Cover Double with Double or Cover Two Swings?

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.

 

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.

 

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.

 

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

 

Keep 1725 bet for BR2 to lose.

 

17025

 

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

 

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

 

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.

 

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.

 

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%

 

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.

 

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

S. Yama

 

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.

 

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.