The situation for the last hand is as follows: Min Bet 25; Max Bet 1000; BJ 2-1 Player ...........BankRoll.............Bet BR2.................3000...............1000 You..................5525...................?...............What do you bet?
Me too, but I would do so regardless of the 2-1 BJ, viewing a remaining balance above 5000 as a virtual lock, beating a 2-bet win from BR2 (a double down or, in this case, also a BJ). Betting 500, rather than, say 25, has the added benefit of taking the high against the maximum possible win for BR2 (6025 : 6000), which I think may be the point of this question. [Edit: Reading the thread back, I'm wondering if you are interpreting the scenario as BR2 starting with a 4000 BR and betting 1000. If so, and if that is in fact what BlueLight means, then nothing I have said in this or my next post will make any sense.]
As for how to play, I suppose it only ever matters if BR2 manages to get three bets down (2 splits, or 1 split and a DD). And in that case you want to correlate with BR2's worst hand (since BR2 needs to win all their hands while you lose or push). I would guess there is no circumstance in which you should ever split, and obviously never DD.
My rule of thumb when in the lead is to start with the maximum bet which does not cross any risk threshold and then consider whether there any reasons to bet more. This automatically covers as many high outcomes and options as is possible, such as the one Colin has pointed out. Assuming BR2 started with 3000, this also leads me to a bet of 500.
Yes 500 is your best bet. If you go by the traditional bet your lead minus a chip you would bet as much as you could here and bet 1000. However a bet of 1000 would not protect you if BR2 wins a doubled bet and you lose your bet. By betting 500 you can lose your bet and BR2 can win his bet and you still win the session. The cards are delt and the following is : Player..........BankRoll............Bet.................Cards BR2.............3000..................1000.............10 +10 You..............5525....................500................6+5 Dealer..............................................................5 BR2 now splits his 10's and gets 3 more 10's and splits to 3 hands with a 7 on the third hand. The situation is: Player......BankRoll................Bet...................Cards BR2a..........3000.................1000..................10+10...............Stands BR2b....................................1000..................10+10..............Stands BR2c....................................1000..................10+7................Stands...... You............5525...................500.....................6+5................Action? Dealer................................................................5 What do you do now ?
As I said, BR2 has to win all three bets while you lose or push. So, with their worst hand being 17, all you have to do is not bust. You can just stand on your 11 if you like, or take exactly one hit card (which is probably advisable from a look-of-the-thing point of view). BR2 should have hit the 17. By standing they have gifted you the win.
London Colin got the situation right. While you can stand a loss with BR2 winning a double bet, you need to win your 500 bet if BR2 wins a triple bet. The only way BR2 wins with his 17 is for the dealer to bust. If the dealer busts then a stiff by you will win. Also if you were to make the mistake of doubling your 11 against the dealer 5 and were delt a low card, then if the dealer ended up with 17 then you would lose the session. BR2 3000+1000+1000+0 =5000. You 5525 -2(500) = 4525. This 2 1/2 max bet + 1 chip lead is a variation of the 1 1/2 max bet + 1 chip lead teaser I posted several years ago which Colin got right. You could also make a teaser with a 3 1/2 max bet + 1 chip lead and so on up.
Everyone's brain is wired slightly differently, but to me these 'magic numbers' are more about setting goals in the run up to the final round than recognising particular situations when you get there. I think Gronbog and I have a similar approach in the final round, in which running through a more-or-less standard procedure (hopefully) arrives at the best choices, without necessarily checking for any special cases. I suppose if I actually recognise that I have achieved a particular goal as I go into the final round, that can give me a head start in my reasoning process, but if a 'magic number' lead arises by accident (or appears in a teaser) then I would only tend to recognise the fact indirectly, not by running through a checklist of lead sizes. That being said, it is years since I last played in a tournament, so I only half remember much of how my thought processes used to go (and often go awry ) in time-limited, pressure situations.
The first thing at the table upon seeing BR2's bet is to think about locks. Locks are the first and most important thing for us to think about. In this case we have a lock with a minimum bet unless BR2 can somehow manage to split, resplit, and win every hand. We can bet up to 500 and still be safe from double downs and 2:1 blackjacks. Our bet of 500 covers the triple up scenario. We never double down or split, and never hit to any stiff total with any hand after BR2 fails to hit his hard 17 on the third hand. Then we will have the lock. BR2 needed to hit his hard 17 to give himself any chance to win - against an opponent who plays optimally. He may have hoped BR1 would double down and get stiffed. In that line of thinking, he was giving BR1 an opportunity to make a mistake. But the dealer would have to draw out to exactly 17 for it to work.
