From: breid@pyrhard2.eng.pyramid.com (Bill Reid)
Newsgroups: rec.gambling
Subject: Re: BJ strategy diff. (need help on  h,dd,s)
Date: 23 Jul 92 02:46:51 GMT
Organization: Pyramid Technology Corporation, Mountain View

Boy, some people!  They dare you to "find a problem with the numbers" 
then bitch when you do it!  I would hope that the "Monty Hall" problem 
would give people pause before they claim ulitmate fealty because 
no errors in math have been made...its how you apply the math that 
is important...

>In article <JACOBS.92Jul18101647@cells.cs.utah.edu> jacobs@cs.utah.edu (Steven R Jacobs) writes:

>The 12.9% is the original bet size, doubling gives 25.8% of total
>bankroll at risk.  You are right, I didn't make this as clear as
>I should have.

Now I may not understand the true Kelly strategy (as opposed to the 
stripped down version typically used), but 25.8% of your bankroll 
sounds high to bet on a 25% ev hand (maybe I really DON'T want 
the Kelly strategy).  Now without casting any aspersions, is it 
remotely possible that pulling this number out of what you have 
now clarified as a utility function may have given a wrong answer? 
It certainly is an answer that most people would feel uncomfortable 
putting on in actual play.  

>Actually, you've (quite accidently) made a valid point here.  

Accidents will happen!  Now we can really compare relative utility, 
as follows:

>The optimal bet size should be plugged into the equations to find out
>what the actual utility is each case, and the "best" bet chosen by
>taking the option which gives the most utility.
>So, utility if we choose the "double down" game (with bet sizes
>that are optimal for doubling):
>   U(.129) = .586*log(1 + .258) + .345*log(1 - .258) = 0.03155
>and the utility if we choose the "stand" game (with bet sizes
>that are optimal for standing):
>   U(.5416)= .686*log(1+.5416) + .204*log(1-.5416) = 0.1378
>So, we get much more utility by standing instead of doubling, even
>if we have the luxury of changing the bet size in each case.

Now aside from how the .129 and .5416 numbers were originally 
generated (not that important), I am wondering if we can settle 
on this as the correct method of evaluating relative utility in 
this case.  No flames, 
just a question.  

I ask this for two reasons:

a) it looks reasonable to me (I know that means nothing to you) 
b) if this is the way, those good at math (not me!) can come up with a 
   simpler equation in which to plug in the expectation and variance 
   numbers, and find the crossover point "at home", without resorting 
   to iterating the bet size down until you're blue in the face 
   (it looks like we are one derivative away from that)

If there is further clarification on the subject, please post it, w/o 
an aggressive and insulting challenge "to find problems with" it.  Because 
when you do that, somebody will, and in the worst way!

>You're right, it is the utilities that should be compared rather
>than the optimal bet fractions.

Agreed.  Please post.

>Sigh.  You've accidently found some problems in my derivation, but
>don't get (more) cocky (than you already are).  It is clear to me
>that you'd never _really_ know that you'd found a problem unless
>I helped point it out for you.

I'll drop the attitude if you drop yours (actually I'll drop it anyway, 
and have on numerous occasions).

>If you are only betting .042% of your bankroll,
>then you have a bankroll of 2380 bets.  Lucky you.

I've said this about two dozen times, but once again: we need to optimize 
our strategies both GLOBALLY and LOCALLY.  In reality, a Basic Strategy 
player does not have a realistic log utility function, but examining 
the LOCAL strategies from that standpoint is a good jumping off point. 
Any ultimate practical advantage to these analyses depends on this concept, 
one that HAS been lost in the blazes (as above). 
So a log optimal bet size for Basic Strategy is important, to get a feel 
for the true advantage that can be gained for different functions.  
 
In article <JJ.92Jul22134306@presto.slc.mentorg.com> jj@slc.mentorg.com (Jeff Jennings) writes:

>I've already run similar simulations that confirm Steve's analysis.

Please post the methodology and results.   

In another article Jacko writes:

>I'm sure this stuff is super-neat-o to all the non-playing experts
>out there, but from the perspective of a practicing player, what I want
>to know is at what (positive) true count is the crossover point where
>doubling A-8 vs 6 becomes more "utilitarian" so to speak?  For example,
>according to Griffin (Peter, not Merv), the removal effect of a 3, 4, or 5
>from the deck for this play is greater than 3%, in favor of doubling.  

I know at a +10 count you gain 2.24% by doubling this hand.  But then you 
run into other hands at that level which become borderline (A7 v 7, if 
I remember right).  So evaluating this at varying counts is possible 
once you know how to do it (and have the necessary data), but is 
additively more difficult.  Finding the quickest way to do it for Basic 
Strategy is the logical place to start.  

>So my wild-ass-guess on this play is that a TC of only +2 or so is going to 
>see doubling as better than standing.  If it helps your calculations, you
>can assume that my maximum initial bet on a given hand is always <= 1% of
>my bankroll (since it is).  (This stuff about 25%-30% bankroll being bet
>per hand makes a nice strawman but has little practical value.)

Anybody who bets 30% of their bankroll on a hand obviously is not 
concerned with risk of ruin.  Unfortunately, even betting <=1% can 
be hazardous to your health, and it may not be possible to ameliorate 
this by playing strategy, at least from a practical standpoint.  A  
total and accurate analysis of global and local utilities 
will provide the answer. 
 
Newsgroups: rec.gambling