Bet limit: 100 min/500 max, no surrender. Last hand: BR1 (me) 1497 chips, first to act and BR2 1001 chips. My bet is 495 and my opponent bet 500. I got soft 17, my opponent hard 18 and dealer up card 10. - What is the best play as BR1: double, stand or hit (multiple hits) ? (..I doubled down..)
Interesting scenario... I definitely like your bet bec if you lose and he pushes, you still win by 1 chip. On the play, personally, I would probably just stand the soft 17. Because the ONLY way you lose is if BR2 wins, and you lose AND you push/lose. So how could that be possible? ONLY if the dealer has a 7 underneath as his 18 would beat your 17. Of course he can try to DD, but he'd have only a 23% chance of improving his 18, so the odds are still in your favor. This is my reasoning/rationale a BJ tournament player with pretty decent success in many tournaments, but would love to hear Ken, or the other heavy tournament players here....
The choice is between hitting and doubling. Standing on S17 doesn't achieve anything :- If you push with 17, then BR2 wins with his 18, and wins the table 1501 to 1497. If BR2 pushes with 18, then you lose with your 17, but still win the table 1002 to 1001. And if you both win or lose a single bet then you win the table. Hitting once cannnot make the above situation any worse (since you can't bust and all totals less than 18 are equivalent for you), but it can improve things if you draw an A,2,3 or 4. A dealer total of 17 then no longer helps BR2 if he doesn't double. (Although doubling is his best option in any case, so you'll only get this benefit if BR2 doesn't realise this.) As to whether hitting or doubling is better for BR1 :- Under time pressure I supsect I might have hit, but with more thinking time I think you probably made the correct play. The win-both-ways hitting strategy when the dealer shows a 10 and BR2 has 18 is close to a no-bust strategy (Wong's table 5 says stand on H13), so I suspect the proper strategy here is to always take only one card any way. In which case you might as well double and take the doubling option away from BR2. The downside of this is that you open yourself up to the possibility of being swung by a BR2 push if you make less than 18 on your DD. (Or less than whatever total BR2 ends up on after playing his hand.) [N.B. Standing on his 18 becomes BR2's best play if you DD to a total less than 17.] So if we assume you should always take just one card, it seems to come down to whether you gain more by protecting yourself against the BR2 double than you lose by exposing yourself to some extra swing possibilities when BR2 gets a push. I can't quite bring myself to tackle the maths at the moment.
I always try to answer these quickly first, with a one minute time limit, in order to see what I would have come up with at the table. In this case my thoughts were that only a dealer 17 can beat you, so my conclusion was to stand. Colin is correct, however, that standing on s17 is of no use, since we can't make things worse by hitting, but could perhaps improve on things. As for whether to double instead, my one minute assessment is to go ahead and double. My gut says that most players would double their 18 on the final hand (even if they don't know why). If you hit, then they win by winning their double. If you double, then they must win their double while you lose (once again assuming that most players will double regardless of what happens). Now I'm off to see what my simulator says.
They only need to push their double while you lose. That's the slight door which BR1's double opens up for BR2, while simultaneously closing a different door. (It applies whether BR2 stands on his 18, in the hope of a dealer 17/18 beating BR1, or hits/doubles to a higher total.) Can your simulator distinguish between the case when BR2 plays his hand perfectly (which will could mean standing, hitting to a particular total, or doubling, depending on BR1's action and outcome) and the case when BR2 follows a more rigid strategy (always double, never double, etc.)?
Right you are. Thanks for pointing that out. Yes, my simulator can generate the optimal strategy for BR1, assuming that BR2 will respond optimally (also generated) or assuming that BR2 will follow some fixed strategy, which can be specified. Having done that, I have the results for both players playing optimally, however I have found a bug in the code where BR2 plays a fixed strategy. I'll have to fix it before presenting any of those results. In the mean time ... Assuming BR2 will respond optimally In this case BR1's optimal strategy is simply not to bust. Whether he does so by hitting or by standing turns out to be irrelevant because BR2's optimal response is to double, no matter what BR1 ends up with. Once BR2 doubles, BR1's hand becomes irrelevant because the outcome then depends entirely on whether BR2 wins his double (and advances) or loses/pushes it (and does not advance). By not busting, BR1 has a 84.3% chance of advancing. If BR1 makes the mistake of busting, then BR2's optimal response is to stand and BR1's chances are reduced to 65%. If BR1 doubles then BR2's optimal response is to hit to a total which is 1 greater than BR1's in search of the push/lose or win/lose swing that Colin mentioned. This is BR2's only option, since BR1 still has locked up both the high and the low by doubling. As good as this sounds, BR1's chances are reduced to 81.5% if he doubles.
That's not a revelation of the sim, though. I already came to that realisation using nothing more than the power of my puny, human brain. - But since we can never be sure that our opponent will play optimally, there is no reason to refuse the free hit. That figure tallies with the 15.7% probability of winning a T,8 v 10 double down, listed in Ken's table. This is where my puny human brain does begin to struggle. It seems my first instinct was correct and then I managed to talk myself out of it thanks to the extra thinking time! It ought to be possible to cross-check the sim result with a purely analytical method, but it's a fiddly business and I quickly gave up on my first attempt. I may give it another go later.
surprizingly (?) no double Very nice posts. This case proves how it is helpful to know two basic blackjack strategy tables: dealer final totals based on the up-card and chances of success for doubling on all hands. If BR1 stands on S17 and BR2 stands on his 18, BR2 advances only with the dealer final hand 17. This happens about 12% of the times. However, knowing that BR2’s wins doubling 18 vs. dealer’s Ten almost 16% of the times, that strategy makes it a preferred play. BR1 hitting S17is the same as standing against good players but may be slightly better (as Colin noted) if hitting improves the hand and BR2 doesn’t double. Results for BR1’s doubling require a bit more mental gymnastics, but using some rounding it could go like this: Doubling will results in 3 category of hands: stiff, 17, and improved hands. 5/13th of the times doubling S17 results with a stiff (12 to 16) and 4/13th of the times with hard 17 which can be rounded to +2/3 or – 70%. BR2 optimal chance – stand; BR2 advances when dealer has 17 or 18 – 24% chance. [Now, a mathematician could jump to conclusion that 2/3rd plus with 24% disadvantage already “gives away” more than 16% - which is a maximum BR2 has when BR1 stands or hits.] 4/13th of the times by doubling BR2 improves the hand. 21 is a lock. 20 loses only if both BR2 and the dealer have 21 or d’s 20 and BR2 21 (3.1% disadvantage). 19 loses to dealer 19 and BR2’s 20 or 21, and d’s 20 while BR2’s 20 and 21, and d’s and BR2 21 (7.8% disadvantage). Doubled 18 with results in a similar manner like above loses 8.8%. On average improved hands still lose about 6.5%. So if we add up 9/13th times 24% plus 4/13th times 6.5% we can see that BR2’s total chances when doubling appear to be about 18.6%. BR1 optimal play is hit (or stand). S. Yama
I think this situation has an interesting psychological side. As BR1 I would probably not double, but would probably hit, thinking that I can not hurt the situation (I would not bust). However, if we assume that most people (what ever percent that is), would double as BR2, then the question becomes - Would my hitting as BR1 and getting a good card (4/13 of the time) convince the percent that would not have doubled their 18 to go ahead and double? I might end up actually hurting myself against the tournament players as a group. Larry
Stand (or hit) Larry, you are absolutely right. I was thinking the same thing (after waking up next morning, lol). Only very inexperienced players would try to not double and hit trying to swing you (or give up by standing) if you improve your hand. Somewhat paradoxically it is mitigated by a chance that hitting to a bad stiff may actually influence BR2 to not double down thus increasing your chances. S. Yama
I had also thought about the mitigating circumstance of me getting a stiff and BR2 not doubling because of it. But I believe the people that were going to double initially would also realize that nothing had changed and would go ahead with their double. I doubt that the people who were not going to double would suddenly change their mind if I got a stiff. Who knows? Unfortunately the exact circumstance will not come up enough to really evaluate it. I just hope I can remember the situation if it ever does come up and I make what I think might be the best answer of not hitting. Larry
I have fixed the bug in my simulator which prevented me from analyzing BR2's likely static strategies (stand or double). (It was a bug in the setup of the situation, not the actual analysis). If anyone is still interested ... Assuming BR2 will double his 18 BR1's best play is to double his soft 17 for a 88.2% chance of advancing. Hitting to any total, even a bust, or standing would all yield the same result of 84.3% since BR2's double would make our undoubled hand irrelevant. Assuming BR2 will stand We take the free hit to 18 or better, as discussed earlier, but do not bust for a 91.6% chance vs 87.9% for standing. Doubling is not a consideration since we already have the high and we also have the low against BR2's push. My puny human brain figured both of these out in terms of what to do, but the percentages came from my simulator.
With the amalgamation of all our puny brains, working in parallel, this forum could be viewed as a supercomputer, albeit one that runs really slowly.
The psychological side of this hand gave me enough interest to look at it in some detail. I believe we can expand up on it to a lot more hands for BR1. We have the following givens: BR1 is lucky enough to be in this situation, does not have 18-20 (a little bit more on this later), BR2 has hard 18 and there are no BJs involved. We assume that BR1 will not double, will not split and will not bust. BR2 will only win if dealer has 17 or wins a double down which has been calculated to be 15.7%. Using Ken's numbers for dealer outcome. If we use 6D stand on all 17s, then if dealer has an Ace dealer will have 17 - 18.81%, with a 7 will have 17- 36.92% and with a 6 will have 17 - 16.57%. With these 3 upcards as BR1, I will attempt to improve my hand w/o busting. If it is 6D hit soft 17, then only with a 7 does dealer have 17 (36.92%) more than 15.7% and BR1 will attempt to improve his hand w/o busting. Of course, BR1 is trying to make BR2 double these situations. As our BR2s, we have Group 1 (the S. Yamas'). They know the percentages and will make the optimal play (double or stand). We can't do anything useful, other than the above paragraph 3, against this group. Group 2 is hazy on the actual percentages, but through playing in tournaments has learned that they are probably better off doubling and will double if BR1 has 18-21. They may or may not double against the other numbers. Group 3 contains the remainder of the BR2s who might consider doubling against BR1s 18-21, but probably not against the other totals. You can build your own groups. Look at the situation when BR1 has 7-11 or AA-A6. Against Groups 2 and 3, BR1 may actually prompt more people to double if he hits any card giving him 18-21, thus worsing his over all chance of advancing. However, what they will do if BR1 stands on these I have no clue. If I had 11, I might get by with saying, I have 12, I stand as those I had miscounted my hand. With a pair of Aces, I could say I don't want to split and then stand. Who knows what will go on in BR2's mind. What if BR1 has a soft 18-20? Would I be better off hitting the hand hoping to get a stiff? Would fewer Group 2s and 3s double? Something to think about. Larry
Where is my brain at? BR2s DD win % varies by dealer up card. Only 15.7 against 10. The rest run from 16.9 against A up to 19.7 against 6. So I still want to convince BR2 to double with dealer 7 or A, since it lower his advancement %, but not against against the other up cards. Also (no affect on the Group 1s), but I believe that the other 2 groups would have a tendency to double more against dealer 2-6, than dealer 7-A. Larry
