Average Insurance Bet

I am trying to figure profit potential using an alternate method of determining when to take insurance.

I was looking at the way the average bet for Insurance was calculated for the I18 and it struck as not quite right. The method used was to determine the average bet that was made at a +3 or higher count, weighted by the frequency of the count occuring from Stanford Wong's Professional Blackjack (okay so far), and then multiply by the frequency that the dealer will have an ACE showing (1/13).

This is probably alright for comparison purposes of determining the I18, but since the HiLo includes the ace in the count, doesn't +3 and higher counts also imply that the dealer will have an ace showing more often when larger bets are out, therefore skewing the average insurance bet even higher?

In other words, the frequency of placing insurance bets increases with the count just like the bet size does and both factors should be accounted for when trying to determine average bet size. Is my logic flawed or are them some other factors to consider?

I've made this point before on the GC pages.
The effect is not that large however and ignoring it does not result in significantly reduced expectation.

Part of the problem is determining what your bet spread is. Its difficult to come up with a general answer.

Give me a few years and I might come up with more accurate figures based on typical bet spreads-but more pressing matters are afoot.

Congratulations on figuring this out-its refreshing to hear from someone who questions things intelligently rather than meekly accepts them.

The point you make applies not only to insurance but, to some degree, to all plays in the I18. For example, if we're supposed to make a certain double or split, we can't be sure that the holding occurs just as frequently at a count of zero as it does at, say +4.

I made no attempt to quantify this effect in the original article because a) I wouldn't have possibly been able to accomplish it back then, and b) I am certain that the significance is minuscule.

But, your reasoning is correct.

Don

In other words, the frequency of placing insurance bets increases with the count just like the bet size does and both factors should be accounted for when trying to determine average bet size. Is my logic flawed or are them some other factors to consider?

You're right that you can't use 1/13 for all counts. Let's say you want to analyse 6D using Hi-Lo.

Prob. of getting an ace
-----------------------
TC = 0 ==> 0.077
TC = 1 ==> 0.079
TC = 2 ==> 0.081
TC = 3 ==> 0.083
TC = 4 ==> 0.085
TC = 5 ==> 0.087

Instead of 1/13 = 0.077

Sincerely,
Cacarulo

Why are we concerned about the probability of getting an ace? We already have the ace, otherwise we would not even be discussing insurance.

What we are concerned with, it seems to me, is the probability of having a 10 under the ace.

Or am I reading this all wrong?

Monty Bancs wrote:

I was looking at the way the average bet for Insurance was calculated for the I18 and it struck as not quite right. The method used was to determine the average bet that was made at a +3 or higher count, weighted by the frequency of the count occuring from Stanford Wong's Professional Blackjack (okay so far), and then multiply by the frequency that the dealer will have an ACE showing (1/13).

That's why I posted the different frequencies.

Sincerely,
Cacarulo

I am trying to quantify the increased profit using a sidecount to improve IC.

I think the effect is somewhat minimized with the other plays because they usually involve a mixture of both high and low cards. As I said, for comparison purposes between plays, using the full deck average frequencies is valid and I was not trying to nit-pick how many hairs can be split on the head of a pin. I'm just trying to come up with an accurate estimate of insurance potential $ to see if the extra work is 'worth' it.

As you reread the I18 chapter, you'll see that, for the 4-deck game in question, when I attempted to rank the importance of the plays, it was necessary to assign an average bet size (based on the spread) to each of the counts. This is because it is obvious that not only is the frequency of the count important, but also the amount of money we'll have riding when we make a departure.

As insurance is a departure, we needed to calculate the average wager on the table when, in fact, we do insure. And, to do this, I followed the methodology outlined in the book.

The point is that, at TC = +5, I'm more likely to encounter an ace than for TC = 0, so I should be weighting the bet size at +5 ever so slightly more than I did.

Cacarulo's numbers confirm that, for all intents and purposes, my not doing this simply doesn't matter.

Don

Thanks for the numbers, they match my calculations. A +1 count in HiLo = 1/10 of an extra ace.

Two years back, I ran a simulation with the unbalanced ten count ,which is perfect for insurance,running parallel to the high-low-count. I discovered that the high-low insurance decisions were wrong in more than 30% of the cases. The additional gain that could have been achieved with insurance based on the UB10 was about 15%.
So when you play with an other counter at teh same table, It can be worthwhile that one of them keeps a separate insurance count (slightly more difficult than high-low).

Francis Salmon

Did you try using this secondary count for playing decisions as well as indurance decisions ? Since the UB 10 count has more playing efficiency than many counts, this should give some advantage ?

Aren't you the one with the gold mine where they are offering a separate face card bet regardless of the upcard? If you can confirm that this promotion is still on, I will give you more information about the UB10 by email.

Francis Salmon

I don't know what you're talking about (is there another Saladin ?), but I'd like to have the information anyway :-)

You need to be careful when you state:
"the additional gain that could have been achieved with insurance based on the UB10 was about 15%."

If you mean that the gain that insurance alone contributes to your overall hourly win can be increased by 15% by using a more efficient insurance count, fine. If, on the other hand, you're implying that your TOTAL hourly win is increased by 15%, then you're way off.

Say you win $150 per hour. Maybe $10 of that comes from insurance (I'm guessing). So, if you increase that by 15%, you now have $1.50 out of $150 improvement, or 1%.

Don

Showed an additional $3 an hour with a bet spread and game giving HiLo return of $16 an hour. I assume a 7-8-9 block side count could be used with similar return for insurance decisions?

I recalled the 15% from memory but now I see that this was just the result of my first uncompleted sim due to randomness.
After that, I included a device which calculated the theoretical gain obtained by each insurance decision, so the only randomness remaining was the card distribution and the frequency of insurance decisions but not their outcome. UB10 outperformed high-low by 45%!
In overall terms, this means that if you make 100$ an hour with high-low,15$ being accountable for insurance, you could improve your win rate by 7$ with insurance decisions based on UB10.

Francis Salmon

With your sidecount of the neutral cards you have still got the ace the wrong way round and it would be too much trouble for the advantage gained. I'm quite puzzled by the figures you gave. Do they apply to six decks?

Francis Salmon

"In overall terms, this means that if you make 100$ an hour with high-low,15$ being accountable for insurance, you could improve your win rate by 7$ with insurance decisions based on UB10."

Where are you getting these outrageous numbers from? An ace appears every 13th card, so we may get about 7-8 aces per hour. The true count is +3 or higher less than 10% of the time in a 4.5/6 game. So, if we get to take insurance once per hour, on average, it's a big deal.

You want that ONE insurance play to add $15, on average, to an otherwise $85 per hour EV? In two words: IM-POSSIBLE!!

You're way off here.

Don