Francis Salmon: I thought the times of the Inquisition were over

[Francis Salmon]

You say that using decimal indices requires more precision with deck estimation. The opposit is true.
Assuming my indices are correct, deck estimation is in fact the only source of error remaining in my system.
Let's take the case 8v5 with an index of +3.5 (another in-betweener).If there are 4.5 decks remaining with an RC of +18, the TC is exactly +4.So an I18 user will also find the right play (double), but only if he estimates correctly at half deck precision.However,many people including myself don't like to divide by 4.5 and will be tempted to round up to 5. Now the TC has dropped to +3.6 with the result that the I18 user will miss the right play.But my decision has not been affected.
So you see that the decimal indices allow a greater tolerance in deck estimation.

Francis Salmon

[T. Hopper]

> The good thing is that I am able to verify other people's
> results. So if Francis or somebody else wants me to
> verify the accuracy of one or two indices I'll be glad
> to do it.

To verify the accuracy of indices, you have to run a sim and wait for the decision to come up in actual play.
Then you can do one of two things. I will use hit vs. stand as the example.

1) Try hitting, then back up the cards and try standing. You can do this once or many times.

2) Calculate the exact EV of hitting and standing.

In either case you continue dealing until the sample size is significant. #1 is faster and you will get more samples in a given time, but since they are random results and not exact values each sample will not have as much significance as #2.

I'm only bringing this up because Francis kept referring to his 1/10 point indices as "exact". I believe "precise" would be a better name for them.

[Roger Harris]

> You say that using decimal indices requires more
> precision with deck estimation.

What I'm saying is that decimal indices don't much sense without precise deck estimation, because you're introducing a false precision.

Suppose that in the case you mentioned with a running count of 18, there are actually 5.3 decks remaining, so the TC is about 3.4. You and the typical player both round down to 5. You calculate a TC of 3.6, compare it to your "exact" index of 3.5 and double. The typical player makes the correct play (and so does the player using half-deck estimates), but you make the wrong play. What I'm saying is that those cases need to be subtracted from the theoretical gain you would have if you were capable of very precise deck estimation (and of course very precise mental division).

The point is, if your deck estimate is an integer, plus or minus 0.5 deck, then it's just not valid to consider that decimal place in the quotient as a significant digit.

[T. Hopper]

I had a program with this capability last summer, but something happened to the computer it was on and I am rewriting it, that's why I said a few weeks. I think MathProf has a program that can do this, you might try him at [email protected].

[Francis Salmon]

> What I'm saying is that decimal indices don't make much
> sense without precise deck estimation, because
> you're introducing a false precision.

You mean I should add to the imprecision by a sloppy calculation.Hmmm.

> Suppose that in the case you mentioned with a running
> count of 18, there are actually 5.3 decks remaining,
> so the TC is about 3.4. You and the typical player
> both round down to 5. You calculate a TC of 3.6,
> compare it to your "exact" index of 3.5 and
> double. The typical player makes the correct play (and
> so does the player using half-deck estimates), but you
> make the wrong play.

This is true but look at the cost of this error: 0.1 TC away from break-even point means only 0.2%. But the typical error of the I18 player as demonstrated above is 1% of the bet.

> What I'm saying is that those
> cases need to be subtracted from the theoretical gain
> you would have if you were capable of very precise
> deck estimation (and of course very precise mental
> division).

I cannot agree with this.If you want to introduce errors in the equation this will actually be at the expense of the I18 player because of the smaller safety margin.

> The point is, if your deck estimate is an integer,
> plus or minus 0.5 deck, then it's just not valid to
> consider that decimal place in the quotient as a
> significant digit.

I don't understand that. You mean I should skip the 0.6 and just consider it as 3 making the error worse? To your information,I'm using full deck precision only in the first two decks and very often I make corrections. For example when I see that only half of a deck has been played, I will treat it as if 1 deck has been played for ease of calculation and then subtract 10% from the result:3.6 - 10% = 3.2 .Like this I reduce the error rate further.
Deeper in the shoe I do use half deck precision or better.

Francisw Salmon

[WallStRunoff]

Without taking sides here I am curious, what does decimal estimation add to my EV?

[Francis Salmon]

> Without taking sides here I am curious, what does
> decimal estimation add to my EV?

We have to distinguish the EV-gain in a specific situation and the long term effect better referred to as win rate.
I showed at several occasions that the EV-gain in specific situations by taking the right playing decision can be up to 1% of your bet.Because of the low frequency of such situations the overall effect on win rate is less dramatic (+0.3% according to Cacarulo).

Yet another and even more important aspect is that correct TC-calculation allows you to make bigger bets compared to the conservative rounding to the next lower integer.
If you take this into account the gain in win rate is probably 5 times as much (1.5% according to Cacarulo).

Francis Salmon

[Designated Driver]

> It was several centuries ago that Galileo Galilei was
> forced to publicly revoke his theory that the earth
> was surrounding the sun rather than the reverse.

Actually, the earth never "surrounded" the sun, it just revolves around it(in an elliptical orbit), but I know what you mean. :-)

> By then almighty Catholic Church saw her authority
> challenged and this couldn't be tolerated.Of course
> the official version was that they had to protect the
> members of their community who might have to go to
> hell for falling for such an illbelief.

Yes, and Giordano Bruno who was burned at the stake for his heretical views was one of the not so fortunate but important figures in the revolution towards a heliocentric cosmological theory.

Francis, I believe that you can be one of those figures who starts a paradigm shift, but it takes time and you must do it wisely; like Galileo who recanted on his statement for the sake of the bigger picture. Being a martyr serves very little purpose in creating a revolution as only the living can work for improvement, and in the end isn't that the final objective?

And as for Galileo, time and history have proven him to be correct, which is why he has just recently been officially pardoned. But originally he realized that the world and himself would be better served if he publically recanted his statements, even if he did still hold(and mutter) his belief that, "it still moves".

Maybe one day we will find the "harmony of the spheres" and the beauty(and god) in the numeric details, but until that day comes I believe we must do the best that we can with what we have now, so that we can reach that illustrious day.

Remember the time of the inquisition is over, so don't sweat it and take it easy...like the Designated Driver, you won't regret it. :-)

Desi. D.

> Don Schlesinger has openly vowed to discredit me
> personnally by all means in order to "protect our
> readers against the harmful theory of decimal
> indices".They might be tempted to take up the
> terrible burden of memorizing these indices for just a
> few cents more per hour,what a catastrophy! Or they
> might learn even more indices than the I18 which will
> almost certainly lead to an overload of their
> activ-memory.In the final stage their heads will
> simply explode.

> Schlesinger's campaign is a serious matter because it
> violates ethical principles to which this site (I
> still think) is committed. I expect the management to
> take swift action.

> Francis Salmon

[Norm Wattenberger]

And Salmon's statement that bigger bets will add to your win rate is simply wrong. Your unit size must be reduced if yout TC calculation method is forcing your bets higher.

[Francis Salmon]

> And Salmon's statement that bigger bets will add to
> your win rate is simply wrong. Your unit size must be
> reduced if yout TC calculation method is forcing your
> bets higher.

I thought we were comparing same units and same spread. It seems to me that an accurate and therefore more optimistic TC-estimation will allow more max bets and higher bets in general according to Kelly.What am I missing?

Francis Salmon

[Roger Harris]

> You mean I should add to the imprecision by a sloppy
> calculation.Hmmm.

Refusing to infer a false accuracy from the false precision that can result from dividing by an estimated value is not "sloppy calculation." Experimental scientists and engineers routinely try to do that, to avoid the consequences of sloppy reasoning.

> This is true but look at the cost of this error: 0.1
> TC away from break-even point means only 0.2%. But the
> typical error of the I18 player as demonstrated above
> is 1% of the bet.

I'll take "this is true but" as a retraction or your assertion that my logic was wrong. Now, apparently, the discussion is how much gain from more accurate play is left after we subtract out what is lost when false accuracy leads you to make the wrong play. Fine.

>> What I'm saying is that those
>> cases need to be subtracted from the theoretical gain
>> you would have if you were capable of very precise
>> deck estimation (and of course very precise mental
>> division).

> I cannot agree with this. If you want to introduce
> errors in the equation this will actually be at the
> expense of the I18 player because of the smaller
> safety margin.

You are championing the gains that can be made from using more accurate indices, because there will be cases where you make the "correct" decision and the typical player will not. All well and good (leaving "worthwhile" aside), if you are really doing things accurately. If not, as is the case if you're dividing by an approximation of the remaining cards, then there will also be cases where you make an incorrect decision but the typical player would make the correct play. (And as T.Hopper has pointed out, there will be cases where you make the wrong decision because your index is not as "exact" as you seem to think.) Why would you not agree to subtracting those losses from your theoretical gains?

[Don Schlesinger]

... of this whole discussion, which, at least for me, makes it really very funny.

You see from Cac's chart that the so-called "precise" indices for the three most important variations -- the one's that garner the lion's share of the I18 -- are 3.0 for insurance (compared to, er, 3!), 0.0 for 16 v. 10 (compared to, er, 0!), and 3.9 for 15 v. 10 (compared to, ahem, 4).

Guess it's just me, but I find the irony of this a riot. :-)

Don

[T. Hopper]

> You see from Cac's chart that the so-called
> "precise" indices for the three most
> important variations -- the one's that garner the
> lion's share of the I18 -- are 3.0 for insurance
> (compared to, er, 3!), 0.0 for 16 v. 10 (compared to,
> er, 0!), and 3.9 for 15 v. 10 (compared to, ahem, 4).

I think that shows why he got better results with flooring than rounding. It could have just as easily gone the other way with a different count.