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For Baby Duckling in re: bj21.com answer
Posted by Clarke Cant on 28 May 1999, at 10:37 a.m.
ON bj21.com I answered Baby Duckling, but gave the wrong z stat for a 5% element of ruin. Until Tusday I am behind a firewall that thinks bj 21.com is a porn site, &*&*#$ Netborders. I have to give my answer here. My policy is that when I screwup I do handhold fully.
These are the correct z stats:
12% ruin z=1.2. This is the normal optimal growth z, but in the answer for baby duckling the number of predicted bankroll units is less than 30, which is more in the range of t-test distributions, and is thus slightly shakey.
5% ruin z=1.64
2% ruin z=2.06
1% ruin z=2.34
You calculate the effective fbv for multiple hands as:
n=number of hands, fbv(n)=fbv+(n-1)*c, fbv = single hand flat bet variance, c=covariance.
For normal variations in the number of hands or predictions of getting an ace or a ten, in the form of prior spot, predicted spot, or next spot use these fbv and c numbers:
DOA, fbv=1.28, c=.47
d10, fbv=1.2, c=.43
Da$ fbv=1.32, c=.48
If your ace or ten spotting predictions are in a definite two card range, you are less likely to double or split and you use:
fbv=1.16 for predicting tens, fbv=1.2 for predicting aces. If the predictions are definite for one spot, but you wish to include the chance of being able to predict 2 or 3 spots are getting the goodies you use: v=1.1, tens, v=1.2, aces. For all you use .13 ev for ten spotting, .53 ev for ace spotting.
Generally bankroll is found by solving (zsd/ev)^2/ev, and hands to double is found by solving (zsd/ev)^2. For normal multihand play you can use my BJF revision normally except to substitute the the proper fbv(n) for the fbv, but DON'T alter the ev estimates. All the multihand adjustment takes place in the fbv term. For some comlex spreads you can solve the required units for each TC you change betting levels at, and then divide and round to get the betting level at each TC. This is what ML was trying to get me to explicitly postup, so that I would show how Kelly bettors can use this bankroill formula instead of the Sharpe's ratio. If you jump to just one high bet the probability of that TC will suffice for BJF users. The BJF only applies to jumped spreads or where a close proportional schedule is followed and an average high bet can be calculated. For the other spreads, especially those out-of-proportion, something like Snyder's, Beat the _Deck(s), series has to be used. For a close proportional schedule the BJF estimate of BA and the Beat...series methods are too close to really call.
For persons who have copies of my BJF revision add this chart where the fbv is discussed, and the * bracketed section below:
DOA fbv=1.28, c=.47; d10 fbv=1.2, c=.43; Da$, fbv=1.32, c=.48; c= covariance.
*For more than one hand calculate eve for each spot and add (n-1)*c to the fbv, where n is the number of hands you are playing. This is another example of my top-down-style. Solve normally for the hands to double and required bankroll units.*
Add the paragraph begining "If you have..." to the end of the bankroll section, just before Zombie's appendix. Then add:
To calculate an optimal betting schedule for table hoppers and large normal spreads first solve the bankroll formula as if the BA component were your only gains, getting required units for each positive ev TC, and dividing your bankroll by that number of units, rounding to get the betting at each TC, and then calculating your average high bet normally. Then use this to calculate the BJF normally, while including the normal spread cap and the PA etc. You will have adjusted for such things as the skew of playing gains per TC and things such as floating advantage too. Jump spreads need no such adjustments.
Legal matters on posting the 1999 versions of what will eventually become Blackjack Therapy 1999 are now clear. I still cannot produce anything from the 1982 version, or... well you know. I hereby authorize the reposting of my BJF revison (which T-hopper, Jake, Baby Duckling and even ML will no doubt be glad for) provided these changes and the previous errata, (such as having a minus instead of a plus in that second interpolation formula) are added. There will be no taking down of this further, until Blackjack Therapy is ready to ship.
I hope this helps, CC out.....
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