OK, after fgk42 requested another puzzler, I just grabbed one from another thread. This is the hand recently posted by BlueLight in the WSOB thread. However, for our purposes here, we'll assume that all double down cards are dealt face up. That will make the calculations easier than the face-down double card answer correctly posted by BlueLight in the other thread. BR2, Bank $100,000, Bet $50,000 Hard 8 doubled down for another $50K. BR1, Bank $135,000, Bet $50,000 Hard 19. Dealer has a 5 up, and dealer stands on all 17s. Surrender is allowed. Since we're looking at face up double cards, what is the appropriate strategy when... BR2 draws an 8 on his double, for a total of 16. BR2 draws a 9, for a total of 17. BR2 draws a T, for a total of 18. BR2 draws an Ace for a total of 19. Just grab one, and start to work. Let us know what the best strategy for BR1 is in each case, and let us know the probability that BR1 wins or BR2 wins. (This question is intended to be easier than some of the other recently posted teasers.) I'll post the answers in a day or two.
Will answer this first as no calculation is required. DOUBLE-DOWN. This is an example of the Free Hit (Double-Down, in this case).
I forgot to mention... Use infinite deck calculations. It's easier, and the resulting strategy rarely differs from 6 decks anyway.
Answers to Problem When BR2 with a 100,000 bank roll has doubled his 50,000 bet and ends with 16,17,18,or 19. Player BR1 with 135,000 bank roll has a 50,000 bet with hard 19 plays as follows BR2 has 16 BR1 doubles for a 64.77% chance of winning BR1 could stand or hit to any hard standing total (20 or 21) or surrender and have the same 58.36% chance to advance. Amazing BR2 has 17 BR1 could either Stand or Surrender for the same 58.36% chance to win Here doubling yields only 54.42% chance BR2 has 18 BR1 can either stand or surrender for the same 46.14% chance to win Here doubling yields only 44.08% chance BR2 has 19 BR1 can double for a 34.12% chance to win Next best is to surrender or stand for the same 33.91% chance Hope I got them right BlueLight
Got the same as Bluelight... Here is my working out anyway. BR2 DD – 16 Standing, hitting and surrendering all have the same outcome. BR2 can only win if the dealer busts – 58.15% If you DD you give yourself an extra way to win. If you don’t bust you lock up the win but if you bust you can still win if the dealer makes a hand – 64.59% BR2 DD – 17 Standing or Surrendering now have the best chance of success for BR1 and are the same as above – 58.15%. If you hit the chance of success decreases to 51.09% and DD gives you a chance of 54.28% The decrease in odds for hitting or DD comes from the fact that if you bust in either case BR2 can now win by pushing as well as a dealer bust which obviously they couldn’t with a stiff hand. BR2 DD – 18 Same as with 17 except BR1 is now the dog no matter what they do. Standing and Surrendering give odds of 45.97% as BR1 can now win with a dealer 17 as well as a bust. If you hit your chances of success are 37.99% and again BR2 has extra ways to win if you bust as they can push. Same applies to DD which gives you odds of 43.93% BR2 DD – 19 You’re in trouble here and the best chance of success is a DD. Just! DD gives you a 33.97% chance of success whereas Standing/Surrendering gives you 33.73%. If you were to hit your odds would decrease to 25.33% Am I right? Cheers Reachy
Ok, here goes my feeble attempt to calculate this problem As a starter when BR2 doubled they put themselves in the position that if the dealer busts, which will occur 41.64% of the time BR2 wins if BR1 doesn’t double. In effect BR2 has “forced” BR1 to double even though BR1 has a hard 19! The ironic part of that is that with a hard 19 BR1 only has a 12.98% of beating the dealer. There is an 85.31% chance BR1 will bust – nevertheless if the dealer makes ANY hand BR1 still wins. So in the case of BR2 pulling to 16 BR1 needs to double to guarantee a victory. This defies common logic and most people, I know myself included, would NEVER have thought to double on a hard 19, especially when in the lead. However, failure of BR1 to double will result in BR1 losing when the dealer busts = 41.64% of the time versus winning 100% of the time when BR1 doubles down – go figure! When BR2 draws to 17 on the DD BR2 can only win in the following: a. BR1 doesn’t DD and dealer busts b. BR1 busts and dealer draws to 17 – push (BR2 100 vs. BR1 35) When BR2 draws to 18 on the DD BR1 has the following options: a. DD and dealer busts BR1 wins same percentage as 16 & 17 b. DD and dealer draws to 17 BR1 would loose if/when BR1 busts (85% of the time) but the odds of dealer drawing to 17 with 5 up = 12.23% or dealer drawing to 18 (still 12.23%) Given the fact that the dealer’s up card is a 5 and has a 41.64% of busting I don’t think of any situation where BR1 SHOULDN’T double down. This is so counter intuitive to regular BJ playing but logically and statistically is only makes sense for BR1 to DD. Please correct my statistics/logic where applicable. Thanks for the example Ken
An idea for future teasers... Just an idea, but in the future, so that we can't see the answers that other members have posted until a certain period of time has elapsed, is there some way we could answer these teasers privately or secretly? It could work like this - Someone posts a teaser and Ken can lock it so that nobody can post "spoilers" on the thread. People then PM their answers to the Teaser setter who can respond privately back to them. After say 5 days or whatever the thread starter thought would be a reasonable length of time the thread gets unlocked, the correct answer is posted along with the PM'd responses assuming the people concerned were happy to have them posted. Others could then respond at will. Sounds a bit complicated I know but I'm sure it'd work well in practice. Cheers Reachy
Just a thought Reachy, Don't make it all the difficult! Just don't read the answers :joker: Besides you already know the answer so what are you griping about Hey how about this: A Blackjack tournaments.com Forum countdown - Just like UBT. Just image a silhouette of Ken jumping up and down and the bottom reads only 3 more days until the answer! What do you think? On a serious note we could have the Tourney teaser of the week. Post it on Monday with the answer to appear on Friday. Subscribers can write and post their answers but it wouldn't be "seen" until Friday - then we call all see everyons's post at the same time and see who is "right" Too difficult to do? Good idea Reachy
I always cheat at hide and seek... Sometimes I just can't resist peeking at what others have put!!! Cheers Reachy
Results so far: BlueLight is correct, and his numbers match mine exactly. Well done! (Well, we differ by 1 in the hundredths column in a couple of places. I'm sure we rounded differently.) Reachy's analysis is sound, but his numbers are slightly different. I'm guessing he used some 6-deck dealer numbers instead of infinite-deck. No big deal. fgk42, You're on the right track, but BR1 shouldn't always double. If BR2 makes 17 or 18, BR1 should not double. (And, in those cases it really doesn't matter what BR1 does: stand or surrender are equivalent.) I like the idea of hiding teaser responses. I'll look to see if the message board software has any facility for something like that. If not, I could lock the thread and use the PM approach. Now if I could add that jumping silhouette of myself, we'd be all set!
Thanks for the input Ken For those of us who are math challenged, or just plain stupid, can you show how and where to get the "numbers" that you and BlueLight agreeded upon? Remember give a man a fish feed him 4 a day. Show a man to fish and you'll make a BJ tourney player out of him in the end :joker: :joker: :joker:
Did use 6 deck numbers fgk42 - I asked the same questiosn before. Here are the links http://www.blackjacktournaments.com/bb/showthread.php?t=1475&page=2 http://www.blackjacktournaments.com/bb/showthread.php?t=1732&page=2 http://www.blackjacktournaments.com/bb/showthread.php?t=1711&page=2 http://www.blackjacktournaments.com/bb/showthread.php?t=1716 There are probably some more threads somewhere but these will keep you going for a bit... Cheers Reachy
Ken, How about the weekly question???? PS. You don't really have to get the jumping silhouette added at this time!
