As my battle ground is Europe, I dont have indices ready for doubling with 10 v ten or ace but my indices for the other plays are the following:
15v10 4.3
16v9 4.5
Francis Salmon
> Your argumentation wants to show that the
> gain is too little to be worth the effort
> but I don't ses where the additional effort
> lies.
I didn't argue any such thing so please don't put words in my mouth. Read my posts again if you didn't understand them - I don't think I could've been anymore objective.
> As my battle ground is Europe, I dont have
> indices ready for doubling with 10 v ten or
> ace but my indices for the other plays are
> the following:
> 15v10 4.3
> 16v9 4.5
I knew you were going to post those numbers
because that's exactly what I get with the
"typical-deck" methodology. The bad news is
that those numbers are incorrect and the
reason is in the flawed methodology.
I agree however that the method is very fast
and in most of the cases it is very accurate.
I still use it to get a first approach to the
exact index but I don't rely on it because of
cases like 15vT.
There is another way I use for calculating
indices which is based on EORs. This algebraic
method is also fast and accurate but I wouldn't
bet my farm on it either.
Now, I know you don't trust on sims but let me
tell you that with the use of sims I can create
precise indices to one decimal point of accuracy.
Besides, there are factors that the above
methodologies ignore like penetration and cut-card
effect.
Here are the correct indices and a comparison among the different methodologies:
Exact EoRs Typical-Deck
Ins 3.0 3.0 3.0
16vT 0.0 0.0 0.0
15vT 3.9 3.9 4.3!
16v9 4.3 4.2 4.5!
Hope this clarifies the issue a little.
Sincerely,
Cacarulo
> Hope this clarifies the issue a little.
Here's what it clarifies -- not surprisingly -- for me: For his entire career of using (the wrong) decimal indices, it is virtually certain that Francis has not only not earned any more e.v. than typical whole-index Hi-Lo player, but it is likely that he has earned less. Cruel irony, no?
Don
> I knew you were going to post those numbers
> because that's exactly what I get with the
> "typical-deck" methodology. The
> bad news is
> that those numbers are incorrect and the
> reason is in the flawed methodology.
I knew from the start that my methodology wasn't perfect because with deep penetration the deck composition is less stable.I understand you made me post the cases where the error was most significant.Naughty boy!
> I agree however that the method is very fast
> and in most of the cases it is very
> accurate.
Coming from you, this is very comforting.I'm a practician and for me any effort to get more accuracy would be a waste of time.
> Now, I know you don't trust on sims but let
> me
> tell you that with the use of sims I can
> create
> precise indices to one decimal point of
> accuracy.
I really admire you for what you're doing and I trust your results entirely.You obviously know how to work on sim results and you don't shy the lenghty efforts.
Now, let me ask you: Once you have established an index to decimal precision, woodn't flooring destroy the whole benefit of your work?
Francis Salmon
I just saw that in your post further up, you claimed that you had known for twenty years that the index for 15v10 was 3.5.
So you were just as far away as I was!
Francis Salmon
EoR?s algebraic derived indexes for 6 dks (linear estimates w/o cut card effects).
Hand analysed 15 vs. T
a) 6 dks and ENHC rules
T,5 vs. T 3.74246 3.7 .014553
9,6 vs. T 3.75459 3.8 .003677
8,7 vs. T 3.75484 3.8 .003677
Here your weighted average index is:
W(i) = (Sum (Ii * Pi))/ Sum Pi = 3.746574 = 3.75
b) 6 dks and American rules
T,5 vs. T 3.7763 3.8 .014553
9,6 vs. T 3.78698 3.8 .003677
8,7 vs. T 3.78835 3.8 .003677
Again your weighted average index is:
W(i) = 3.780115 = 3.8
Once a player goes serious into understanding how a ?precise? index is extracted and/or generated (simulated or mathematically derived),
the answer, to all the noise this thread has brought in, is already in front of our eyes. That is:
A critical index should be used only as a guide, and not as a ?precise? point over which you have to go nuts, continuously. It would take lifetimes (a lot, btw) to take advantage of this statistically minutia.
As a practical example we have the player Mr. Salmon, doing quite fine handling his hand 15 vs. T with a somehow incorrect ?precise? index. Had he employed the more standard TC = 4, he would do exactly as good.
Index generation is a tough field, full of misconceptions and mirages. Nothing strange that even BJ giants like SW have had his doubts with the stuff (that?s back into the 80?s). Fortunately for us, computer programmers, like Braun, Imming, Karel, Norm and Cac have been always handy. Delusions killers!
Sincerely
Zenfighter
> I just saw that in your post further up, you
> claimed that you had known for twenty years
> that the index for 15v10 was 3.5.
> So you were just as far away as I was!
I never should have put the decimal as a 0.5, instead of calling these plays "in-betweeners," where I knew that the precise index lay somewhere in between the lower and upper integer, close to the halfway point. I didn't mean to imply that each was exactly at the halfway point, although I'll state, for the record, that I believed 15 v. 10 to be closer to 13.5 than Cac says it is.
Mind you, I have paid zero attention to this over the years, for the reasons I've already stated: Knowing the decimal is virtually useless information.
Don
> I knew from the start that my methodology
> wasn't perfect because with deep penetration
> the deck composition is less stable.I
> understand you made me post the cases where
> the error was most significant.Naughty boy!
> Coming from you, this is very comforting.I'm
> a practician and for me any effort to get
> more accuracy would be a waste of time.
> I really admire you for what you're doing
> and I trust your results entirely.You
> obviously know how to work on sim results
> and you don't shy the lenghty efforts.
> Now, let me ask you: Once you have
> established an index to decimal precision,
> woodn't flooring destroy the whole benefit
> of your work?
I can't replicate my POM here but at least I'll quote the conclusions of that post:
----------
"The first thing we can observe here is that Floored indices are a little bit better than Rounded indices. Truncated indices were not analyzed since it was already proved that they perform worse than floored or rounded. Now we can compare Exact indices against Floored indices. I took two spreads for comparison purposes: 1-10 and 1-20.
1) Using 1-10 the gain by using Exact indices is about 1.7%
2) Using 1-20 the gain goes down to about 1.4%.
Considering that RA-indices get almost 3% over EM-indices we can conclude that the use of these indices are not worth the time and effort. Moreover, the analysis of optimal betting on exact indices requires different optimal bets for each TC ranging from minimum to maximum in steps of 0.1. Nobody can play this way and nobody can do exact divisions while playing."
----------
A follow-up of this post shows what happens when instead of optimally betting on TCs like 1.0, 1.1, 1.2, etc. we bet on floored TCs while keeping the same "exact" indices.
The gain here is about 0.2% - 0.3% over floored indices (w/floored buckets).
----------
Hope this helps.
Sincerely,
Cac
That's all very well but again you insist on the one example where the typical deck methodology shows a significant error.
But Cacarulo said that in most cases this (my)method was "very accurate", so let's rather talk about these cases.
Wong gives an index of +4 for splitting 10/10v6 (I think it's also in I18).So a player would have to split with RC+8 two decks from the end.However the EV for splitting is only 71.4% whereas the one for standing is 72.1%.
So,with a bet of say $200 this premature splitting would cost $1.40.In my view this is not negligible.
My index says to split only at TC+4.4.
Francis Salmon
> That's all very well but again you insist on
> the one example where the typical deck
> methodology shows a significant error.
> But Cacarulo said that in most cases this
> (my)method was "very accurate", so
> let's rather talk about these cases.
> Wong gives an index of +4 for splitting
> 10/10v6 (I think it's also in I18).So a
> player would have to split with RC+8 two
> decks from the end.However the EV for
> splitting is only 71.4% whereas the one for
> standing is 72.1%.
> So,with a bet of say $200 this premature
> splitting would cost $1.40.In my view this
> is not negligible.
> My index says to split only at TC+4.4.
I get the same for TTv6 and +4.8 for TTv5. The correct indices are practically the same: +4.3 and +4.8. But, as I said, even with the use of precise indices the gain is not worth the effort. If you learn the RA indices for these plays you'll do much better.
Sincerely,
Cac
> Wong gives an index of +4 for splitting
> 10/10v6
That's his problem! :-)
>(I think it's also in I18).
No, it isn't. Page 213 of BJA3 gives floored multi-deck Hi-Lo indices of +5 for both plays.
> So a
> player would have to split with RC+8 two
> decks from the end.
For Wong's advice, yes. For mine, no.
> However the EV for
> splitting is only 71.4% whereas the one for
> standing is 72.1%.
> So, with a bet of say $200 this premature
> splitting would cost $1.40. In my view this
> is not negligible.
Define "negligible." :-) A TC of +5 or higher (my index) occurs 2.76% of the time in a 4.5/6 game. A holding of T,T v. 6 occurs, in a neutral deck (slightly higher occurrence for +5, but no matter), 0.73% of the time. So, the opportunity to make the split occurs .0276 x .0073 = .02% of the time, or twice every 10,000 hands dealt! That $1.40 that you just called "not negligible" is actually saved once every 50 hours and is thus worth to you, the black-chip player, the magnificent sum of $1.40/50 = 2.8 cents per hour!!
Add up the rest of your plays, and you may just get those hot dogs in A.C. that I mentioned, but you will fall way, way short of the aforementioned annual subscription to Don's Domain. :-)
Are you beginning to understand?"
Don
Posting Permissions
Bookmarks