MJ: TC Frequency Distribution Question

[MJ]

Let us say that simulation software indicates that a counter will play 16% of rounds dealt employing a backcounting strategy. If 100 rounds are dealt/hr, then on average, he should play 16 rounds/hr.

Does the standard deviation for the TC frequency distribution resemble that of a normal distribution curve? For example, suppose during the course of an hour this backcounter only plays 12 rounds. According to the math, this would place the TC frequencies for this one hour of play 1 SD to the left of the mean. Similarly, it would be virtually impossible for the counter not to play any rounds in an hour if this logic is correct (4 SD to the left of the mean).

I hear of counters playing for hours on end without seeing any advantageous counts. Perhaps TC frequency is not subject to a normal distribution. But then again, for a balanced system like Hi-Lo I do not see how it could not be.

MJ

[Katarina Walker]

There are a few reasons why some counters play for hours on end without seeing any advantageous counts:
1. The penetration is terrible.
2. The house edge is greater than 0.5%, which means that you have to wait until +2 to get an advantageous count. This knocks off a HUGE chunk off the percentage of playable hands (even thought they are only SLIGHTLY advantageous). This is the "playing BJ in Australia" experience. There is NO game where the HE is less than 0.5%.
3. Some players will want to wait until the count is even higher, so that if it goes down again, they won't have to wong out again after playing just one hand. It gives them a buffer.
4. It SEEMS like hours when you are standing behind a table, because waiting for advantageous hands to play is so boring.
5. The table you are back-counting might be full of slow players, with a slow dealer. In Australia, there might be 3 bets per box that need to be paid out when she busts on 2,3,4,5,and6 (and it takes AGES to pay out 21 winning wagersm as well as splits and doubles). A table like that can take over a half an hour to play a shoe. I get 30 hands an hour on a table like that, PLAYING EVERY HAND!!!
6. The standard deviation factor. Yes, it is normally distributed.

Have I told you anything you didn't already know, MJ?
I very much doubt that.

[MJ]

> Have I told you anything you didn't already know, MJ?
> I very much doubt that.

Thanks, but you realize I am talking about blackjack and not SP 21, right?

Either way, if the TC frequency is subject to a normal distribution in SP21 then I expect it would work the same way in BJ.

Does that mean if the backcounting percentage is 16%, then it is virtually impossible to go an hour without playing a round (assuming there are spots open at the table and 100 rounds dealt/hr)?

MJ

[Trapper]

"2. The house edge is greater than 0.5%, which means that you have to wait until +2 to get an advantageous count."

This may be nitpicking but I think you are overstating the value of the house advantage number to counters. HA is based on basic strategy house advantage only and doesn't directly apply to counters. There are rules which are undervalued by HE that are extremely important to counters. Late Surrender comes to mind. Insurance isn't calculated at all into HA because the rule has no value to a basic strategy player but is important to counters (there are no or restricted insurance games out there). And we aren't even considering pen.

I am looking forward to receiving your book. Should be here any day.

[Brick]

I dont think she's overstating the house edge. The insurance bet has no value to us counters untill a count of 3tc is reached. Even at that count,it is virtually a break even bet against the shoe. Basic strategy rules have much value when I determine what game to play. I never play a poor game and assume my insurance bet will make it better because it has value. The only nit pick I have is, at times' the best optimal bet is at a 1 tc, instead of 2.

Brick

> "2. The house edge is greater than 0.5%, which
> means that you have to wait until +2 to get an
> advantageous count."

> This may be nitpicking but I think you are overstating
> the value of the house advantage number to counters.
> HA is based on basic strategy house advantage only and
> doesn't directly apply to counters. There are rules
> which are undervalued by HE that are extremely
> important to counters. Late Surrender comes to mind.
> Insurance isn't calculated at all into HA because the
> rule has no value to a basic strategy player but is
> important to counters (there are no or restricted
> insurance games out there). And we aren't even
> considering pen.

> I am looking forward to receiving your book. Should be
> here any day.

[Katarina Walker]

> This may be nitpicking but I think you are overstating
> the value of the house advantage number to counters.

You are absolutely correct that in Blackjack, the surrender rule has a huge impact on SCORE. A bigger impact than HE. You are better off playing H17 LS than S17, despite the S17 having the lower HE.(This is not the case in SP21, where the fewer tens and unconditional win on 21 make surrender less valuable).
But the discussion was about what proportion of hands the back-counter gets to play, if he only plays when adv > 0.
If we have a 6-deck S17 player (HE 0.40%) and a 6-deck H17 LS player (HE 0.55%), the percentage of playable hands (i.e. hands with advantage > 0) is going to be greater for the S17 player than the H17 LS player, even though the H17 LS game has a higher SCORE.

[Trapper]

>The insurance bet has no value to us counters untill a
> count of 3tc is reached. Even at that count,it is
> virtually a break even bet against the shoe.

That is the case with most of the valuable bet variations. It doesn't matter when the insurance bet has value in the shoe - it is a question of what it adds to overall EV. Insurance is one of the most important, if not the most important, bet variation.

> Basic strategy rules have much value when I determine what
> game to play. I never play a poor game and assume my
> insurance bet will make it better because it has
> value.

The problem is that HA doesn't give a counter enough information to know which is the poor game. Late surrender subtracts less than .1% from the HA but adds 40% to the SCORE of a typical H17 DAS 4.5 wonging game. It is even 20% better than a S17 DAS game although the HA of the S17 DAS game is considerably better (.54 versus .41). House Advantage is a useful rough guide for a counter but it is not adequate. That is why Don went to the trouble of coming up with SCORE which is the only really useful way to compare games with different rules and penetration.

[Trapper]

True about the S17 and H17 with LS. I have heard counters say that they would never play H17 which is fine if better games are available but passing up an H17 LS game for a S17 game with no surrender is not the AP choice. I find that lots of counters will choose lower value games based on preconceptions. A "bad" game dealt heads up can be much more profitable than a game with excellent rules and a full table. That is probably why so many counters have stayed away from SP21 (and also because no one had done the study of the game until your recent book).

> H17 LS player (HE 0.55%), the percentage of playable
> hands (i.e. hands with advantage > 0) is going to
> be greater for the S17 player than the H17 LS player,
> even though the H17 LS game has a higher SCORE.

I had a look at the count frequencies on CVCX Online and I don't find a difference between S17 and H17 with LS. With Hi Lo (Ill 18 and Fab 4) 6 decks, 75% pen and a 4:1 spread I get 16% for both S17 DAS and H17 DAS LS with a TC of 2. I get 27% hands played for both at a TC 1. I am not sure how accurate the CVCX numbers are for count frequencies.

I realize that you were using house advantage as a rule of thumb in your previous post. That is why I said I was probably nit picking. I suspect that we probably agree that the best way to determine a betting strategy is to do a sim or use the SCORE of the game rather than house advantage.

[Trapper]

> That is the case with most of the valuable bet
> variations.....bet variation.

Not sure why I wrote bet variation. Of course, I meant playing strategy variations.

[Don Schlesinger]

> I had a look at the count frequencies on CVCX Online
> and I don't find a difference between S17 and H17 with
> LS. With Hi Lo (Ill 18 and Fab 4) 6 decks, 75% pen and
> a 4:1 spread I get 16% for both S17 DAS and H17 DAS LS
> with a TC of 2. I get 27% hands played for both at a
> TC 1. I am not sure how accurate the CVCX numbers are
> for count frequencies.

You're speaking at cross-purposes. Kat didn't say that the frequencies of the true counts were different (why would they be??); she said that the frequencies of the counts with advantages would be different. Clearly, you get the edge earlier in the H17 LS game; therefore, you play more counts with an edge at that game than with the S17 game.

Clear?

Don

[Trapper]

Thanks Don. This isn't my strong point but I am trying to learn. Maybe you can show me where I went wrong.

> You're speaking at cross-purposes. Kat didn't say that
> the frequencies of the true counts were different
> (why would they be??);

They wouldn't.

> ..... she said that the frequencies
> of the counts with advantages would be different.

Can the "frequency of counts with advantages" be derived by summing the count frequencies for each count with a positive IBA in the tables from CVCX (or BJA3). I get 27.3% for both sample games in my previous post by using that method. Is there another calculation?

> Clearly, you get the edge earlier in the H17 LS game;
> therefore, you play more counts with an edge at that
> game than with the S17 game.

> Clear?

The above is clear but I am finding it hard to square with the post from Katarina that I was responding to.

From Katarina's post:

> If we have a 6-deck S17 player (HE 0.40%) and a 6-deck
> H17 LS player (HE 0.55%), the percentage of playable
> hands (i.e. hands with advantage > 0) is going to
> be greater for the S17 player than the H17 LS player,
> even though the H17 LS game has a higher SCORE.

How can the H17 player "play more counts with an edge" and have a lesser percentage of hands with an advantage > 0? I would be interested in knowing what I am missing here.

[Don Schlesinger]

> Thanks Don. This isn't my strong point but I am trying
> to learn. Maybe you can show me where I went wrong.

I owe you a more complete explanation. This is actually a somewhat confusing phenomenon, and, looking back at p. 187 of BJA3 (which I urge you to take a minute to reread now, before continuing), you'll see that a similar discussion was actually the genesis for the entire concept of the Chapter 10 charts!

> Can the "frequency of counts with
> advantages" be derived by summing the count
> frequencies for each count with a positive IBA in the
> tables from CVCX (or BJA3). I get 27.3% for both
> sample games in my previous post by using that method.
> Is there another calculation?

No, that's correct. The distributions for TCs, by integers, are the same, as can be seen from, say, Tables 10.43 and 10.67, in BJA3, which I'll use for the rest of this illustration. So, that's not where the extra edge comes from in the H17, LS game, and I apologize if either of us gave you that impression.

> From Katarina's post:

> How can the H17 player "play more counts with an
> edge"

See below. "Same counts, each with greater edge" would have been better.

> and have a lesser percentage of hands with
> an advantage > 0?

Very tiny difference, actually.

> I would be interested in knowing
> what I am missing here.

Here's a slightly better explanation. If you compare the two aforementioned tables, you'll see that, at each SAME true count, in the two tables, the H17, LS advantages are slightly higher than their S17 counterparts. And, paradoxically, this is true even though the starting house advantage for S17 is less than the equivalent house edge for H17, LS vs. the BS player.

This is because of the "explosive," "inflatable" value of late surrender that I discuss on p. 187. Its value to the counter can be double, triple, or more, than its value to the BS player, whereas this not the case for the penalty of H17 to the counter (it not only doesn't "inflate" from its BS value, it actually "deflates" a couple of hundredths as first pointed out, I believe, quite correctly by Bryce Carlson, in "BJFB.")

So, it would be more correct to summarize in the following manner: Although the HE for S17 is smaller than for H17, LS vs. the BS player, the actual edges attainable, pairwise, true count by true count (same frequencies!), are greater for the counter playing the H17, LS game, because of the explosive feature of LS and the (tiny) deflationary nature of the H17 rule for the counter.

Clearer now?

Don

[MJ]

> Does that mean if the backcounting percentage is 16%,
> then it is virtually impossible to go an hour without
> playing a round (assuming there are spots open at the
> table and 100 rounds dealt/hr)?

I would think that if the backcounter played zero rounds in an hour, then he would be 4 standard deviations to the left of the mean as far as TC frequency is concerned. The probability of such an occurrence is practically 0%, right?

MJ