To Cover, Or Not to Cover (the double downs)

Bet $5000. You are BR1, two out of 4 advance. You should keep more than the most unbet chips and bet the remaining. The most unmet chips 9,500 (Villan3). So, you bet max. If everyone wins you are BR1. If everyone lose, you are BR1.

 

Maybe, but what if you bet $4800? You still have the most unbet chips, so if everyone wins or everyone loses, you are still BR1. However, if villain 1 & villain 2 both double for max and win, you can still beat them both without needing to bet more than your original bet. (V1 = 20,200; V2 = 20,300; Monkey = 20,500). Since you act last, you'll see what your opponents have after doubling. You can stand on a good pat hand, or hit more than once if needed, but you won't HAVE TO limit yourself to one card by doubling. Plus if either V1 or V2 are able to split and double on one of their splits, the most that can be wagered is by V2 at 10,300. A win on both splits gives him 20,600. You still advance with 20,500.
But what about Blackjacks? Suppose V3 AND either V1 OR V2 gets a blackjack and you and the fourth player lose. You would still have the second-most chips at 10,900. V3 would have 10,750. The fourth player would have, at most, 5,300.

Now, I just realized this analysis took me over 45 minutes to figure out, double-check, change and re-check. And that's without being in the heat of the battle. I doubt I would even think this deep at the table, let alone be given enough time to work it out. But these are great exercises and I really appreciate being able to work out my answer and then read answers and responses from others. Even if my reasoning here is way off, it's still very helpful to try. And I don't mind hearing that I'm wrong. I would much rather learn that I'm wrong this way than through the painful self-analysis following another losing round in a tournament!

 

I'm not sure how this compares, but another option might be to lock out all single-bet wins by betting just 300.

V3 would then be totally locked out, which means that in order for you not to advance, both V1 and V2 need to double down and win, or get dealt a blackjack.

I don't know the probability of that; there must be some correlation between winning doubles, but presumably they are less correlated than winning hands in general.

Added to that, there is the uncertainty over whether they will actually double at all. (The cards may make it more attractive for V1 to play for a swing against V2, or either one of them may simply misplay their hand.)

 

My quick bet would be 4,600.
This would apply to either good players or not so good but aggressive (especially if BR3 bets in front of BR2)
The reason to bet not more than 4.6K is to protect your position against losing your hand and BR4 (V3) winning his “free” double, in addition to only one of V1 or V2 winning at least their single bet.
Of course with your opponents’ diminishing chances of deviating from basic strategy and not doubling on almost everything your chances grow from somewhere in 80’s % to almost 100% if you bet 100 to 300.

S. Yama

 

My 1 minute answer is to cover the doubles with a bet of 4,600. As a general rule of thumb, it is almost always better to cover a double even if it exposes you to a 1/2 or full swing.

 

But this would be covering two doubles, which (potentially) puts a different complexion on things.

 

My quick analysis came up with the same answer as SYama and Gronbog - 4600.

 

I'll not be wasting any time with this. If both S Yama and Lefty say it's 4600-------------- it's 4600.

 

Yes --- I believe that it would make it even more important to do so!

 

Why do you say that?

To be clear, we are talking about two opponents, both of whom need to win doubles. If we take the probability of one player doing this as 0.33, then if their hand results were completely uncorrelated, the probability of that would be 0.33 * 0.33 = 0.11. Except, of course, they are correlated to some degree. If I'm reading S. Yama's last sentence correctly, he is assigning a value 0f 0.20 to the probability of two doubles both winning.

But then we have to factor in our assessment of the two opponents, and decide on the probability that they will indeed both double down. If either one doesn't, then betting small gives a lock. Hence the 80% to almost 100% range that Yama mentions. (If I've understood correctly.)


The 4600 bet, acting last, means we just need to avoid being swung by both opponents. I guess the probability of that must be very low indeed (maybe about 3%, with the proper strategy?), so you'd have to be pretty sure someone was not going to double before choosing to bet 300!