If you have a hard 15 vs. an Ace, I'd like to know the probability of the following events. I don't know how to figure it out so asking for help. (6 deck game, H17) A) Hit 15 vs. Ace and beat the dealer B) Stand 15 vs. Ace and beat the dealer C) Stand 15 vs. Ace and dealer makes a hard hand of 17 to 20. (Exclude 21s) Comes from a BJ tournament situation. Prior players had made 20s by hitting against the dealer's ace. I had a 64 and then hit with a 5 for 15. Wasn't sure what to do. It wasn't a make or break hand but it was an important one. I wasn't all in. I had bet about 10% of my chips. Anyway know how to simulate these possibilities?
You can use the Dealer Outcome Charts to easily answer the last two questions. 2) Stand with 15 vs Ace and win. That's the dealer bust probability. Answer 20.13% (assumes dealer already peeked and has no blackjack.) 3) Dealer upcard Ace turns into 17-20. Add up the columns. Answer 70.35% To answer question 1, it takes a little more work. Also, we need to know a final total where you are willing to stand. If you choose to hit it once and only once (stand at 16 or better), you'll bust 7/13 of the time. 1/13 of the time you'll make 21: Win: 90.47%, Push 9.53%, Lose 0.00% 1/13 of the time you'll make 20: Win: 69.74%, Push 20.73%, Lose 9.53% 1/13 of the time you'll make 19: Win: 49.07%, Push 20.68%, Lose 30.26% 1/13 of the time you'll make 18: Win: 28.41%, Push 20.66%, Lose 50.94% 1/13 of the time you'll make 17: Win: 20.13%, Push 8.28%, Lose 71.59% 1/13 of the time you'll make 16: Win: 20.13%, Push 0.00%, Lose 79.87% If you multiply each of these W/L/P figures times the 1/13th factor and add it all up, you get these results: Hitting 15vsA once: Win: 21.38%, Push 6.14%, Lose 72.48% Does that give you enough info to decide your real question?
Thanks so much Ken. I unfortunately do not have the exact chip stacks and exact bets available right now (but can get them!). All I remember was I was in the middle of the pack, and most people had bet around 10% of their chips, which is also what I had bet. A swing where I lose and they win wouldn't have been life-threatening but it would have really increased the pressure on me. I was 5th to act (I think) and 3 people in front of me hit stiffs to 20, while one person busted (or had a blackjack). Anyway, I had hit the 64 with a 5 for a hard 15, and elected to stand on the 15. It looks like I sacrificed about 1% in winning percentage, but I'm trying to see if there might be some correlation arguments where my stand was justified. I don't know if there's enough information there to decide or not, without the chip stacks etc. I also could be slightly off on the number of players and hands, but what I wrote above is accurate enough to describe the hand situation, IMO. Thanks for the link to the dealer outcome charts. Great stuff.
By the way, my thinking about the dealer's chances of making 21 might be a red herring. Perhaps, that is inconsequential in this case and the only thing that is best is to maximize my chances of winning the hand, which was to hit. Maybe I'm overthinking it. Any thoughts on the correlation aspect, or was it clearly a bad play? (This wasn't a final or elimination hand situation)
BR1 Stands on These Totals If Win Both Ways Perhaps, page 131 of Wong's book is what you are looking for.
basic strategy, but no big deal David, the answer to your question is highly correlated to.... the details of your question. Your chances are determined by your skill level versus your opponents’ skills. We know nothing about probable betting position on the last hand. Hands in the beginning or in the middle part of a tourney bear lesser significance. There is no linearity for players’ bankroll ratios, but until last few hands it is the best indicator of your chances. I will make up the situation to illustrate it. Let say that you were in the middle of the pack, had $50K and bet $5K. Disregarding skills and betting position (which is relatively very important) you could assume that your chances of advancing would be still almost average, assuming that the gap to the top two players was small. Being in the lead or being a BR2 would carry some advantage but it would be really minimal. The correlation of winning/pushing/losing would not last through many hands. Three of your opponents got totals of twenty – you should look at their hands as almost sure winners. Their hands had actually very little correlation to your hand. Result of your hand depended on what you would draw, as the dealer ends up almost equally with 17 through 20 and bust. If you win your hand your chances of advancing are almost average, if you lose -you worsen you situation by anywhere from zero to slightly more than 20% of your previous chances. How much exactly? It would depend on their plays and consequently on number of “strikes” you would be afforded to position yourself for the end play. (Put the specific numbers to the above mentioned brls to play with it.) Now, standing on 15 helps you only if the dealer breaks and makes no difference if the dealer makes 21. Hitting 15 bust you most of the time but whenever you win or push (push with 20 or 21 is like a winner) you help yourself a lot (well, it is about 5% of what the difference of losing or winning would bring and another 5% of somewhere in-between). Your play should be basic strategy play but it wasn't a big deal. Hope it helps, S. Yama
Thanks Yama. I thought that I was overthinking it a bit too much. BS makes sense, but also, as you say, in a tourney, it doesn't matter all that much just like card counting doesn't matter either. It's going to be on TV one of these days so I won't say the result. When it's out maybe we can break it down a bit more specifically, although I have a feeling BS play will still be the "right" answer.
