Two Brain Cramps at the Meadows

[gronbog]

I probably shouldn't have posted this due to the extreme embarrassment involved, but the situations below should make for interesting discussion, regardless of my unbelievable errors (especially brain cramp # 2).

I found myself on the final hand of the final table at The Tony Dorsett Celebrity Blackjack Tournament at The Meadows in PA:

BR1: Bankroll: 4500, Bet: 1500
BR3: Bankroll: 1800 and change, Bet: all in
Me : Bankroll: 3210, Bet ???

All bankrolls are before the bets were placed. Normal doubling rules, double for less allowed, may split twice (up to 3 hands) except aces, late surrender allowed.

Brain Cramp #1: I saw that I could take first low. Both players were celebrity players, and did not even know what surrender was, so BR1 would not have realized that he could lock me out if I did so. Another possibility was to split my bankroll so that I could go after the first high by doubling or splitting. For some reason, I became focused on BR3 and thought that if I covered his win, then I would be ok if BR1 lost --- WRONG. For some reason, I did not realize that by doing so, I would give up the low to BR1.

So, not knowing exactly how much "change" BR3 had, I confidently bet 600 to cover his win. I've since run some numbers (and will post my results once I get some input from you all) and it looks like I made pretty much the worst bet possible.

So the cards were dealt and came as follows:

BR1: Bankroll: 4500, Bet: 1500, cards: hard 17
BR3: Bankroll: 1800 and change, Bet: all in, cards: busted
Me : Bankroll: 3210, Bet 600, cards 7,7
Dealer: 9

At this point BR3 is gone and as I contemplate hitting my 14, I suddenly realize that I've given up the low to BR1 and that if I bust, it's over, I can't double or split for the high and if I don't hit to at least 18, it's also over.

Brain Cramp #2: It came into my head that, if I surrendered, BR1 would be forced to win his hand (17 vs dealer 9) and I wouldn't have to go for the swing (oh, so WRONG!).

So, feeling pretty proud of myself for being so clever, I went ahead and surrendered. Turns out, the dealer drew to 17, so BR1 pushed and won the tournament. I was second. It was all hand shakes and "good game" and I was in a good mood despite finishing second. After all, I thought I had made a clever play. I even went as far as to explain to BR1 why I surrendered and he agreed that it was clever and confirmed that he didn't even know about surrender.

I realized my error when the chips were counted down and my total was 2910. I thought there was a mistake and then the light went on. I don't remember how the cards came and what would have happened had I hit to 18 instead, so I don't know for sure if this mistake cost me anything, but locking oneself out of first place has got to be the stupidest thing one could ever do. :bomb:

Ok, so let's have something good come out of my incompetence:

1) What would my best bet have been off the top?
2) What is the actual optimal strategy for the position I found myself in?
3) If I actually had 3310 instead of 3210, would surrendering have been the best move?

I look forward to your thoughts and yes, fire away. I can take the heat! :flame:

 

[London Colin]

1) What would my best bet have been off the top?

That might depend on whether or not the goal is to maximise the chance of taking 1st place (which might not always be optimal in terms of EV, depending on what 2nd and 3rd pay.)


From the calendar entry it appears that the max bet was 2000. So a bet of 2800 to take the high is not available.

It seems to be a choice between 400 and 1400 -

400 covers a BR3 win and also offers the opportunity to surrender back to 3010, which will be particularly tempting if BR1 busts, as you can then do no worse than 2nd. But if BR1 looks like winning, there is nothing you can do about it. (And if he should happen to surrender, then you need to win a double.)

1400, on the other hand, covers a BR3 push and is also just enough to beat BR1 by doubling.

I think I would tend to go for 1400, though I haven't done the maths to establish which is actually better. (And I've confused myself a little, but I think 400 would the one to gain favour as 2nd place is given more value.)

 

[LeftNut]

The problem here is that BR3 has "1800 and change." Without knowing exactly what that number is, it's almost impossible to determine your ideal bet. Colin is right, though, the difference between 1st and 2nd cash would be a factor in my decision. Having great position is huge here no matter what the exact chip count.

Let's assume BR3 has 1800 even. If the difference in cash is enormous, then I'm shoving Colin's excellent 1400 bet with the mindset that if BR3 busts (as he did) I'm going to double almost anything or split 88 or higher with a no-bust approach. If the difference isn't enormous, then I'm betting his 400 with the mindset that surrender looms large. After BR1 had stood on his 17 v. 9 and BR3 busted, I surrender knowing that BR1 is toast unless the dealer breaks or makes 17 exactly.

 

[S. Yama]

Colin and Leftnut are right taking into consideration value of finishing first, second, or third.
However, in this case, if going for first is the main objective, frequency of finishing in the second place may be close, regardless the bet.
Without running numbers I have a feeling that bet of 400 would perform slightly better than 1,400. Just a guess, 400 gets first in low 40’s % and 1400 high 30’s %, with second place close to 50% in both cases. It may be a very close decision even if BR3 had 1,890 as when BR1 loses our bj (and winning double) adds to chances to overcome BR3 all-in win. Gronbog, how much off am I, compared to your invaluable sims?
S. Yama

 

[London Colin]

The problem here is that BR3 has "1800 and change."

Oops. Didn't spot that. So 400 does not cover a BR3 win in gronbog's actual scenario. Nor does 1400 cover a BR3 push.

Let's assume BR3 has 1800 even. If the difference in cash is enormous, then I'm shoving Colin's excellent 1400 bet with the mindset that if BR3 busts (as he did) I'm going to double almost anything or split 88 or higher with a no-bust approach.

Similary if BR3 stands on a stiff total, you have a lock on 2nd and can take a free double, striving for 1st.

 

[gronbog]

Simulation Results

Thanks for your thoughts (and thanks for no shots) everyone! I apologise for leaving out the important information about the betting limits (25-2000) and the prize structure (1st 20,000, 2nd 5000, 3rd, 2500). "And change" referred to an amount less than 100. It looked to be somewhere around 60 to me at the time.

With regard to question 1) What would my best bet have been off the top?

I ran sims for the following bets with me playing optimal strategy and the other two playing basic strategy. The results are as follows:

Bet P 1st P 2nd P 3rd EV Comment
----------------------------------------------------------------------------------------------------------------
200 34.35% 33.93% 31.73% $9,360 Takes 1st low
400 32.29% 36.22% 31.49% $9,056 Can surrender to 1st low, can double to take BR3 win
600 20.45% 57.51% 22.04% $7,517 My actual bet (ouch)
1600 35.80% 40.31% 23.89% $9,773 Takes BR1's push, can double or split for the high
2000 24.95% 48.33% 26.72% $8,075 BJ takes BR1 win, can double for the high

I didn't consider Colin's suggested 1400 because of the "and change". However, it looks like the instincts of Colin and Lefty are correct in that going for the high via doubling or splitting has both the best chance for finishing first and the best EV for prize money. Note also the value of being able to split as betting 2000 has both a lower chance of finishing first and a lower EV for prize money.

However Colin's and Yama' feeling about a better probability of finishing second with a bet of 400 vs going for the high was incorrect. Both the probability of finishing second and EV for prize money are lower for the bet of 400.

As for protecting 2nd (should the prize structure have warranted it) it seems that my actual bet did a pretty good job of that.

With regard to question 2) What is the actual optimal strategy for the position I found myself in?

My strategy generator generated the following recommendations with their respective probabilities. Once again, the model was me playing optimal strategy and my opponent playing basic:

Action P 1st Comment
------------------------------------------------------------------------------------------------
Split 23.53% 3 bet win takes BR1 push
Hit to 19 or better 17.08% Need 1/2 swing
Double (any amount) 13.15% Fewer chances than hitting
Stand 00.00% Lose both ways
Surrender 00.00% Only an idiot would ...

I don't think anyone would have been surprised to see "hit to 18" up there since BR1 had stood with 17. However it turns out that stopping at 18 is 1.26% worse than hitting again.

Finally with respect to question 3) If I actually had 3310 instead of 3210, would surrendering have been the best move?
i.e. If I could have actually surrendered to take the low.

My strategy generator generated the following recommendations with their respective probabilities. Once again, the model was me playing optimal strategy and my opponent playing basic:

Action P 1st Comment
----------------------------------------------------------------------------------------------
Surrender 65.52% Force BR1 to win or push
Split 25.70% 2 bet win takes BR1 push
Hit to 19 18.33% Need 1/2 swing
Double 18.30% 2 bet win takes BR1 push
Stand 00.00% Lose both ways

Turns out, had I made the 400 bet or had a bit more bankroll, surrender would have been a clever move indeed.

 

[London Colin]

I ran sims for the following bets with me playing optimal strategy and the other two playing basic strategy. The results are as follows:

Bet P 1st P 2nd P 3rd EV Comment
----------------------------------------------------------------------------------------------------------------
200 34.35% 33.93% 31.73% $9,360 Takes 1st low
400 32.29% 36.22% 31.49% $9,056 Can surrender to 1st low, can double to take BR3 win
600 20.45% 57.51% 22.04% $7,517 My actual bet (ouch)
1600 35.80% 40.31% 23.89% $9,773 Takes BR1's push, can double or split for the high
2000 24.95% 48.33% 26.72% $8,075 BJ takes BR1 win, can double for the high

I didn't consider Colin's suggested 1400 because of the "and change". However, it looks like the instincts of Colin and Lefty are correct in that going for the high via doubling or splitting has both the best chance for finishing first and the best EV for prize money. Note also the value of being able to split as betting 2000 has both a lower chance of finishing first and a lower EV for prize money.

However Colin's and Yama' feeling about a better probability of finishing second with a bet of 400 vs going for the high was incorrect. Both the probability of finishing second and EV for prize money are lower for the bet of 400.

I can't speak for Yama, but all my comments were predicated on the assumption that BR3 had exactly 1800, having not spotted the 'and change'. That would boost the probability of finishing 2nd.

 

[London Colin]

sim

Hi gronbog,

Would you mind running your bet sim for 400 and 1400 (and maybe 200 too) with the BR3 bankroll of exactly 1800. I'd be curious to see the results.

Thanks,

 

[gronbog]

Sure. I'll get back to you as soon as I have the results.

 

[gronbog]

Hi gronbog,

Would you mind running your bet sim for 400 and 1400 (and maybe 200 too) with the BR3 bankroll of exactly 1800. I'd be curious to see the results.

Thanks,

I ran the sims, and here are the results:

Bet P 1st P 2nd P 3rd EV Comment
----------------------------------------------------------------------------------------------------------------
200 35.09% 32.75% 32.16% $9,460 Takes 1st low, can double to take BR3 high
400 33.28% 39.94% 27.78% $9,298 Can surrender for 1st Low, takes BR3 win
1400 36.00% 41.99% 22.01% $9,850 Takes BR3 push, BR3 win, can double for 1st high

(How does one get columns to line up without using CODE or PHP? The "remove formatting" button does not appear to work).

So, the "and change" was definitely a factor. The best bet here (1400) beats the best bet of the original example (1600) both in terms of finishing 1st and EV of prize money. Also, as Colin surmised, betting 400 does the best job of protecting 2nd place, should the prize structure have warranted it.

 

[London Colin]

Thanks

I ran the sims, and here are the results:

Bet P 1st P 2nd P 3rd EV Comment
----------------------------------------------------------------------------------------------------------------
200 35.09% 32.75% 32.16% $9,460 Takes 1st low, can double to take BR3 high
400 33.28% 39.94% 27.78% $9,298 Can surrender for 1st Low, takes BR3 win
1400 36.00% 41.99% 22.01% $9,850 Takes BR3 push, BR3 win, can double for 1st high

(How does one get columns to line up without using CODE or PHP? The "remove formatting" button does not appear to work).

I've always found CODE to be the easiest way to do it. There is no formatting to be removed; the standard font simply has a variable width. Picking a different, fixed-width font from the list should work too, I think.

So, the "and change" was definitely a factor. The best bet here (1400) beats the best bet of the original example (1600) both in terms of finishing 1st and EV of prize money. Also, as Colin surmised, betting 400 does the best job of protecting 2nd place, should the prize structure have warranted it.

Looking at the figures, 1400 appears to protect 2nd place better?

 

[gronbog]

I've always found CODE to be the easiest way to do it. There is no formatting to be removed; the standard font simply has a variable width. Picking a different, fixed-width font from the list should work too, I think.

Yeah, I've tried CODE, but don't like the way if ends up in its own small (scrollable) window. I also tried various fonts from the list, but didn't discover a fixed width one. I'll try again next time.

Looking at the figures, 1400 appears to protect 2nd place better?

Oooops. Right you are.