Insurance Mucks Up the Works..?

I would bet $400. This way I would win if either or both of BR1 and BR2 loses even if I lost. I would not get the high unless I get a chance to double or split. If only one took insurance then not taking insurance will give me the high over that person. I would take insurance only if both BR1 and Br2 took insurance and one of them too insurance for less, then I will put full insurance.

 

My priorities for this bet are (in order):

• Take the low on both opponents: Any bet of 422.50 or less accomplishes this.
  
• Have the option to take the high on either opponent with a double/split. A bet of at least 290 is required.
• Beat either player with a blackjack, if possible: In this case it is possible with a bet of 385 or more.

So, I would bet 385. This leaves me with 422.50 - 385 less a chip (2.50) = 35 to play with for insurance without compromising my main bet and I'm acting last. In the event that the dealer shows an Ace:

1. If either opponent declines insurance, then I can decline as well and advance with the low if the dealer has blackjack
2. If Villain 2 takes insurance, then I can take insurance for 15 to 35 more than he does to beat him if the dealer has blackjack.
   
3. If Villain 1 takes insurance, then I can take insurance for 27.50 to 35 more than he does to beat him if the dealer has blackjack.
4. If both take insurance for an amount within 7.50 of one another, then both can be covered by one insurance bet of 27.50 more than [edit] the largest of their two insurance bets. [/edit]

[edit]
Note that points 2 and 3 are superseded by point 1 above, since this is a two advance situation. They would apply when trying to win the table only (1 advance, or final table with a top heavy first prize).
[/edit]

In this case, since there is so little room for error, and since insurance considerations were last on my priority list, I would probably not have given any though to it until the dealer was showing an Ace and one of my other opponents had already taken insurance.

 

I was going to post something but Gron covered everything pretty good. I could add nothing to his analysis.

 

I admit that possible insurance would not cross my mind when I am making a bet in this situation. Playing last I have the options and would decided what to do on insurance the 7.7% of the time it comes up.

I can not handle both villains having max DDs/splits (without getting 3 bets on table), but I can handle one DD and one BJ if I bet enough. I would need to bet 390 for a villain 2 BJ and 415 for a villain 1 BJ. If I was at the table, since I can not make a bet that would give me spot 2 if we all win or lose, I would probably end up betting 420 and keeping the low

 

Ahh, perhaps the goal of covering the blackjacks of both villains is what Monkeysystem was getting at. The required bets eliminate the possibility of insurance for our hero. I suppose betting to cover the blackjacks of our opponents should take precedence over worrying about insurance for a dealer blackjack, since there are two opponents and only one dealer.

 

I've been trying and failing to put together some formulas to describe the situation, and use them to arrive at numbers. Having more or less given up on that idea, I'll just ramble about the subject instead..

When a villain declines insurance, that's just a special case of insuring for less, where the amount of the insurance is zero. So long as the villain's insurance is small enough, a door is left open for you to beat them by winning a larger insurance bet of your own.

As you consider varying your main bet from the minimum of 290 to the maximum of 422.50, each chip added to the main bet also adds an additional chip to the insurance bet which you could afford to make while still being able to double/split for the high after losing it.

The amount by which a DD win overshoots the required target (win > 575, to overtake villain 1) determines how much is available for insurance.

At the two extremes - a bet of 290 means you can't take any insurance, while a bet of 422.50 means you can take full insurance (210?), should you wish.

Losing the extra chip from the main bet is compensated for by the 2:1 payout of insurance, meaning that by betting more initially you are extending your reach forwards with regard to the total you can reach by winning the corresponding insurance bet.

Things change when you reach the point where adding a chip to your main bet does not allow you to add a whole chip to the insurance (i.e. when you can afford full insurance). At that point you cannot extend the reach of a winning insurance bet any further forward - an additional chip lost on the main bet is exactly balanced by an additional 1/2 chip paying 2:1 on the insurance.

Trailing Villain 1 by 75, we want 2B - I > 575, where B is our main bet and I is our ins bet. I maxes out at B/2, so that is 3B/2 > 575, B > 383.33. So once we pass this threshold, increasing the bet size has no insurance-related benefits.



But I guess the question is also focusing on the low side. With two villains, one of them might insure and the other not. So there might be scope to factor in their most likely max insurance amounts (<50 for Villain1 and <25for Villain2 ?) and bet just enough to be able to make an insurance bet big enough to leapfrog either of those in the event of a dealer BJ, while at the same time keeping the low against the other, non-insuring Villain, in the event that the dealer does not have it.

This is the point where the complexity really starts to defeat me...

 

Don't forget that this a two advance situation. If you have the low over either villain who does not insure, then you don't need insurance. That's why my analysis and limits were based on the low. It hadn't occurred to me to analyse this from the perspective of preserving the high while taking insurance because the situation seemed tailor made for taking the low and only taking the high by doubling/splitting as a last resort.

 

Ah, I did not so much forget as fail to notice in the first place!

 

I think doubling (for less) to get into the 'advance if everybody gets the same result' position might come into play if there is a sufficient difference in the insurance amounts of the two opponents.

So, if possible, the bet size needs to leave the maximum wiggle room for both an insurance bet (in case both opponents insure) and a double for less, while still keeping the low against one opponent if both the insurance and the dd are lost.

It also occurs to me that a sufficiently large difference between their two insurance bets could allow a variation of the same tactic to be employed with the insurance bet itself. It would require some pretty clueless play from someone, but a window might open up for an insurance bet size such that you advance in 2nd place if you win it, and otherwise are left with the high and the low against the villain who took too much insurance.

 

If you play for the low on both players you only need to consider insurance if both players take insurance. If only one insures you advance if the dealer has a BJ.

 

That's understood. The issue is how best to size your initial bet in order to have the most flexibility in responding to whatever combination of insurance bet sizes the two of them might come up with. [Or perhaps even to influence their choice of insurance bet size to your benefit?]

 

The reality of the situation is you have position and 2 of 3 advance. You only need to beat 1 opponent BJ and can't cover an opponent double down. You only need to even consider insurance if both players insure. Otherwise you have the low over at least 1 player should the dealer have a BJ. The best strategy in general is probably the best strategy considering surrender. If you want to consider the odds of a dealer BJ that allowed for insurance into your strategy you are assuming both opponents take insurance. As I see it for this particular situation you need to give up on beating another players BJ with a double or split and just try to cover their initial wager straight up.

Given the specifics either insurance is irrelevant because the opponents don't both take insurance or take insurance for small enough amounts (as they should) to not open the door for a high. So you either bet $390 to $422.50 to cover a BJ by either player or you bet $290 to $422.50 to take the low and cover the opponents bets as made with a double or split. The lower you bet the more you can put toward insurance and you will see the players hands before you need to decide so you can weigh needing to double down versus the opportunity afforded by the other 2 both taking insurance. If BR1 takes full insurance a beat of $330 takes the high if the dealer doesn't have BJ. Since 2 advance I think a bet of $330 might give you the most ability to use your position but perhaps just ignoring insurance altogether makes the most sense. I doubt both players will insure for enough to make considering it worthwhile.