Go for gold or stay with hope ?

Min/max bet 100/500 & no surrender. Hand 9 out of 10.

BR1 1000 chips bet 100 and BR2 801 chips (me) bet 400.

BR1 got hard 16 and stand, BR2 got hard 13 and dealer up card 6.

I could stand and hope for the dealer to bust so I could achieve a 101 lead, or double and go for a 501 lead. Knowing that I will be first to act on the last hand, ultimately I went for double, which I am not sure is correct ? - And I was thinking what about if I had a hard 14 (or even higher) instead of hard 13, still double?

But what about if my opponent would have got a better hand, such as a 19 or 20 how much would that affect my doubling down decision in this given situation?

 

I'm liking these second-to-last hand teasers. So much emphasis is placed on final hand scenarios while these show that the second to last hand can be important as well. The analysis is, unfortunately, a 2 stage process and therefore more complex.

I don't have the answers you want, but I would like to say that if your goal was to gain a max bet+ lead going into the final hand, you would have been better off betting 800 instead of 400. You would have a better chance of winning a single bet then relying on a possible double/split to get you there. Also, if you lost your 400, you would have been pretty much out of it anyway as your opponent would have a lead of at least 499 vs your bankroll of 401. Might as well bet the chips in that case.

 

I completely agree with GronBog. Betting half your bankroll on the 2nd to last hand was a very bad thing to do because if you lose, you're out of it! So you should have went ahead and bet the max and DD'd otherwise you'd have no hope on the last hand. Gotta take a chance in tournament play! Anyway, what ended up happening?

Do you have Wong's book: Casino Tournament Strategy? It is excellent.

 

The max bet is 500.

Plus this sounds like GameAccount, where there is no doubling for less, so a bet of 400 is probably preferable to 500 -

If you bet 400 you have the option to double, and your single bet win covers a double from BR1.
If you bet 500 you cannot double (but you cover a 3-bet win by BR1).

The former seems more valuable to me.
Edit: Actually, on reflection I'm not entirely sure about that. The min bet of 100 makes a lead of 201 very valuable when you are acting first on the last hand (as has been discussed before), which would be the case with a 500 bet if BR1 does not double.

And a lead of 101 is also preferable to a lead of less than 100, as it means you can bet 100 on the last hand and cover a push by BR1. A bet of 500 means you will lead by 101 even if BR1 doubles.

 

Colin, you are right it was GameAccount and the max bet is 500 and no double for less allowed, thats why I bet 400 to be able to double/split if I needed to.

Now if we are about to compare which bet is better 400 or 500, I thank you for bringing this up too as I am not 100% sure either ! (But BR1 should bet more)

And as for your saying about what betting first when you have 101 lead, it is not better to bet 200 instead of 100, because of the max bet which is 500 ?

*BughouseMaster you have asked me what happened in the end. - Well, this is a really tough question for me because I really do not remember ! I kept this situation in mind because it is a common case when situation like this arise, and I think it is very important for the general outcome to create rules of thumb.

My idea was that even if the dealer has a 6 up card, it still bust less than 50% and if the dealer was not going to bust, was going to be pretty much game over for me. On the other hand doubling my 13 sounded kinda cool, because I was going to bust less than 40% and going to a ma max bet lead on the last hand about 36%. (So from here I have all the other additional questions as exposed in the first post) - I think would be of real high value if we can solve this thread..

 

Do you mean so that you can double to beat a single, max-bet win? If that turns out to be worth more than covering a BR2 push then I hope it's not by much, because that will mean I've been playing it wrong for a long time now!

 

Certainly I would like to see some percentages about it ! I am not sure how valuable it is, but I am certain is valuable because there is no surrender for BR2..

 

I ran two sims with BR1: bankroll 1301, BR2 bankroll 1200 (setting up the situation described above). Both players played optimally in both sims.

Sim 1: BR1 bets 100, BR2 bets 500: BR1 advances 56.27% of the time, BR2 advances 43.73% of the time
Sim 2: BR1 bets 200, BR2 bets 500: BR1 advances 56.05% of the time, BR2 advances 43.94% of the time

So it is extremely close, but covering the push appears to prevail. I suspect that the value of being able to double for the high is not very much when one must act first and your opponent can also double to retake the high. In both cases BR2 advances approximately 43-44% of the time which suggests to me that he advances mainly by simply winning his hand which in turn suggests that it is rarely optimal for BR1 to double.

 

Thank you Mr. Gronbog for the sim ! So Colin, you was right, no worries. And, ultimately, after this sim, it means that I will improve my game play a little !

 

My own statement got me thinking about how the skill level of our opponent might affect this decision. So I ran 2 more sims. This time BR1 plays optimally, but BR2 plays basic strategy.

Sim 1: BR1 bets 100, BR2 bets 500: BR1 advances 57.49% of the time, BR2 advances 42.51% of the time
Sim 2: BR1 bets 200, BR2 bets 500: BR1 advances 66.86% of the time, BR2 advances 33.14% of the time

With BR2 only making basic strategy doubles and splits, the value to BR1 of being able to double for the high increases greatly.

One more case where getting a good read on your opponent could make the difference.

 

Well, after reading that I think it should worthy to bet 200 instead of 100 when playing against people you don`t know because once in a while you may double and end up with a 18 and your opponent nicely stand on his 19 vs dealer 7 (that was only an example) - I think it worth trading 0.22%EV in exchange for this.

Thank you Mr. Gronbog for clearing up the best bet issue, which is indeed very important ! - But, can we somehow getting to the bottom of the initial issue ?

My idea was that even if the dealer has a 6 up card, it still bust less than 50% and if the dealer was not going to bust, was going to be pretty much game over for me. On the other hand doubling my 13 sounded kinda cool, because I was going to bust less than 40% and going to a ma max bet lead on the last hand about 36%. (So from here I have all the other additional questions as exposed in the first post) - I think would be of real high value if we can solve this problem.

PS: I have a few (four) books related to blackjack tournament strategies, including the one from Mr. Wong suggested by BughouseMaster, but either I have forgotten what I have read (which I believe is not the case), or really none of these books can help me with this common problem I have described in here.. :sad:

 

Wong's book is tilted towards going into the last hand as the leader (or at least one of the advancing positions) or busting out trying.

As Gronbog said the situation becomes much more complex if you start looking at the hands before the last one even against one player. With more than one player it becomes even more convoluted.

I am not sure some one could write a book looking at all the different scenarios.

Your examples are enlightening at pointing out things to think about. It is a shame that most of the tournaments I play in will not have just 2 people towards the end of a round.

If you keep coming up with these things and Gronbog keeps running his sims , who knows we may get a little clue. I doubt that I will remember the specifics, but it could put something in my brain that comes out at the right time.

 

Yes, I am very interested in solving these second-last hand issues. It's mainly a matter of finding the time. I have a couple of personal projects related to upcoming tournaments that I would like to finish, before attending the events. Once I'm done with those, then I will try to address these. It's not a matter of difficulty. It's just that multiple simulations will be required to solve them.

 

I posted a proposed series of sims for solving another teaser to this thread by accident. I have reposted it to the proper thread:

http://www.blackjacktournaments.com/bb/showthread.php?t=7907

 

I have completed the analysis of this situation. The results are in a spreadsheet which can be found at http://gronbog.org/results/blackjac...y With Hope/Go for Gold or Stay with Hope.xls. Despite the strong possibility of being locked out, should he lose his double, BR2 (Player 2) also has a strong possibility of a max bet+ lead, which ends up being more valuable. Our hero has a 35.29% chance of advancing by doubling vs 31.89% by correlating (standing).

The balance would clearly shift, the stiffer your hand becomes. The probability of being locked out would increase while the probability of attaining that max bet+ lead would decrease.

Your opponent's hand would have less of an effect on the decision (perhaps none), since you don't need him to lose in order to gain the max bet+ advantage.

 

I really do not want to be a pain, but now I dare to affirm that doubling on a hard 14 would still be very very close, if not optimal. I`ll try to explain why: your analyze shown that with the given bets and bankrolls standing on a stiff hand as BR2, will have chances to win of ~31.9%. And doubling on a hard 13 on the next to last hand (with the given bets and bankrolls) will yield a ~35.3% win chance. - I look at the doubling down chart and I see that this is very close to the winning percentage on doubling down/hitting on a hard 13 in a regular game of blackjack, which is ~36%. And if I look at the winning percentage on doubling on a hard 14, I see it is about ~32.7%. - Concluding from here, I believe that the winning chances for BR2 should be just about ~32% for doubling on a hard 14 ?

 

While the numbers may be coincidentally close for doubling on hard 13, and most of the contribution to Player 2's success does come from winning his double, I would be hesitant to conclude that his overall chance of success can be determined from the chance of winning his double alone.

You need to recompute the probabilities in column B for each of the possible outcomes in order to get the answer for how to handle hard 14.

 

Correction

It has been pointed out to me that a better bet for Player 1 on the final hand for the situation of

P2 BR: 801, Bet 400
P1 BR: 900, Bet ???

would be 449, as opposed to the 450 I used in the analysis. This allows him to retain the low should he need to double to retake the high. This reduces Player 2's chances of prevailing in that situation from 0.3429 to 0.2832. His overall chances of advancing by doubling on the 2nd last hand are then reduced to 0.3522. Doubling on the 2nd last hand is still his best option. I have updated the spreadsheet on my web site.

This is an illustration of how the skill level of one's opponent can change things and why this type of multi-hand analysis, while interesting, may not have much practical value.

 

Thanks for the update, it really helps ! But I think that these kind of situations may be more valuable than they look. - I am thinking that a non advanced blackjack player may see for example, my double on hard 14 vs dealer 6 like a very fool move, and think of me that I am a poor skilled player. If this happens, I believe it may have more of a psychological value, in making him play more with games with me regardless of the actual game result. - And this only helps..