OK, I played in the semifinal round at the Planet Hollywood $100K invitational a couple of days ago. That round is 5 players, 1 advance, only 11 hands. 6D, S17, DAS, No surrender, betting $100 to $5000 in $100 increments. All decisions have a 15 second time limit. On hand 10, I doubled 11 vs 10 and won it to take the lead. Better yet, I have last bet on the final hand. Things are looking good! I'm going to "make up" the numbers to make the scenario I faced roughly accurate. A: $13,000 bets $5000 B: $13,500 bets $5000 C: $10,000 bets $5000 D: $9,000 bets $5000 Me: $15,000 bets $4500 Gotta love this. I have first high, first low, and I am last to act. Then, the cards were dealt. I like it even more! A: Hard 19 B: Stiff C: Stiff D: Stiff Me: TT The dealer has a two up. Looks great at this point, until... B, C, and D all double without busting. The best hand among them is player B with a total of 18 after his double. Therefore we can safely ignore C and D from this point forward. Updated scenario, with only the important players: A: $13,000 bet $5000 Hard 19 B: $13,500 has $10,000 working with a hard 18 Me: $15,000 bet $5000 TT Dealer has a two up. What now? Do I stand and let B have the high, or split and give up the low to A? You've got 15 seconds. What do you do? I'll go ahead and fill in the blanks for what actually happened. I split, made a 16 and a 12. Dealer made a hand of 18 and A advanced to the $100K final table. Things looks so very promising for about a minute and a half. *Sigh*
Without knowing the exact numbers (odds) right off the top of my head like some folks here..... Of course it's easier to think clearly while at home pondering your scenario, but I think I'd have stood on that hard 20. With your principal villain sitting on that 18, and having a lockout against the rest of the table, the dealer must turn that 2 into exactly 17 or bust to send me to the rail.
I think that's probably right but with 15 seconds to act I would have split, I think. I saw that tournament and was over at PH checking it out. A few people playing the $500k at the Bellagio were playing in it -- but I skipped it to concentrate on the B tournament (which I didn't win, sadly).
Which only goes to prove that BJ tournies are 96.87 percent luck, when even the best player in the known universe makes a wrong move.
15 Seconds To Act With only fifteen seconds to act, a rational player can become a guesser in any nuanced, complex situation. Three of those precious seconds are needed just to count your bet and push it into the circle. A format like this one at Hard Rock makes it important for us to rationally analyze these kinds of situations here on the forum after the fact. Then we can distill the results of the analysis into rules of thumb that are easy to remember at the table and that capture most of the results of the analysis. Not that it makes the poor guy who got caught in the situation feel any better. In this situation Ken had Player A locked out before he split the 20. In multiplayer situations lockouts are so important that we should sacrifice them only with great caution. If it weren't for the presence of Player A splitting the 20 would've been a nearly reflexive response, because of the importance to the leader of getting the same money out on the table. But the lockout over Player A may have trumped this consideration. Let's find out. There are some minor rounding errors in the following calculations: If Ken hadn't split he would've been a 50.7% favorite to advance, needing the dealer to draw out to 18 or above. By splitting Ken was a lock to advance if both hands draw to 19 or above (21.3%). If the dealer breaks Ken advances no matter what his hands. Dealer break (35.4%) times Ken NOT drawing both hands 19 or above, because we already counted that, is 35.4% * 78.7% = 27.4%. We are now up to a total of 48.7%. If dealer hits to 17 (14%) and Ken hit one hand to 18 and the other to 18 or above (4.1%) = 0.6%. If dealer hits to 18 (13%) and Ken hit one hand to 18 and the other to 18 or above (4.1%) = 0.6%. If dealer hits to 19 (13%) and Ken hit one hand to less than 19 AND the other to 20 or above = 1.9%. If dealer hits to 20 (12%) and Ken hit one hand to less than 19 AND the other to 20 or above = 1.8% If dealer hits to 21 (12%) and Ken hit one hand to less than 19 AND the other to 21 = 0.3% Chance of Ken advancing if he splits is 53.6% 53.6% > 50.7%. Splitting was the most profitable decision. In this case locking out Player A did not trump correlating Player B. In some cases it will. The best player in the known universe made the most profitable decision and Lady Luck liked someone else anyway. Thanks, Ken, for sharing this with us!
Immediately after the round I was confident that splitting was the best move. Then after more time, doubts set in, and I told a couple of people that I felt I had made a mistake that probably cost me a seat in the finals. It wasn't until I ran some numbers that I again found out that I was right all along. This is a frustrating game sometimes! My infinite deck numbers are higher than MS's on the split, getting around 60% to advance. I don't have time to research the difference now, but will likely take a closer look in a few days. I took some shortcuts in calculating, which are now suspect.
Correction I made a slight error in analyis. It doesn't affect the overall decision. If the dealer hits to 18 (13%) and Ken hit one hand to 18 and the other to 19 (not 18) or above (3.6%) = 0.5%. Ken's chance of advancing by splitting is revised downward by 0.1% to 53.5%.
One More Change This is what happens when you let a monkey do probability mathematics. I keep forgetting to use combinations instead of permutations when figuring the probability of two different events both occurring when you don't care about the sequence. You have to multiply the probabilities together and also multiply by n! for n number of events. Ken's probability of advancing if he split and didn't bust was 58.7%. Oops... Sorry for any confusion.
OK, I'll admit that my first impression was not the best, but here's a thought that I didn't notice covered in the extensive mathematical probabilities above - and this played into my decision to stand on the 20. The situation of Ken getting "bricked" on both hands isn't in there. All of the scenarios are assuming that Ken will get at least 18 on at least one hand. If he gets double-bricked, his only prayer is a dealer bust - which would make him a 64%-65% dog.
Brick And Mortar Ken getting bricked on both hands is accounted for in the logic below in the dealer busting times Ken not drawing both hands to 19 or above, which gives him another 27.4% chance of advancing. For what it's worth, my first inclination on reading this scenario was to stand on 20 too, based on the logic that a sure lockout of Player A was better than a potential lockout of Player B. This logic didn't stand up to the numbers, however. Goes to show just how complex and nuanced this game can be.
Thanks Monkeysystem for the revision. Now I don't have to look at my analysis again. Your number is now very close to mine. I was surprised to see this big a difference, especially since I played it right at the table but became convinced afterward that I had made a mistake. Once I considered that if I stood I advanced with a dealer 18,19,20 or 21, it sure made standing sound strong. As you note, it's a complicated game.
I still think there's something missing in the analysis, simply because I can't seem to wrap my brain around the idea that standing on the 20 & being a lock (unless the dealer pulls 17 or busts) is inferior. However, I'm sure that in a couple of weeks Monkeysystem will be somewhat relentless about trying to convince me of that, until he starts throwing beers at me to drive the point home. :laugh: On another note, I'm going to bookmark this thread. As I'm sure has happened to many others here, I've got a myriad of local friends who claim that they wish to get into this goofy game of ours. They've seen what I've been fortunate enough to accomplish in a short time and many have said that it must be easy (I think there's an insult buried in there....), so they want to get in. I always encourage them but caution that it isn't as easy as it seems. Sending them a link to this thread would be a wonderful illustration of that point.
just my 2 cents worth. Dealer break 35.4%, if not break 20% final total is 17. Ergo 35.4+12.9 = 47.4 %. But Ken is NOT starting with very bad cards. Splitting 10's vs 2 is not a hugh dog. That's where the difference is. I cannot do the math on the fly but my initial instinct was to go with Ken's decision and split. John R.
My numbers for standing vs splitting when dealer stands on soft 17 and player playing not to bust for infinite deck. Stand 50.66% Split 60.83% ..............................BlueLight
