits of both different playing options. Hitting increases the chance of finishing with a good hand that can be more difficult to correlate by BR2 and BR1 - counterbalanced by an increased chance of busting out – thus, not advancing. Doubling down necessities BR2 and BR1 to double their hands, which decreases absolute values of BR1’s and BR2’s hands by not being able to draw additional cards but by the same token whenever BR1 double card is an Ace, or a deuce he is practically doomed. Some players may feel that hitting to more than seventeen would be the right play. Some may even think that hitting to nineteen is the right play as the dealer’s up card was nine and the chance for the dealer finishing with nineteen is the greatest of all hand totals possible. And then, we need to contend with, and make an adjustment to the fact that we are not playing against computers but against often times imprecise human beings (yes, our opponents are human beings) making less than perfect decisions. In our case any chance that BR2, and especially BR1 with his natural-double hand, would double down decreases BR1 motivation to double down, for the opportunity of opponents losing more than their leads were. Yet, another factor slightly stipulating hitting, is that many players as BR1 and BR2 would not adjust their playing in accordance to BR3’s final hand but would play basic strategy, which differs significantly from the optimum plays, especially when BR3 ends up with a total of seventeen and eighteen. Hitting hard fourteen to 17 doesn’t bust 44.6%, and hitting to 18 doesn’t bust only 38.4%. What is even more disappointing for BR3’s situation is the reality that even if he ends up with a pat hand both opponents will have the same or better hand total 11.2% out of 44.6% and 7.1% out of 38.4% respectively, assuming they do hit to seventeen or better. So, would it be hitting to seventeen or hitting to eighteen, or doubling down? Numbers: This is for an infinite deck and BR1 and BR2 doubling when BR3 doubles, and hitting to seventeen (not the optimum play but one the will be most commonly encountered at the tournament table even against experienced players) whenever BR3 hits and have hand total of seventeen or better. Hitting to 18 - 21.926% Hitting to 17 - 21.877% Doubling .....- 16.711% Personally I had a feeling that the difference would be much smaller. I am glad I could do these numbers - the only tool to develop a better intuition so much needed for situations under stress of winning/losing big prizes and with the time limits. S. Yama
I thought it'd be closer! I suppose, as Joep said, because BR2 and BR1 are on good doubling hands anyway doubling into them is not the best option. Not that I was questioning Joep's strategy in this scenario anyway, I just needed a more in-depth explanation and stats always help . I'm afraid that I'm one of those people who need to have something proved to them so I can understand the why's and the wherefore's. I'm also reassured by S. Yama's post insomuch as it confirms some of my assumptions about the scenario and the implications of different actions. It's just the end result that I got wrong! Still if it were an exam I'd of got 90% for the working out and 0% for the answer. S. Yama - Can I just confirm that the numbers you came up with at the end of your post are for the probability of BR3 beating BR2 OR BR1 rather than both of them? In your post you say that Can you give examples of where BR3 acting first should have doubled rather than hit? I'm guessing any good doubling hand from BR3 and at least 1 stiff form BR2 or BR1. What about when BR2 and BR1 have made hands? Often I think they are worse than some stiffs because you have more chance of busting out if you need to DD. In fact in a close final hand where anybody can take it anything more than 11 is a nightmare! Cheers Reachy
will be back I will be travelling, busy and with limited Internet access for about ten days. Expect delays in my responses, sorry. But I will be baaaaack. S. Y.
In elimination BJ-with the DD card face down-does that change the play? Also, what is the % for hitting to 19??????
shortcut or too complicated math? The short answers to Tinker’s questions, with the above stated assumptions, are: hit to 18 – 21.93% hit to 19 – 20.87% It makes no difference what face-down card BR3 gets on double down; both BR1 and BR2 have to double. But it would be fun to analyze right plays if players’ actions were completely secret and only known information was the original cards and bets. I may write something about it in my next post tomorrow. Originally, I didn’t post numbers for hitting to 19 because I knew it would not be as good as the other plays. If we know numbers for each final total contributing to the chances of success there is a shortcut, that may be of interest to some players on this board, to find out (or at least get a better feeling about it) how to determine if hitting to one point higher is a better play. I calculated chances of BR3 success for hitting hard fourteen to seventeen against other players (two advance) and it came out to be 21.88%. BR3 had almost equal chances of ending up with seventeen to twenty-one. 17 contributed about 1.5% 18 contributed about 2.4% 19 contributed about 5.0% 20 contributed about 6.2% and 21 contributed about 13.0% for the total of 21.9%. When we play “hitting to 18” we also hit our hand whenever it is seventeen - so in our final hand there would be no seventeen but all other higher totals would be increased by 1/13th, which would be caused by one card out of thirteen possible for each of the higher totals. If we eliminate benefits of x (by hitting it instead of standing on it) the sum of benefits for all higher totals must be greater than 13x to make it a better play. X must be smaller than one fourteenth of the total chance. In our case 1.5% times 14 is 21%, which means x was smaller, but not by much, than one fourteenth of the total chance. Hitting to eighteen contributed to the total chances as follow: 18 contributed about 2.5% 19 to 21 contributed about 19.4% for the total of 21.93% If we hit eighteen we lose 2.5% but we gain one thirteenth of all other totals. 2.5% doesn’t fit in 19.4% thirteen times, or fourteen times in the total chance of 21.9%. Consequently, hitting eighteen would decrease chances of BR3 advancing. Knowing that hitting to nineteen (20.87%) has chances of success as follow 19 —5.7% 20 – 7.2% 21 – 7.9% we can easily calculate that hitting to twenty would have a chance (7.2+7.9)x14/13 = 16.3% What I wrote here applies only if the hit card ten busts you (it wouldn’t be 1/13th like the other cards but 4/13th) and all other players’ playing strategy would remain the same regardless of your final hand. S. Yama
