Teaser from St. Ignace

How it went down

Agreed. Thanks to everyone who checked in on this one, and I hope you got the mental wheels spinning on it.

Here's what I did - and why. Betting first, I bombed in for the max $500 bet. The reasoning was that my opponent had already shown me that he wasn't a terribly sophisticated BJT technician. You see, on the last hand of regulation, he had a significant lead over me but bet small enough to allow me a max DD to catch him. Even though I was dealt a hard 17, I did it anyway because I had 0% chance without it. The cards smiled on me with a 3 - and that's how we got to the playoff.

Going into the final playoff hand, with my scant $50 lead and betting first, I thought about the $50 bet that seems popular in this thread. However, if I bombed in, there's actually a fairly narrow range of excellent bets that he could make and I was certain enough that he wouldn't know those. And I was right - he bet the $50 minimum. As it turned out, I got 17 and he got a soft something around 14 or 15 (don't remember exactly) - with the dealer showing 5. Had his bet been a little more savvy, he had a stone-cold DD opportunity. Dealer busted and that was that.

Billy, kudos on chiming in right away with your answer, I would expect nothing less. But I'm afraid that I don't like the $480 part of your range because $480 vs. $500 gains you nada, but that missing $20 could kill you in the end if both players managed to get 3 bets on the table. You'd give away the high. Admittedly a long shot, but since holding back the extra $20 gains you nothing, might as well go whole hog. Kudos also to toolman and Colin for some well-thought-out ideas. Solid reasoning from both.

Edited to say - My apologies for overlooking your 480 bet, Barney - but I still disagree with it!!!

 

Teaser part 2

Now for the second part of the teaser. You are the opponent in the same situation, down by $50.
I have already bombed in with the $500 max. What do you do now?

(P.S. Bets must be in $10 increments.)

 

390

As BR2 I would bet $390. That's the most I can bet such that BR1 can't surrender without allowing me to do the same and win.

If BR1 does not double or get a 2:1 BJ, then we have the strong version of Curt's Revenge - double for the high if that offers the best chance.

If BR1 doubles and I have a pair, then it's a similar situation, but with the need to get three bets out if going for the high.

If BR1 gets a 2:1 BJ and I have a pair, then winning three bets is my only hope.

And, of course, if I should get the 2:1 BJ, then it's BR1 who must double.

 

Anyone else wish to take a swing at this one?

"Bueller? Bueller?"

 

Monkeysystem's writeup is quite extensive and I wouldn't dare "take a swing" at it. But I do have 2 questions:

1) Isn't Mrs. Monkeysystem a little upset because of Mr. Monkeysystem spending so much time with "the boys" writing up these extensive analysis?

2) What is "Bueller"? (it's not in my spell-checker or dictionary)

 

Toolman, you sure got that right. It's why Monkey scares the crap outta me at a TBJ table, he's forgotten more about the odds & numbers in this game than I'll ever know.

A reference from the hit movie "Ferris Bueller's Day Off" with Ben Stein delivering the line as his teacher attempting to take attendance. Bueller was absent, of course! It's become slang for waiting on a response or reaction from someone.

 

Leftnut mentioned a 'range of excellent bets'. In this situation, I think the top of the range must always be the best bet, and is certainly the easiest to calculate quickly. The minimum BR2 bet to cover the high with a double would be $280, so I would say the range is actually $280 to $390. But $280 does not allow you to beat a two-bet win with a three-bet win.

I would arrive at $390 by subtracting twice my deficit, plus a chip from BR1's bet. That, then, is the largest bet possible that guards against the surrender, and it automatically covers as many multiple-bet possibilities as can be achieved. (In this case, three bets beat two, and four bets beat three.)

 

The Count

The problem I see with the questions and answers in most all of the "strategy and teaser" threads is that everything is based on a 0 (neutral) count. The people that DO count tell me that a neutral count is rare (other than first hand dealt after shuffle, of course).
If you look at London Colin's post #8, he/she gives percentages based on a neutral count. How do you think those figures would change with a +12 true count?
That is why I think the count needs to be factored in on all close percentage bets.
The counters don't weigh in on this because they don't "out" themselves.
Now LeftNut, if I was a counter I probably wouldn't have said my bet would be in the $480-$500 range when acting first because that would be a bad bet if the count happened to be -12.

Billy C

 

Count me in

Billy C, counts could and should effect bets, and even more so playing strategy, and for less than a handful of tournament players it makes significant difference, but for 99.99% of all players it would rather be a distraction. There is also a group of people that enjoy the process and try to apply it (more or less successfully) – more power to them.

To keep things in the right perspective hands in the range of plus one to minus one (rounded) constitute 70% of all played hands. The chance of True Counts of +12 or better is 0.000076 – that is one in 13 thousand played hands. TC of plus 4 or better happens about 4.4% of the times, one in one hundred hands will have TC of +9 or better.
That +4 count still wins 44.4%, loses 45% and ties 10.7%

With so many close decisions any help is welcomed (but don't count on immediate big help, it would make difference for players who evenly mastered all other aspect of the game and play lots and lots of live tourneys)– happy counting

S. Yama

 

Yes---But

What you're not telling us noncounters is that you're going to increase your bet size at +4 because BJ's and doubling down possibilities make it advantageous to do so.

Billy C

 

I think what Yama is saying is a +4 count brings the expected win-loss ratio to even. The difference between winning or losing a hand comes to a negligible difference. So, a bet of at least 480$ or a bet 50$ is A O K. if we ignore the second player's tourney experience and use the raw numbers.

 

OK, here's my thoughts on the opponent's situation in the second part of this teaser. Then I'll get out of the way and let you guys debate the value of counting in a BJT - or to tear me a new one for whatever reason strikes your fancy.

Colin hit it clear into the centerfield bleachers with his quick response. It's my feeling that 390 is the best bet here. The "range" I mentioned was 360 - 390. You can't bet 400 or more because you do, indeed, give away the chance to surrender into a win, so the ceiling is 390. A bet of 350 or less forces you to get FOUR bets out to take away the high against BR1's max bet double (you must win $1,060 to accomplish that), so the basement is 360. Granted, it's a longshot, but since you give away nothing by betting 360-390 vs. the 280 you'd need to DD and beat BR1's single bet, you might as well leave that little bitty door open.

When I blasted in with the max bet, I was playing against someone who had already chicken-bet in a crucial spot - on the last hand of regulation. He gave me a chance by doing that. I had a feeling that he wasn't experienced enough to make a good move with the tiebreaker final hand bet.

Thanks to everyone who responded. I think this is the first teaser I've ever posted, and it was nice to see a lively discussion develop!

 

Back to basics

When I first saw this teaser, I assumed it must revolve around the complications of the possible tie which is implied by a lead of exactly a min bet. I posted the figures which I had arrived at for the $50 BR1 bet - Tie:5%, BR2:44%, BR1:51%.

If you assume a roughly equal chance for BR1 and BR2 to go on and win, following a tie, that makes BR1's chances 53.5%, as opposed to the 56% which would be the case with a slightly bigger lead.

I was going to work out some further numbers, to show the probabilities in the actual scanario that played out, but reconsulting Wong has got me slightly confused. Could someone clarify the following for me -

Am I right in thinking that this assumes a small bet from BR2? (less than their deficit, which seems like an odd assumption.) Otherwise, BR1's chances are surely worse than 52%, since BR1 could push while BR2 wins. And indeed Example 6 gives a figure of 49%.

Using the figures in Table 4, I arrive at -
BR1 Advances =>
BR1 wins or both push or (BR1 pushes and BR2 loses) = 44% + 1% + 5% = 50%

BR2 Advances =>
BR1 loses or (BR2 wins and BR1 pushes) = 48% + 2% = 50%

Is the 1% difference between this and Example 6 just a rounding issue, or is there a subtle flaw in my logic?

 

Thanks Monkeysystem

I think what had me confused was that the assumption was unstated, and then flatly contradicted in the later example.

So my figures for the BR1:$500, BR2:$50 case would be -
Tie: BR2 wins and BR1 pushes = 2%
BR1: BR1 wins or both push or (BR1 pushes and BR2 loses) = 44% + 1% + 5% = 50%
BR2: BR1 loses = 48%

- making BR1's overall chances about 51%, compared to 50% if BR2 had bet at least $60, and 47.5% if BR2 had bet at least $280 (45% without the 2:1 BJ).

In contrast, a bet of $50 would have guaranteed at least a 53.5% chance for BR1, regardless of BR2's response.

Leftnut,

I might be misinterpreting your comments, but you seem to have been more pleased to see BR2's $50 bet than is warranted. The only reason for you to bet $500 was the hope/expectation that BR2 would match you. Failing that, a $50 BR2 bet is the next best result, but it represents a gamble that was lost (but only at the cost of a few percentage points, so quite possibly a worthwhile gamble).

 

Contradiction?

Wow, if I contradicted myself in this teaser, then I certainly apologize. :yikes:

Colin, the reason I was so happy to see my opponent min bet after my max bet was that he shafted himself out of any chance to DD for the high. Which was what I was fairly certain would happen. Figured I was within maybe 1% of being 50/50. The only two choices I really had was either min or max, had I pushed out something like 250 then he would have had more choices. He'd already shown a tendency to underbet in a crucial situation, when thoroughly pondering the situation first would have been better. Of course his max bet would have pleased me even more, but he still acted in a way that handcuffed himself unnecessarily.