MJ: KO vs Hi-Lo: Question and Analysis

[MJ]

I looked on bjstats.com and found the following information for KO and Hi-Lo using the criteria below:

Spread: 1-12 units
Play All
Rules: DAS, DA2, LS, 6D, 75% Penetration

For KO:

EV: .93%
SCORE: 24.36
NO: 40,879

For Hi-Lo:

EV: .99%
SCORE: 30.67
NO: 32,656

In the above situation Hi-Lo earns an extra $6/Hr or 25% greater earnings then KO. This may not seem like a lot of money but over the course of lets say 1000 hours thats $6000 in increased earnings. Whats more bankrolls grow exponentially not linearly so the gain from using Hi-Lo would likely be more then 6K. Finally, if you look at NO for each system you will see that Hi-Lo requires only 80% of the number of hands that it would take if playing with KO to realize SCORE.

(40,879 - 32,656)/40,879 = 80%

If my reasoning is incorrect I'm sure you guys will correct me. :-)

Moving along on bjstats NO is defined as "the number of hands needed to obtain a result reasonably close to the expected result".

How close is reasonably close? If I were to play with KO does that mean it would require roughly 41,000 hands for my hourly earnings to equal $24.36?

I realize NO is just an estimate so how likely is it that I will realize the given SCORE of $24.36/Hr (or greater)given the NO of 41,000 hands? Is it 80%? 90%? 95%? 99%? I think you guys understand what I'm asking.

Finally, why does Hi-Lo require fewer hands to be played then KO to be certain of achieving a given SCORE? If my understanding of NO is correct then it would appear as though Hi-Lo gets to the long term faster then does KO. At 100 Hands/Hr, 8,000 fewer hands played is 80 hrs less spent at the tables with higher earnings. Thats not something which should be taken lightly.

Perhaps these are some of the reasons why professional teams use balanced systems; namely increased earnings in less time. Sounds good to me. :-)

-MJ

[Don Schlesinger]

> I looked on bjstats.com and found the
> following information for KO and Hi-Lo using
> the criteria below:

> Spread: 1-12 units
> Play All
> Rules: DAS, DA2, LS, 6D, 75% Penetration

> For KO:

> EV: .93%
> SCORE: 24.36
> NO: 40,879

> For Hi-Lo:

> EV: .99%
> SCORE: 30.67
> NO: 32,656

I'd say you made a mistake somewhere. You may have a wrong penetration for K-O, or you may not have included surrender. something is wrong. See BJA3, p. 176, where the SCOREs are given as 30.85 and 32.91.

> Finally, if you look at NO for
> each system you will see that Hi-Lo requires
> only 80% of the number of hands that it
> would take if playing with KO to realize
> SCORE.

No, not to "realize SCORE." SCORE and N0 are basically the same thing. In fact N0 is simply 1,000,000/SCORE.

> If my reasoning is incorrect I'm sure you
> guys will correct me. :-)

See above.

> Moving along on bjstats NO is defined as
> "the number of hands needed to obtain a
> result reasonably close to the expected
> result".

> How close is reasonably close?

Actually, N0 (read "N-zero") is the number of hands needed to be played until expectation equals one standard deviation. In other words, e.v. - s.d. = 0.

> I realize NO is just an estimate so how
> likely is it that I will realize the given
> SCORE of $24.36/Hr (or greater)given the NO
> of 41,000 hands? Is it 80%? 90%? 95%? 99%? I
> think you guys understand what I'm asking.

Bad question. Better question: If I play N0 hands, what is the probability that I will my expected value or greater? Answer: 15.86%.

> Finally, why does Hi-Lo require fewer hands
> to be played than KO to be certain of
> achieving a given SCORE?

You're never "certain" to achieve anything. See above. If SCORE is greater, N0 is smaller. The two terms are, basically, reciprocals of each other.

> If my understanding
> of NO is correct then it would appear as
> though Hi-Lo gets to the long term faster
> then does KO.

That's one way to put it, but, again, your numbers above seem off to me.

Don

[Dewayne]

> Bad question. Better question: If I play N0
> hands, what is the probability that I will
> my expected value or greater? Answer:
> 15.86%.

> Don

You seemed to have missed a word in this question, what do you have a 15.86% chance of doing ? Winning or not winning at least 1 ev or greater?

Dewayne

[MJ]

> I'd say you made a mistake somewhere. You
> may have a wrong penetration for K-O, or you
> may not have included surrender. something
> is wrong. See BJA3, p. 176, where the SCOREs
> are given as 30.85 and 32.91.

I rechecked the numbers on bjstats.com. These figures are given for the rules and penetration I specified on the site.

> No, not to "realize SCORE." SCORE
> and N0 are basically the same thing. In fact
> N0 is simply 1,000,000/SCORE.

> See above.

> Actually, N0 (read "N-zero") is
> the number of hands needed to be played
> until expectation equals one standard
> deviation. In other words, e.v. - s.d. = 0.

> Bad question. Better question: If I play N0
> hands, what is the probability that I will
> my expected value or greater? Answer:
> 15.86%.

How do you come up with 15.86% probability of reaching the EV or greater given N0 hands? This figure seems to be on the low side given a sample size of 41,000 hands played. I thought the greater the sample size(# of hands played) the greater the chances of reaching the EV/Hr.

Does 15.86% apply to all cases when N0 is calculated or just this one?

> You're never "certain" to achieve
> anything. See above. If SCORE is greater, N0
> is smaller. The two terms are, basically,
> reciprocals of each other.

Ok I dont understand then what is the purpose of N0 if it provides hardly any certainty with regard to achieving a given win rate per hour?
Why go through the trouble of calculating it?

Also I'm not sure if reciprocal is the correct word in this case. If N0 = 1,000,000/SCORE then I think that would constitute an inverse relationship. The graph would be similar to the hyperbola y = 1/x excluding the 3rd quadrant or
y = |1/x|.

> That's one way to put it, but, again, your
> numbers above seem off to me.

I just quoted what is provided on bjstats.com. You could be right though.

-MJ

[Norm Wattenberger]

The bjstats sim numbers were created many years ago and I no longer remember the assumptions. Use the numbers in BJA. (Or CVCX.)

[Don Schlesinger]

> You seemed to have missed a word in this
> question, what do you have a 15.86% chance
> of doing ? Winning or not winning at least 1
> ev or greater?

I'm sorry, I wrote too quickly here. Please see my further explanation below.

Don

[Don Schlesinger]

> I rechecked the numbers on bjstats.com.
> These figures are given for the rules and
> penetration I specified on the site.

See Norm's reply.

> How do you come up with 15.86% probability
> of reaching the EV or greater given N0
> hands? This figure seems to be on the low
> side given a sample size of 41,000 hands
> played. I thought the greater the sample
> size(# of hands played) the greater the
> chances of reaching the EV/Hr.

I didn't write what I meant to write. Sorry. When you play NO hands, your e.v. now equals one s.d. So, if you were to experience a one-s.d. LOSS after playing NO hands, you would still break even (not lose anything). This probability is what is equal to 15.86%.

In other words, after playing NO hands, you have only a 15.86% chance of being behind. Some will consider that the "long run." Some require even more hands, equal to two s.d.s, for example. Sorry for the confusion.

> Does 15.86% apply to all cases when N0 is
> calculated or just this one?

All.

> Ok I dont understand then what is the
> purpose of N0 if it provides hardly any
> certainty with regard to achieving a given
> win rate per hour?

There is no such thing as a "certainty" of achieving a win rate. The longer you play, the smaller s.d. is, expressed as a percentage of e.v. That's all the "certainty" you get. :-)

> Why go through the trouble of calculating
> it?

See above. It's a measure of how long it takes for e.v. to catch up to s.d. -- which isn't a trivial value.

> Also I'm not sure if reciprocal is the
> correct word in this case. If N0 =
> 1,000,000/SCORE then I think that would
> constitute an inverse relationship. The
> graph would be similar to the hyperbola y =
> 1/x excluding the 3rd quadrant or
> y = |1/x|.

The reciprocal of 3 is 1/3. The reciprocal of SCORE is NO, once you multiply that reciprocal by one million.

> I just quoted what is provided on
> bjstats.com. You could be right though.

I'd use the charts in BJA3.

Don

[Parker]

Most Hi-lo sims use the I-18 indices. Most KO sims use the KO Preferred strategy matrix. There is so much info at bjstats.com that I was unable to determine exactly which sims you were looking at.

This isn't really a fair apples-to-apples comparison since the I-18 includes splitting 10's against dealer 5 and 6, while the KO Preferred replaces these with doubling 8 vs 5 and 6, two considerably less powerful indices.

The KO creators did this because they felt that splitting 10's draws too much heat. In addition, it is a high variance play that many counter just plain don't like to make.

It could be argued that the systems should be compared in this way because it is the way most people play them. However, I doubt that the majority of counters routinely split 10's every time the count calls for it.

There are also differences in the KO Preferred surrender strategy and the Fab 4 surrender indices. It is even possible that the sim in question did not include the KO surrender indices at all.

At any rate, as others have mentioned, you can certainly trust the numbers in BJA3.

[JohnAuston]

BJRM Web Site

[JohnAuston]

Further showing the closeness of these two simple systems, here are the real world versions of the two charts ( normal chip denominations and no bet jumps greater than double).

[Norm Wattenberger]

> This isn't really a fair apples-to-apples
> comparison since the I-18 includes splitting
> 10's against dealer 5 and 6, while the KO
> Preferred replaces these with doubling 8 vs
> 5 and 6, two considerably less powerful
> indices.

Yes and also the KO indexes are compromise indexes. That is, there are only three index values designed for simplicity instead of accuracy. The BJA sims are based on I18 indexes. The bjstats sims are based on the strategies as presented in the respective books. I prefer this method since it compares the way most people actually play a strategy instead of comparing tag values.

[Norm Wattenberger]

> Further showing the closeness of these two
> simple systems, here are the real world
> versions of the two charts ( normal chip
> denominations and no bet jumps greater than
> double).

No bet jumps greater than double cannot be accurately calculated in this manner. This only reduces the number of bets jumps greater than double.

[Don Schlesinger]

> No bet jumps greater than double cannot be
> accurately calculated in this manner. This
> only reduces the number of bets jumps
> greater than double.

What do you have in mind here, Norm? What does "in this manner" mean to you such that you don't think that BJRM is eliminating all of the bet jumps?

Don