This last hand (modified) comes from another round at the GN in Laughlin. Min Bet = 10, Max Bet = 500, Bet Interval = 10 Insurance bets in 5 interval, No Surrender Dealer H17 S18 One Player Advances Player......BkRll.........Bet..........Cards.......Action Allen.........215.........210............9+6........Stand Baker........345.........340............9+8........Stand Chuck........240.........230............8+6........Stand Dealer.......................................3 What were the betting and playing mistakes of the players? .....................................BlueLight
As far as I can see - Playing: Both Allen and Chuck passed up the opportunity to take free hits and maybe swing Baker. Betting: Baker overbet, sharing the low with Allen, and letting Chuck take the low from both of them with his bet of 230 (while still taking the high against Allen). A bet of 260 from Baker would have been enough to cover a BJ from Chuck. No need to bet any higher.
Bakers Bets A bet of 260 by Baker is a good bet. What is Chuck's mistake(s) when Baker bets 340? ...........BlueLight
I like a bet of 100 by Baker. It takes Allen high and low with the chance to double for a tie if Allen gets blackjack and itbeats Chuck's push. Betting 110 would allow doubling to beat Allen's blackjack, but gives up the push to Chuck. I think that's a bad trade off. Colin is correct about the free hits given up by Allen and Chuck. Once Baker bet 340, I don't see the problem with Chuck's bet of 230. He has the first low and he has Allen high and low. I can't see how betting anything less would improve anything.
I'd have said the same thing. It's only the memory of a previous BlueLight teaser that leads me to the answer - If Chuck bets $10 less, then he covers the possibility that the dealer gets an ace and Allen or Baker use their last $5 for an insurance bet, potentially leaving them with $15.
About betting About betting. Player A .........215 Player B .........345 Player C .........240 Player A, Not knowing what his opponents will bet, has the most detective/deductive work to do. Since we also don’t know their skills and preferences, we assume they bet good to optimal. First thing Player A should know is that if he bets at least chip more than the difference to the leader he will advance when he wins and his opponents push or lose and when he pushes and they lose more than the difference between their bankrolls. That is 11% for basic strategy players if P2 (the leader) bets more than 130, but only 8% if P2 bets less than 130. P1 can also overcome them with blackjack on a big bet if P2 doesn’t win his big bet (or doubled bet). That’s additional 3%. Not great chances. Additional possibility of P2 and P3 giving P1 the low would be welcomed, even if it was the only chance and happening only a bit more often than 1/3rd of the times. Checking for “getting the low” bet: Minimum bet (10) leaves P1with the most unbet chips. That would change the dynamics of the game drastically. Now, P2 instead of going for high can lock out P1 completely by betting no more than 100 and have low to both opponents and double/bj to overcome P3 all-in win. Betting minimum to advance with win when P2 bets 100 or more and loses and P3 pushes or loses (still hoping for the low) – that would be bet of 50. In this case P1 would get the low if P2 bets 190 or more and P3 more than 80. However, if P2 bets that much P3 can take the low with bet of 70 and have additional advancement on high side with swing to P2. Chances for getting low are minimal, so, P1 can bet all-in for a chance of a gain to both or blackjack and opponents betting not enough to cover it. Player B, Assuming P1 has bet 210, The seemingly obvious bet is to guarantee advancement if he wins or the other players don’t gain to him. Winning 260 covers P3’s all-in bj, 190 covers P1’s bj, and 140 covers P3’s all-in. Even the smallest of the above bets allows P3 to take the low, thus reducing P2's chances to a win and others no bj, and the others bj while winning double, and push and the opponents push or lose. This accumulates to total chances of about 45%. Perhaps there is a better bet? The alternative is to bet small enough to advance when the other players lose or push. This number maybe surprising to some and for bs players is 42%. By betting only 100 P2 has the low (including the opponents pushes) and has the high (win/win [no bj]) to P1 and offers in specific situations double to cover P3's big bet, and no need to double with a blackjack. This action makes P2 a favorite to advance over 60% of the times. Player C, Assuming P1 bets 210 and P2 bets 340, Bet of 230 is a good one, and the right range is 200 to 230 (P3’s bj covers P1’s bj). P2’s mistake of betting too much gives P3 about 45% chance for winning the round. Assuming P2’s bet of 100 P3’s range is 210 to 230 (bj with the bet of only 200 doesn’t cover P2’s winning double bet) giving him around 30% chances to advance. S. Yama
Answers? Right, Chuck needs to hold at least 15 to cover an insurance bet from only one of the players and still have the low. A situation could have been as follows: Player........Hold........InsBet..............New BkRll........New Hold ...................................................after Dlr BJ......after no BJ Allen...........5..............0.......................5...................5 Baker..........5..............5......................15...................0 Chuck........10..............? Dealer...............A If Chuck takes no insurance and the Dealer HAS a BJ then Baker ends up 15 winning the round. If Chuck takes 5 insurance and the Dealer does NOT HAVE a BJ then his hold is 5 and he is tied with Allen for the LOW. Since Chuck cannot always correctly guess wether the dealer has a BJ or not he needs to hold at least 15 bact initially. The situation the becomes as follows. Plyr............Hold........I Bet................N BkRll..............N Hold Allen............5............0......................5.....................5 Baker...........5............5.....................15.....................0 Chuck.........15...........5......................25...................10 Note even if Chuck had to act 1st he simply confidently takes 5 insurance and doesn't need to worry wether Allen OR Baker insure. If 2 or more players had held 2 chips then Chuck needs to hold 5 chips. Below is the hold requirement for a Chuck to hold when 2 or more other players have X insurance betting units. Allen and Baker...................Chuck ........1.................................3 ........2.................................5 ........3.................................6 ........4.................................8 ........5...............................10 ........6...............................11 ........7...............................13 ........8...............................15 ........9...............................16 .......10..............................18 .......11..............................20 ......100............................168 For most situations you just have to remember if: Allen and Baker have 1 chip then Chuck holds 3 chips. Allen and Baker have 2 chips then Chuck holds 5 chips. Allen and Baker have X chips then Chuck should hold 2X chips. Chucks Insurance bet is to make his insurance so that he now holds 1 more chip than what A&B held back. Wong teaches us to hold an extra chip but it is better to hold more if you can afford it. I got the idea for this teaser when in the last 5 tournaments the dealer got a BJ 4 times in some sessions and I lost out 3 times (but not because I didn't hold enough). Interestingly the situation was essentially as follows: Allen..........215.........210..............9+6...........Stand Baker.........345.........340..............9+8...........Stand BlueL.........240.........230..............8+6...............? Dealer............................................................3 If I stood I would advance if The Dealer makes a hand 18 to 21 and I would lose if the dealer busted; it didn't matter if I won or lost the hand. However Baker would also advance if he pushed with the Dealer. I could try to take the push away from Baker by hitting to a total of 18 or higher. I took a hit and was delt an 8 busting me. So now I'm back to Baker losing and not pushing. (See that 8 and the Dealer up 3.) The Dealer now turned over the hole card a 10 and took a hit and now got a 10 busting and paying Baker and I was done. I played the better percentage play but it changed the order of the cards and I took the Dealer's "make" card. If I had stood as basic strategy says I would have advanced. Sometimes you make the higher percentage play but that's all it is a higher percentage but no guarantee it will be a better result. ................................BlueLight
Formulla for keeping low with insurance protection BlueLight, Very nice teaser, excellent points on keeping low that includes protection against opponents taking insurance. Here is the exact formula that works for all amounts of unbet bankrolls, that are not necessary alike. In order to protect against multiple (can be more than two) opponents we have to keep the highest amount of unbet chips plus anything (“one chip”) and exactly two thirds (or more) of the second biggest unbet stack. Exact matching is required and rounded up if it is a fraction of a betting unit. When it comes to making insurance bet we keep back amount that is anything more than the highest opponent’s unbet stack (whatever they have left after buying insurance) and we buy insurance for the rest. Examples: P1 keeps 60...P2 keeps 100 ---We keep 100 + 1+ 2/3rds of 60 (40) = 141 If P1 buys full insurance and P2 keeps 100, we keep 101 and buy insurance for the rest (40) If dealer has bj we get paid 80 and easily win with P1. If dealer has no bj we lose insurance but still have more than P2. If P1 doesn’t buy insurance (keeps 60) and P2 buys it for whole 100, we keep 61 and buy insurance for the rest (80) If dealer has bj we get paid 160 and finish with 301 and P2 ends with 300. If dealer has no bj we lose insurance but still have one chip more than P1. P1 keeps 625...P2 keeps 900 ---(betting 25 minimum) We keep 900 + 25 + 2/3rds of 625 (425) = 1,350 P1 buys insurance for 500...P2 buys insurance for 450 (keeps 450 back). We keep 475 and buy insurance for the rest. It is obvious that we have most money left and buy insurance for more than the others; But if with the same bankrolls: P1 doesn’t buy insurance (keeps 625) and P2 buys full insurance for 900 -we keep 650 and buy insurance for the rest (700). If dealer has bj we get paid 1,400 and finish with 2,750 and P2 ends with 2,700. If dealer has no bj we lose insurance but still are left with 650 and P1 is left with only 625. Hope it helps, S. Yama
Ahh, yes. The insurance factor. I had promised myself that I would study it further after that teaser but never did and it slipped my mind once again. :whip:
