# Cover Double with Double or Cover Two Swings?

Discussion in 'Blackjack Tournament Strategy' started by Monkeysystem, May 2, 2018.

1. ### MonkeysystemTop MemberStaff Member

This situation came up last night:

Last hand, one will advance. Bet range 100 to 10,000 in increments of 25. Blackjacks pay 3:2. No surrender. You can insure for up to half your bet and insurance pays 2:1.

The first-to-act button is on BR4.

The following are the bankrolls and the action in the order everyone acted:

=>BR4 = 1,000 bet 1,000
BR3 = ~8,500 bet ~8,500 all in
BR2 = 18,000 (me) bet 9,000
BR1 = 22,700 bet ?

What would you bet if you were BR1, and why?

BR1 must choose from these options:
- Bet low enough to protect against a half swing by BR2, which also protects against a full swing by BR3.
- Bet high enough to be able to double down to cover BR2's all in double down.

There is another factor here affecting BR1's bet choice. Can you identify it?

The actual play of the hand was interesting as well, but let's talk about the betting first.

johnr likes this.
2. ### MonkeysystemTop MemberStaff Member

I should have added in the opening post in this thread that the next decision point in this hand will be more interesting. It will open a line of inquiry into blackjack tournament strategy that I haven't seen before.

I hope it will spark spirited debate and that several players here will want to contribute their thoughts.

But let's get past this betting question first.

3. ### gronbogTop Member

Seat of the pants assessment --- bet enough to cover BR2's double. I believe that the chance of him winning a double is greater than the chance of the swings.

4. ### London ColinTop Member

BR1 can cover a BR2 natural with a single bet. So the best approach looks to be simply to match BR2's bet of 9000. (Could actually bet slightly less than that, but with no additional benefit.)

Whether or not it would be better for BR2 to bet 10,000 in this situation (rather than half the bankroll) is an interesting question.

5. ### gronbogTop Member

I want to add that BR2's bet of exactly half of his chips tells me that he is planning on doubling if necessary or, depending on my read, no matter what the cards are.

6. ### The_ProfessionalActive Member

I choose the second option.
- Bet high enough to be able to double down to cover BR2's all in double down.

7. ### johnrTop Member

Keep 1725 bet for BR2 to lose.

17025

9. ### johnrTop Member

I am thinking better to keep 18025 to cover a push by BR 2

10. ### MonkeysystemTop MemberStaff Member

I'll give the regulars a few more days to log in to the site and comment.

Lurkers: You are welcome to comment here as well. This thread will open a line of inquiry into a strategy element that has not been deeply explored before, so your contribution will likely teach all of us something.

11. ### nomanTop Member

or to have the option to split, if it occurs.

12. ### nomanTop Member

BR 1 is last to bet and to act. I'd go 7,000 with the option to double it depending on the results of the preceding players. You then know whether you have to double for less against BR3 win. Or not with a BR 3 bust. And then whether to double for the 7K against a successful double by BR2. Or as things work out, just play the hand out. If both BR2 and 3 bust, you win regardless. If Br 3 pushes you've covered him. If BR 2 pushes you need a normal win or push.

13. ### MonkeysystemTop MemberStaff Member

These are all great answers. The fact that we don't have a consensus here tells us that the decision is a close call.

I'm leaning towards the small bet of 4,675. The reason for that is the other factor I alluded to earlier - - the lockout of BR3.

In multiway situations like this lockouts affect the math a lot, and can be of primary concern. BR1 can get the lockout by betting as much as 5,375, but the bet of 4,675 yields the additional benefit of covering a push by BR2 while still taking the high. If not for the threat of BR3, BR1 would have a standard correlation bet.

BR2 (me) probably made a mistake by betting 9,000 instead of 9,425+. It's important to retain the option to split a pair, but it's probably more important to force BR1 to choose between covering the push and taking the high. A good rule of thumb for application at the table is to bet at least double the deficit when behind and out of position.

I'd be very interested to see the results of a computer simulation on this situation, both for BR2 and BR1 as it actually happened.

Anyway, here's the next decision point as it played out in real life:

BR4 bankroll 1,000 bet 1,000 cards hard 16, no insurance
BR3 bankroll ~8,500 bet ~8,500 all-in cards hard 20, no insurance
BR2 (me) bankroll 18,000 bet 9,000, cards hard 14, insurance?
BR1 bankroll 22,700 bet 10,000, cards 55
Dealer Ace

What would you do if you were BR2 (me), and why? Would you be able to do it quickly? What would be important about doing it quickly?

14. ### gronbogTop Member

Quick assessment: Take the insurance because it may be your best chance at advancing. If you do it quickly, BR1 may not insure because he probably does not want to insure for the full 5k (and he shouldn't) and he may not be able to do the math for insurance for less. Also, whether you insure or not, you are probably going to be doubling your hand for any chance of advancing and BR1 can defend that by also doubling with no fear of busting. Finally, there is an ugly monster lurking here: If you double and end up stiff, then BR1 can lock you out by doubling and getting anything.

15. ### gronbogTop Member

During the past few days I ran some simulations against the betting situation and the suggested bets. I eliminated BR4 as irrelevant in order to speed up the sims. The sims assume that the other three players play optimally, except that my software does not handle taking insurance.

Betting 9000 to match BR2 finishes first with the highest percentage, but all of the results are extremely close.

BR1 Matches BR2:
Code:
```Player 1:
Finishes 1: 14,806,730/211,034,100 = 7.0163%   Standard Error: 0.001758%
Finishes 2: 38,007,882/211,034,100 = 18.0103%   Standard Error: 0.002645%
Ties for 2: 28,377,858/211,034,100 = 13.4470%   Standard Error: 0.002348%
Finishes 3: 129,841,630/211,034,100 = 61.5264%   Standard Error: 0.003349%
Reaches goal: 14,806,730/211,034,100 = 7.0163%   Standard Error: 0.001758%
Player 2:
Finishes 1: 53,668,375/211,034,100 = 25.4311%   Standard Error: 0.002998%
Finishes 2: 93,119,011/211,034,100 = 44.1251%   Standard Error: 0.003418%
Ties for 2: 28,377,858/211,034,100 = 13.4470%   Standard Error: 0.002348%
Finishes 3: 35,868,856/211,034,100 = 16.9967%   Standard Error: 0.002586%
Reaches goal: 53,668,375/211,034,100 = 25.4311%   Standard Error: 0.002998%
Player 3:
Finishes 1: 142,558,995/211,034,100 = 67.5526%   Standard Error: 0.003223%
Finishes 2: 51,529,349/211,034,100 = 24.4175%   Standard Error: 0.002957%
Finishes 3: 16,945,756/211,034,100 = 8.0299%   Standard Error: 0.001871%
Reaches goal: 142,558,995/211,034,100 = 67.5526%   Standard Error: 0.003223%```
BR1 Bets 6675 so as to be able to cover BR2's double/split with a double/split:
Code:
```Player 1:
Finishes 1: 1,832,552/27,365,469 = 6.6966%    Standard Error: 0.004778%
Finishes 2: 4,826,558/27,365,469 = 17.6374%    Standard Error: 0.007286%
Ties for 2: 3,913,000/27,365,469 = 14.2990%    Standard Error: 0.006692%
Finishes 3: 16,793,359/27,365,469 = 61.3670%    Standard Error: 0.009308%
Reaches goal: 1,832,552/27,365,469 = 6.6966%    Standard Error: 0.004778%
Player 2:
Finishes 1: 7,084,822/27,365,469 = 25.8896%    Standard Error: 0.008373%
Finishes 2: 11,736,440/27,365,469 = 42.8878%    Standard Error: 0.009461%
Ties for 2: 3,913,000/27,365,469 = 14.2990%    Standard Error: 0.006692%
Finishes 3: 4,631,207/27,365,469 = 16.9235%    Standard Error: 0.007168%
Reaches goal: 7,084,822/27,365,469 = 25.8896%    Standard Error: 0.008373%
Player 3:
Finishes 1: 18,448,095/27,365,469 = 67.4138%    Standard Error: 0.008960%
Finishes 2: 6,889,471/27,365,469 = 25.1758%    Standard Error: 0.008297%
Finishes 3: 2,027,903/27,365,469 = 7.4104%    Standard Error: 0.005007%
Reaches goal: 18,448,095/27,365,469 = 67.4138%    Standard Error: 0.008960%```
BR1 Takes the low by betting 4675:
Code:
```Player 1:
Finishes 1: 2,062,650/109,503,153 = 1.8836%    Standard Error: 0.001299%
Finishes 2: 19,648,399/109,503,153 = 17.9432%    Standard Error: 0.003667%
Ties for 2: 33,211,380/109,503,153 = 30.3292%    Standard Error: 0.004393%
Finishes 3: 54,580,724/109,503,153 = 49.8440%    Standard Error: 0.004778%
Reaches goal: 2,062,650/109,503,153 = 1.8836%    Standard Error: 0.001299%
Player 2:
Finishes 1: 34,013,614/109,503,153 = 31.0618%    Standard Error: 0.004422%
Finishes 2: 22,687,321/109,503,153 = 20.7184%    Standard Error: 0.003873%
Ties for 2: 33,211,380/109,503,153 = 30.3292%    Standard Error: 0.004393%
Finishes 3: 19,590,838/109,503,153 = 17.8907%    Standard Error: 0.003663%
Reaches goal: 34,013,614/109,503,153 = 31.0618%    Standard Error: 0.004422%
Player 3:
Finishes 1: 73,426,889/109,503,153 = 67.0546%    Standard Error: 0.004492%
Finishes 2: 33,956,053/109,503,153 = 31.0092%    Standard Error: 0.004420%
Finishes 3: 2,120,211/109,503,153 = 1.9362%    Standard Error: 0.001317%
Reaches goal: 73,426,889/109,503,153 = 67.0546%    Standard Error: 0.004492%```

16. ### The_ProfessionalActive Member

I agree, taking the insurance creates an opportunity for BR1 to make a mistake by either not taking insurance or taking full insurance. In either case, he gives you a chance.

17. ### S. YamaActive Member

Hey gronbog and others!
What would be numbers for bet of 13,400?

S. Yama

18. ### MonkeysystemTop MemberStaff Member

Hi S. Yama!

The maximum bet is 10,000.

19. ### gronbogTop Member

When I made my original post, I had missed the 10,000 maximum and the intention of my advice was to cover the BR2's double with a single bet such as this one. I can run the sim for informational purposes but as Monkey points out, it would not have been allowed in this case.

20. ### London ColinTop Member

I'd seek to insure for just enough to win if BR1 doesn't insure. My mental arithmetic at the table would be painfully slow! [12700-9000=3700. 3700/2 = 1850. Therefore insure for 1875.]

But I suspect you must have another amount in mind.