Min/Max bet 100/1000 in increments of 1. Surrender allowed and double down on blackjack (soft 21) also allowed. No double for less allowed. I was BR1 with 5002 chips betting first on the last hand. My opponent BR2 had 4100 chips. Question 1: - What is the correct bet range here for this lead as BR1 ? (I placed a 900 bet, but now I`m thinking that something in 599-700 range could have been better) - BR2 did a max bet of 1000 chips. BR1 got hard 12, BR2 got hard 13 and dealer up-card was showing a 10 value. Question 2: - What BR1 should do in either case assuming BR2 bet was 1000 ? *- I think that in the case if BR1 had made a bet in the 599-700 range, he should double down. - But what in the other case if BR1 was betting higher than 700: stand or hit up to at least 18 ?
Another Good One! Another good teaser! Looks straight forward on the surface, but there is some complexity lurking. Might I suggest that you post the teaser first without immediately posting your own conclusions? It gives the rest of us the chance to work it out before being lead in one direction or another. For example, in this case, once you said that a bet of between 599 and 700 might be better, it is easy to see why. Perhaps not so easy to come up with that betting range without the hint. With that said, 599 is the minimum you would want to bet, because it covers your opponent's max bet blackjack without giving up anything. Since you can not cover your opponent's max bet double/split with a bigger bet, but you could still cover it by doubling/splitting your 599, should you feel it necessary, one could stop there and simply make the bet. However, since you raise the possibility of an upper limit (you suggested 700), we can explore that as well. The upper limit of 700 prevents your opponent from surrendering to beat you should you decide to double and lose. This, of course assumes that you can not double for less. However, the bet of 599 is actually superior to betting 700 and there is a smaller upper limit which preserves that edge. What is that upper limit, and why?
Yes. In this case BR1 should double because he can retake the high without giving up the low, or the surrender-low to BR2. It does give up a possible push by BR2, but covering the double is worth more. In this case we can still double if we don't think that BR2 knows enough to surrender when appropriate. Otherwise we don't double because we give up the surrender to BR2. Once we decide not to double, if we stand, then BR2 is forced to either double (best choice) or try for a swing by hitting to 18 or better (inferior choice). We could try hitting to counter the possibility of the inferior choice, but hitting is not free, since we could bust, meaning that BR2 could win by simply winning their hand. In reality, I think that as long as we have a hand, most players would double, whether they knew why or not, leaving any small gain made possible by hitting completely irrelevant. i.e. there would likely be no reward for the risk. I think I would stand.
Thank you, yes I will try and do so not posting from the start what my choice was. But in this teaser I posted it in order to be able to ask my second question. Yes, forgot to mention, no double for less allowed. (I`ll try to edit my original post regarding this) The upper limit bet range would be from 734 up to 900. With a blackjack for BR1 in this bet range would cover a max bet double down for BR2. Now comparing the two ranges 599-700 vs 734-900, it shows that 599-700 range is the better choice.
I don`t think double is an option. If we bust, is easy for anyone to see a guaranteed win with a surrender on their turn. If we don`t bust but we get anything lower than 18, again I think is easy for anyone to see that they stand a much better chance at winning the game with their surrender. Now between hitting (to an what total ?) or simply standing, here is where I really don`t know what is the best option for me to do and what is the reasoning behind each decision in part. - Seeing people thoughts I believe it helps. Still at this point, whether to simply stand or hit (up to what ?), I remember a chart about "Strategy to avoid a full swing, acting first. Opponent has a hard total." by Ken and it says that with a dealer 10 up card and a BR2 hard of 12//13/14 we should hit to at least hard 14 or soft 18. - But since this is not really a full swing scenario (because BR1 can push while BR2 win), I wonder if that chart should apply to this current scenario as well ?
I think I may know what you have in mind. As an experiment, I've tried to put my answer in invisible ink: "676" (Highlight the space between the quotes to hopefully reveal it. If that works, it could be a good way of answering teasers without spoiling things for those who want to continue thinking about them.) I've omitted my reasoning for the moment. If it's right, it's certainly not something I'd have come up with at the table.
Nice trick!. I like it. Your number is not the one I had in mind. The number I had in mind is "644". I will likewise omit my reasoning, for now. This is also something I would never have come up with at the table. I had to solve 2 equations in 2 variables to compute it.
streamlining decisions Process of thinking at the tournament table can get complicated, so it is important to streamline it and determine decisions (in this case betting amount) by the most important and then narrow it down to more precise. My train of though in slow motion could look like this: My brl 5002, my opponent 4100. My lead 902. 1. I can bet no more than 901 (900 if double down cards are dealt face down, so I can hide my final score if I do double) 2. Are there benefits of betting less than maximum of the “keep the low”? In some situation I may want to cover opponent winning doubled bet but if I double and get not a good hand s/he may surrender and end up with more unbet chips. He should/can bet at least 903 but most likely will bet 1000. If he surrenders 903 he loses 451.5. Plus my lead of 902 = 1,351.5 Since I can double only for a full amount my bet should be no more than half of 1,351.5 = 675 3. Is bet of 675 enough to cover my opponent double and triple bets? If I double 675 plus my lead of 902 I would have 2,202 more than the opponent current bankroll. This is enough to cover the opponent max bet double. This is not enough to cover his triple bet but even betting 901 will not cover it. 4. Is bet of 675 enough to cover my opponent getting blackjack with max bet? 902 + 675 =1577 – enough to cover his bj. If it was not enough I would weigh in what are the better chances covering bj with a single win against covering it with a double versus chances of me being forced to double and loosing and the opponent surrendering. My bet is 675 If I have time (and just for fun) I may try to figure out the lower limits of my bet with the same coverage as above but betting the high limit may offers additional advantage if my opponent makes a mistake with a different lower bet. Hope it helps, S. Yama
That was broadly how I looked at it. You made a slight arithmetic error - 451.5 + 902 = 1353.5. Which would give you 676, the same as me. However, I had it in mind to ensure that if BR2 wants to keep the option of surrendering into the low if I double, then I want to force him to bet less than 902 in order to achieve that, meaning that a single-bet win will not even tie with me if I push. As it happens, that still works out as 676.
Looking at this, reminded me that Grosjean had written an article on a surrender trap. http://www.beyondcounting.com/pdfs/surr_trap.pdf Looking at the table on page 9, your attractive bet would be 800. Whether 800 or 676 is the better bet, I have no idea. I feel that the end result %s would be very close. Once you take the straight low, then your opponent has little option except shove it out there, but who knows they might make a mistake. I appreciate S. Yama's reasoning process and it is a wonderful way of doing it if you can calculate correctly at the table. Each person would have to evaluate whether they can remember key things from a table or calculate. Larry
another aspect/idea Does have any relevance if this was happening on a true count of +3 ? But over the hitting (up to ?) versus standing aspect on my hard 12 ?
Sorry to be so long in following up. I was out of town and unable to find time to post. As always S. Yama and Colin combine excellent logical and arithmetic skills and, I have no doubt that S. Yama would have come up with the same bet even in the heat of battle at the table (Colin was less confident). My train of thought revolved around PlayHunter's original observation that a bet less than 700 prevents his opponent from surrendering a bet of 1000 to beat his losing double. I asserted that his lower limit of 599 was a better bet and asked what the advantage was and what upper limit would preserve that particular advantage. The advantage that I saw was that when betting 700, his opponent could respond with a bet of 994 and still retain all of the advantages of the 1000 bet (can beat BR1s single bet win and his blackjack with with a double, can surrender to beat BR1's losing double). With a bet of 599, BR2 must bet 590 or less in order to beat BR1's losing double by surrendering and he can no longer beat BR1's single bet win by doubling. The threshold for preserving this particular advantage is 644 (for protecting the single bet win) and 694 (for protecting blackjack).
You'll find varying opinions on the value of counting during tournaments here. I'm in the "there are far too many more important things to keep track of" camp.
comments Dah....I just now have realized that the invisible ink was not just a funny joke (you got me Colin) but really if you run the courser over the space it shows the number. The wonders of technology! Nicely done. As gronbog posted, most people would double as BR2s, and if you hit your 12 to a nice total like 20 or 21 the chances of them doing so increase, thus, the minimal benefits of improving your score can backfire. Similarly, like in a recent teaser post where I would have s17 and opponent 18 and his chance being better by doubling than by waiting for the dealer finishing with 17. If I impulsively hit and get 20 or 21, now, learning from this board, I would attempt to pretend of making a mistake and hit it again hopefully getting a stiff. Back to the Ken’s chart to avoid a full swing. If the chart means full swing, where you can’t lose and your opponent must win, in your round you looking at slightly different situation. In addition to L-W (Lose-Win) you want to protect yourself against P-W. So, in a full swing if you improve your hand to a push-win you seceded. In your case your push doesn’t help. By hitting marginal decisions stiff hands you improve your EV by not losing the bet (push) but at the same time lowering both won hands and lost hands. But since if in the tournament a push is as bad as a loss and the total of loses and pushes is greater than standing and losing you may be better off by not hitting. That means that the table for your situation should call for hitting to a lesser total than in “avoiding full swing”. Now, counting. That could be a separate thread or a big chapter in the book. I am in the camp saying: sure, use it if you can without harming any other aspect of your game. Here are just some points: Counting helps not in making bets (they are in most part a reaction to your opponents’ bankrolls and their bets) but in playing decisions. For this reason Hi-Lo system is very poor and Hi-Opt with side counts (or multiple side counts) is better. As in counting and playing for money it makes sense only if you can do it perfectly and for rather thousands (not hundreds) of hours, hundreds not tens tournaments. By making deviations from basic strategy in a single round statistically you can improve your bankroll by fraction of one percent only. But in a particular one it can be a bigger fraction of a percent –done in middle of a round, which can put you at slightly bigger advantage going into the final hands, and so on. Advantage related to the size of bankrolls is not linear. For example having two dollars more on the last hand, that makes us being ahead/below of half of your opponent bankroll, even if the bankrolls are a few thousands dollars, makes a huge difference. My opinion is that counting and proper utilization of it can improve overall advantage for the very good players by about 5% and somewhat proportionally less for less skilled players. Top players in a tournament with great rules can have success ratio of 140% per round. This means that in a long run if 2 of 6 advance they will pass to the next round 40% more often than average player - 46.7% of the times not 33.3%. With counting it would go to 147% ratio = 49% advancement, and for the 110% advancement ratio player with 2% help form counting it becomes 112.2% = 37.4% instead 36.7% advancement. These are small changes if looked by a single round. Let’s see how it would work in an example tournament with 162 players where 2 of 6 advance, so we have 54 in the second round, 18 in semis and 6 players in the final, and the quality of playes skills doesn't change. In a tournament where all entry fees are fully returned in prizes our players should win: for 10% better ratio players 46% more than the entry fee and 58% with counting, and for 40% better ratio player net him 3 times the entry fees and 4 times with the counting. It is clear that tournament skills outweigh counting but for good players full value of the entry fee is nothing to sneeze about if done many times. However, with not so good rules, vigorish, and dumbing/averaging it down by having wild cards even the best of the best rarely can play with such a big multiple advantage. S. Yama Will try to post on counting and your specific hand in the next few days.
Thank you so much for your very detailed explanations Mr. S. Yama ! Your examples really given me all the answers I was mainly looking to.
