David Spence: Non-integer indexes for insurance

[David Spence]

Does anyone know the precise gain for using a hi-lo insurance index of 1.4 instead of 1 for single deck and 2.4 instead of 2 for double deck games?

[Don Schlesinger]

> Does anyone know the precise gain for using a hi-lo
> insurance index of 1.4 instead of 1 for single deck
> and 2.4 instead of 2 for double deck games?

Probably nil. :-) Why do you presume that you should use 2, instead of 3, if not using 2.4? I think insuring too early is most costly than insuring too late.

By the way, how do you figure to get a TC of 1.4 in SD? Will you be true counting card by card?

Don

[Norm Wattenberger]

that. I just put in my notes that I wanted to look at that exact question. But when I do get around to it; I expect the answer to be exactly what Don said.

> Does anyone know the precise gain for using a hi-lo
> insurance index of 1.4 instead of 1 for single deck
> and 2.4 instead of 2 for double deck games?

[David Spence]

> Probably nil. :-)

I don't doubt that the gains will be very small, but possibly no smaller than some of the non-I18 indexes I'm already using. The question is more academic than practical, but that doesn't make me any less interested in the answer :-)

>Why do you presume that you should
> use 2, instead of 3, if not using 2.4? I think
> insuring too early is most costly than insuring too
> late.

The decision was pretty arbitrary, granted, but I'm not so sure that I agree that insuring too early is worse than insuring too late. On a natural, for example, if the two integer indexes are "equally wrong" in terms of e.v., 2 is better because it decreases s.d. If you insure a natural, you'll definitely win 1 unit instead of possibly winning 1.5 or winning 0. For non-naturals, of course, the s.d. issue may not be so straightforward.

> By the way, how do you figure to get a TC of 1.4 in
> SD? Will you be true counting card by card?

Well, if the running count is +1 on the first heads-up hand with a dealer ace up, the true count is still less than 1.4. On subsequent hands, however, a running count of +1 may justify taking insurance.

David

[David Spence]

I ran some CVData sims to see the effects of non-integer insurance indexes. Here's a summary for a 2D game:

2.0 for insurance: TBA=.478% (SE=.003), SCORE=17.55
2.4 for insurance: TBA=.478% (SE=.003), SCORE=17.43
3.0 for insurance: TBA=.472% (SE=.003), SCORE=17.03

The low values result primarily from a modest 1-3 bet spread. See below for details.

The details of the sims are as follows:
* 1 billion hands per sim
* 2D, 60.6%pen, S17, DAS, 1 player
* Wong Basic Hi-Lo (I multiplied all of the card values and indexes by 10. For example, aces and tens are worth -10, 16v9 has an index of 50. This allowed an insurance index of 24).
* 1-3 spread (this explains the low TBAs and SCOREs. Multiplying the card values by 10 limited the effective range of counts for bet spread).

In a nutshell, it doesn't make much difference which index you use of the three tested, as Don and Norm hypothesized.

The data suggest that insuring too frequently is less costly than insuring too rarely, as I hypothesized, since the insurance index of 3.0 produced the worst results. The differences are at the edge of the SE range, however, so this is only a moderately strong conclusion.

So, at long last, we have an answer to a question that has plagued every card counter. Armed with the indispensable knowledge in this post, you can expect to make an extra $0.00 over the course of a lifetime.

David

[Don Schlesinger]

I have more interest in this than you might imagine, because, with floored indices (you didn't specify your methodology), on p. 213 of BJA3, Norm gives +3 (and not +2) as the optimal insurance index for DD.

So, if that isn't correct, we'd certainly like to discuss why. It may have to do with other assumptions, such as spread, number of people at the table, pen, etc.

Don

[David Spence]

I ran the sims both with floored and rounded true count calculations. The floored method performed better (probably due to non-insurance and betting decisions more than the insurance decision, but I'm sure you could analyze that better than I could), and the floored method is the one I reported. Deck resolution was 1/4 deck for all levels of penetration.

It was interesting that 2.0 and 2.4 performed equally in terms of TBA. I would have thought that 2.4 would give the higher TBA, since it's optimal in terms of ev. That they have roughly equal SCOREs is less surprising to me, though, since the sub-optimal ev using 2.0 might be balanced by the potentially reduced sd.

I'll try it with 3 people at the table, and with a 1-8 bet spread (though there will only be three betting levels). I could also just double all of the card values and indices (e.g. tens and aces are worth -2, the index for 16v9 is 10), which would allow an insurance index of 5, equal to 2.5 for normal Hi-Lo. This is pretty close to 2.4 and would allow a more realistic bet spread.

David

> I have more interest in this than you might imagine,
> because, with floored indices (you didn't specify your
> methodology), on p. 213 of BJA3, Norm gives +3 (and
> not +2) as the optimal insurance index for DD.

> So, if that isn't correct, we'd certainly like to
> discuss why. It may have to do with other assumptions,
> such as spread, number of people at the table, pen,
> etc.

> Don

[David Spence]

> I have more interest in this than you might imagine,
> because, with floored indices (you didn't specify your
> methodology),

One thing I should point out: with card values of -10 and +10, and indexes like 50 and 24, floored vs rounded doesn't make much difference.

[Norm Wattenberger]

CVData wasn't designed for a Level 10 strategy. I'll run the sims without multiplying the tags by ten when I get a chance.

[David Spence]

I ran some more sims to compare using 2.0 versus 3.0 for the two-deck insurance index. This was done using ordinary, unmultiplied hi-lo card values and indices, which, presumably, will give more accurate results than multiplying them by 10. I multiplied these by 10 earlier, since I saw no other way of using an insurance index of 2.4 in CVData. If CVData "wasn't designed for a Level 10 strategy," any other suggestions for how to test an index of 2.4?

Anyway, without further ado:

Insurance Index = 2.0
TBA=1.116% (SE=.003), SCORE = 59.66

Insurance Index = 3.0
TBA=1.120% (SE=.003), SCORE = 59.51

Here are the details of the sims:
* 1 billion hands per sim
* 2D, 60.6%pen, S17, DAS, 1 player
* CVIndex-generated Hi-Lo indices (about 70 indices).
* 1-8 spread (optimal spread according to CVCX).
* 1/4 deck resolution, floored TC division, rounded deck estimate.

So the SCORE's a little higher when using 2.0, but he TBA is a little higher when using 3.0. "a little," in this case, can be read as "almost imperceptibly, and probably meaninglessly."

David

[Norm Wattenberger]

> any other suggestions for how to test an index of 2.4?

I was going to add this to V4. But in the end didn't think it was worth the effort. Not only because I didn't think it made a significant difference; but because player's wouldn't actually calculate TCs accurately to tenths.

[David Spence]

> I was going to add this to V4. But in the end didn't
> think it was worth the effort. Not only because I
> didn't think it made a significant difference; but
> because player's wouldn't actually calculate TCs
> accurately to tenths.

Those sound like pretty good assumptions :-)

They are especially good given the results in this thread. If non-integer indices don't matter for the most important index, which also happens to fall almost as far as possible from an integer, they're probably not ever going to make a difference. Nevertheless, I am still curious to see the exact results for 1D. Can you think of a better method than multiplying everything by 10 (other than just not bothering, of course :-) )?

[Norm Wattenberger]

It's on my list to add support for fractional indexes for Insurance. Insurance isn't just the most important index. It is also the only linear standard BJ index. That's the only reason it's on my list at all

> Those sound like pretty good assumptions :-)

> They are especially good given the results in this
> thread. If non-integer indices don't matter for the
> most important index, which also happens to fall
> almost as far as possible from an integer, they're
> probably not ever going to make a difference.
> Nevertheless, I am still curious to see the exact
> results for 1D. Can you think of a better method than
> multiplying everything by 10 (other than just not
> bothering, of course :-) )?