Here's one from an early round at the recent Sault Ste. Marie BJT. Last hand, two advance, three are left. 500 max bet, 50 min, increments of 10 only. BR1 is so far ahead that he's not an issue. I was BR3, unfortunately, and my opponent - we'll call her Nice Lady because she really was - turned out to be a top notch BJT player from the Minnesota/Wisconsin area although I didn't know that until later. Not that it would have mattered. Let's run this teaser from her point of view because I think she made a mistake, but won't tell you what she did (or what happened) until all have had a reasonable chance to take a whack at this one. BR1 has 10 gazillion chips, bets 50 BR2 (you) has 4,000, bets ? BR3 has 3,760 OK, BR2, what do you bet - and why? P.S. No insurance and surrender on dealer Ace only.
Off the cuff.... As BR2, my bet is 390, which will take me to 4780 if I'm forced to double or split due to BR3 doubling for 500. BR3 can go to 4760 with a max bet double. I win by 20 if we both win. We both lose I win. BR3 wins and I lose I'm toast.... Skipper
I would guess that the actual bet was 230... ... but what you spotted was that she should have bet 270, giving the high against a BR2 max bet of 500, as well as the low against a min bet of 50.
I'm betting 230, my lead is 240, BR3 is betting after me. BR3 must win, push not good. I can double to cover a potential 500 br3 win, my blackjack will force br3 to double. There is no way I'd allow br3 to take the low.
Thanks for the replies, guys! Anyone else want to try this one before I reveal my answer - and what actually happened? Colin, you were incorrect, she did not bet 230 and my conclusion was not 270. And that's all I'll say for now.
But a bet of 270 does not allow BR3 to take the low, because BR3 has to bet at least 50 (and there is no surrender). So 270 gives both the high and the low against any bet BR3 makes. It's much better to cover 'both win / both lose' than 'BR3 loses or pushes'. It's the same situation as this thread: https://www.blackjacktournaments.com/threads/4441
BR2 should bet 280 BR2 with a chip count of 4000 can bet as high as 280 and still keep the low (and the high) since BR3 must bet the minimun of 50. Normaly BR2 would hold 3770 (one chip more than BR3's bankroll) so as to get the low and survive the push loss swing. However BR2 would lose the win-win outcome (if BR3 bets the max 500). The win-win outcome occurs 44% of the time and the push loss swing occurs only 5% of the time. As a bonus a doubled bet of 280 by BR2 allows BR2 to overcome a BR3 BJ by doubling down, while a doubled bet of 230 falls short. Even though the betting interval is 10, it's the minimum bet of 50 which gives BR2 a big advantage even though he has less than 1/2 max bet lead. .....BR2....BR3.....................BT2=230........BT2=280 ......W......W.......... .30.......BR3 wins<>.<>BR2 wins ......W......P........... .02.......BR2 wins........BR2 wins ......W......L........... .12.......BR2 wins........BR2 wins ......P.......W.......... .02.......BR3 wins........BR3 wins ......P.......P........... .01.......BR2 wins........BR2 wins ......P.......L........... .05.......BR2 wins........BR2 wins ......L.......W.......... .12.......BR3 wins........BR3 wins ......L.......P........... .05.......BR2 wins<>.<>BR3 wins ......L.......L........... .31.......BR2 wins........BR2 wins ..................BR2 totals........ .58 .............. .81 ......................BlueLight
280 and 270 are equivalent bets, the top and bottom (and entirety) of the range that gives the high and low. However, it does make sense to pick the top of the range in situations like this, just in case the extra chip(s) in action make a difference if you are able to get mutiple bets in play. So in that sense 280 is perhaps the better bet.
It's been about a week since this teaser started, time to tell the true tale of what actually happened. First of all, my own idea of the better bet was 280 for exactly the reasons outlined by BlueLight and Colin in the two previous posts, in addition to Acemachine's idea that my BJ would put a serious hurt on BR3's already slim chances of overtaking my chip stack. Dreamer's 390 would be my distant second choice because I'd be unwilling to donate the low, but that bet would have been better than what she really did. If you wish, scroll up to the original post and review the situation & chip counts. I was BR3, Nice Lady was BR2 and betting before me. As already mentioned, she is an accomplished player but she messed this one up (as she admitted to me later) with her max bet of 500. This made my job rather easy, simply take the pure low with 250 and hope she doesn't get a strong hand against a weak dealer. This also gave the highly unlikely bonus that she could possibly surrender v. dealer A and allow me to either push or win the hand to advance. I don't remember what Nice Lady got, nor what I got, but I do remember the dealer getting a face card, checking the hole, and turning over an A to seal the deal.
What if full surrender were available? Would 270..280 still be BR2's best bet? Or would it now be 390..470? (with a view to surrendering back to > 3760 if need be)
bets... BR1 is beyond our reach BR2 (you) has 4,000, bets ? BR3 has 3,760 What makes this teaser interesting is that, with minimum bet set relatively high and BR2 lead smaller than half max bet, BR2 betting enough to cover opponent’s max bet would still advance when both players lose, even if the opponent bet only a minimum. Also, as if often the case in real situations, different bets and plays may be more effective depending on opponent skills (and ours). Since all players have huge stacks of chips that are significant multiples of maximum bet it can be easier to consider not numbers representing total bankrolls but just the differences between them. So it goes: Betting 230 - “true low” advances us when BR3 doesn’t win big bet, also we can “steal” some hands by doubling/splitting, or receiving a blackjack, which forces BR3 to win doubled bet – total chance of advancing about 60%. Betting 270/280 – unfortunately is not as advantageous as basic strategy would suggest (or fortunately if it is us departing from basic strategy, lol). If we win our bet, or even get bj, or win double, BR3 double and bj with a big bet eliminates us. Depending on both players’ skills -- total chance of advancing is in low to high sixties %. Betting 390/430 – value of this bet depends mostly on whether BR3 responds with a small bet (against bet of 390 optimal bet would be 130/150, but with BR2 bet of 420 or more BR3 should bet 170) or fires up 250 and up. The goal is to make this bet in a manner that would induce BR3 to bet big. Against small bet our (BR2) -- total chance of advancing are below 50%. However, if BR3 bets big, which also indicates that he is prone to make mistakes, our total chance grows to almost 80%. We need to be right, guessing that opponent will bet big, about 7 out of 10 times to make it the most valuable bet. With surrender available 390/420 should be the bet (betting 430 and surrendering ties us with BR3 surrendering his bet of 50. S. Yama
stand corrected Colin, Right, Instead of deducting 25 (result of surrender of 50) I added it. Seen weirder things than that in casinos, lol. Top range moves to 470 - a pile of chips that means big/max bet pushed in a way saying: "Lets see who gets lucky on the last hand". S. Y.
my non-pro 30 sec bet 230 for the garanteed low. "can't teach an old dog new tricks". I enjoyed all the math answers. Thanks for the posts. tgun
I agree with Acemachines $230 bet. It assures the low in basicly a head to head battle for the last spot. The $230 bet here covers nice ladies $50 "Push" which would give her the lead should you lose any bet over $230. This still gives you a DD if needed.
