Questions from Blackjack Hack A.K.A. The Dealer 21 Magnet!
The NO column in BJA3 is for fixed betting?
To compute SD's?
Ex.
If NO is 50,000 = 1 SD
50,000 (4) = 200,000 = 2 SD
50,000 (9) = 450,000 = 3 SD?
Is there a formula to convert NO to kelly fractional betting?
Thanx in advance
P.S.
I am no hack! I am a winning player because I know to make side bets that the dealer will draw to 21!
> Questions from Blackjack Hack A.K.A. The Dealer 21
> Magnet!
> The NO column in BJA3 is for fixed betting?
Yes.
> To compute SD's?
Yes.
> Ex.
> If NO is 50,000 = 1 SD
> 50,000 (4) = 200,000 = 2 SD
> 50,000 (9) = 450,000 = 3 SD?
The N0 doesn't equal the standard deviation; rather it's the number of hands necessary for the e.v. minus the loss from that many standard deviations to equal zero. But, if you understand that, then, yes to the above.
> Is there a formula to convert NO to kelly fractional
> betting?
What exactly, are you looking for?
Don
> Yes.
> Yes.
> The N0 doesn't equal the standard deviation; rather
> it's the number of hands necessary for the e.v. minus
> the loss from that many standard deviations to equal
> zero. But, if you understand that, then, yes to the
> above.
> What exactly, are you looking for?
> Don
Ok,
Let's see if I am on the right track.
Time for me to get a headache!
From BJA3
Page 244
Table 10.59
Spread 1 -2 practical
NO = 31.856 = hands needed to overcome 1 negative SD
(4) NO = 127,424 = hands needed to overcome 2 negative SD's
(9) NO= 286,704 = hands needed to overcome 3 negative SD's
Better?
Are these numbers of hands needed "if" or "when" you are down the negative SD's?
Now SD
From David D 'Aquin
Long run for fixed bets (time needed for expected win to exceed 3 standard deviations):
Long run for fixed kelly betting:
[( SD per bet * 3)/expected win per bet]^2
[(599.70/100)* 3)/(33.62/100)]^2 = 2,864
Long run for fractional kelly betting:
[( SD per bet * 6)/expected win per bet]^2
[(599.70/100) * 6)/(33.62/100)]^2 = 11,455
Does this simple formula work?
fractional kelly long run = 4 * fixed kelly long run.
Are all of these hands; NO and long run, based on hands seen and played together?
So roughly based on 100 hands per hour?
Is there a simple formula to convert fixed NO to fractional NO?
> From BJA3
> Page 244
> Table 10.59
> Spread 1-2 practical
> NO = 31.856 = hands needed to overcome 1 negative SD
Let's hope I wrote 31,856! :-)
> (4) NO = 127,424 = hands needed to overcome 2 negative
> SD's
> (9) NO= 286,704 = hands needed to overcome 3 negative
> SD's
> Better?
Fine.
> Are these numbers of hands needed "if" or
> "when" you are down the negative SD's?
I don't understand your question. For the first one, for example, N0 represents the number of hands needed to play such that the s.d. for that number of hands is equal to the e.v. for that number of hands. Don't make this more complicated than it needs to be! :-)
> Now SD
> From David D'Aquin
> Long run for fixed bets (time needed for expected win
> to exceed 3 standard deviations):
> Long run for fixed kelly betting:
> [( SD per bet * 3)/expected win per bet]^2
> [(599.70/100)* 3)/(33.62/100)]^2 = 2,864
The above answer is, of course, hours and not hands. Multiply by 100 to get our previous answer.
> Long run for fractional kelly betting:
> [( SD per bet * 6)/expected win per bet]^2
> [(599.70/100) * 6)/(33.62/100)]^2 = 11,455
> Does this simple formula work?
> fractional kelly long run = 4 * fixed kelly long run.
What fraction?? "Fractional Kelly" has no meaning until you define the fraction! Or, do you mean by "fractional" that you constantly adjust your bet size after every hand, whereas with "fixed," you never adjust?
> Are all of these hands;
Mine are hands in the book. Apparently, David's number was hours.
> NO and long run, based on
> hands seen and played together?
> So roughly based on 100 hands per hour?
Played for play-all; observed, for back-counting.
> Is there a simple formula to convert fixed NO to
> fractional NO?
First, define fractional Kelly (not N0!) for me. A Kelly fraction can be any percentage. You seem confused here.
Don
> Let's hope I wrote 31,856! :-)
> Fine.
> I don't understand your question. For the first one,
> for example, N0 represents the number of hands needed
> to play such that the s.d. for that number of hands is
> equal to the e.v. for that number of hands. Don't make
> this more complicated than it needs to be! :-)
> The above answer is, of course, hours and not hands.
> Multiply by 100 to get our previous answer.
> What fraction?? "Fractional Kelly" has no
> meaning until you define the fraction! Or, do you mean
> by "fractional" that you constantly adjust
> your bet size after every hand, whereas with
> "fixed," you never adjust?
> Mine are hands in the book. Apparently, David's number
> was hours.
> Played for play-all; observed, for back-counting.
> First, define fractional Kelly (not N0!) for me. A
> Kelly fraction can be any percentage. You seem
> confused here.
> Don
This is the language as I understand it:
fixed betting - no resizing
fractional betting - resizing
Kelly bet or optimal bet - bankroll times edge times variance. Ex. If a $10,000 bank and a 2% advantage with a one hand variance of .77, your one hand bet would be = $154 and $112.42 on each of two hands.
fixed Kelly - 13.53% ROR with no resizing, commonly called Kelly.
fractional Kelly - start at 13.53% ROR and as your bankroll fluctuates you reset your bets at Kelly. The theoritical ROR is 0%.
So I can say 1/3 fixed Kelly and it means to fix your bets to Kelly and then divide by 3 for your bet sizes with no resizing. For ROR (.1353 ^ 3)= .24% (about 1 in 400) ROR with no bet resizing.
I can say 1/3 fractional kelly and it means set your bets to Kelly and then divide by 3 for your bet sizes. You would resize your bets to 1/3 Kelly as your bankroll fluctuates. Your ROR is 1/3 of 0% or obviously redundant.
The fixed 1/4 kelly bankroll can be considered the practiacal 0% ROR?
The fixed 1/5 Kelly bankroll is the mathmatical 0% ROR?
Have I invented my own language? LOL
If I am correct on the above and you want to cut to the chase. I am considering the decision between these two choices.
Wanting a 0% ROR
Either bet fixed 1/5 Kelly. Which I understand has a shorter time horizon to long run.
or
Bet fractional Kelly. Longer time horizon to long run but higher hourly EV.
I was trying to nail down the concepts of long run and NO to help me with this very important decision. In the literature I have read it appears to be a more subjectivc vs objective decision.
Does the long run and consideration of NO make playing fractional full Kelly impractical?
hmmmmmm Can you apply the DI formula to this question?
Perhaps a subjective answer for if you want to play full fractional Kelly would be if you intend to play the required hours to reach 2 or 3 SDs?
Perhaps a recreational or part time player should consider a more fixed betting approach while someone who plays professionaly or many hours should consider a more fractional approach?
Don, thank you for your time.
To everyone, I apologize for my ramblings and any potential headaches I may have caused. Perhaps you can take comfort in the fact that I make my own head hurt.
> This is the language as I understand it:
> fixed betting - no resizing
OK.
> fractional betting - resizing
How often?? Constantly?? That simply isn't practical. Once you lose half your bank? Double it? It's too vague.
> Kelly bet or optimal bet - bankroll times edge times
> variance.
No, bankroll times edge DIVIDED by variance.
> Ex. If a $10,000 bank and a 2% advantage
> with a one hand variance of .77,
No such thing. Variance would be 1.30, and you'd be multiplying by the reciprocal of variance, which, of course, is dividing by variance.
> your one hand bet
> would be = $154 and $112.42 on each of two hands.
Right. But the latter is a separate idea, having nothing to so with the discussion, and it involves the covariance between two simultaneous hands of blackajck.
> fixed Kelly - 13.53% ROR with no resizing,
Right.
> commonly called Kelly.
No, commonly called "fixed Kelly"! :-)
> fractional Kelly - start at 13.53% ROR and as your
> bankroll fluctuates you reset your bets at Kelly. The
> theoritical ROR is 0%.
To me, this isn't "fractional Kelly," which implies that you're betting some FRACTION of full, or 1.0, Kelly. For example, we'll say that pros play fractional Kelly when they bet only 1/2, or 1/3, or 1/4 of full, or 1.0, Kelly. This has nothing at all to do with constant resizing, which is a completely separate idea and which, itself, can be applied to any of the above schemes.
> So I can say 1/3 fixed Kelly and it means to fix your
> bets to Kelly and then divide by 3 for your bet sizes
> with no resizing. For ROR (.1353 ^ 3)= .24% (about 1
> in 400) ROR with no bet resizing.
Yes, you can say that if you like.
> I can say 1/3 fractional kelly and it means set your
> bets to Kelly and then divide by 3 for your bet sizes.
> You would resize your bets to 1/3 Kelly as your
> bankroll fluctuates. Your ROR is 1/3 of 0% or
> obviously redundant.
Well, you can say that, if you like, but, to me, the "fractional" is unnecessary, because, to me, it doesn't indicate "constant resizing." The "1/3" immediately implies that you are betting "fractional Kelly" (you don't have to say "fractional") and you STILL need to say that you are "constantly resizing." In short, no matter how many times you say that "fractional" = "constant resizing," it doesn't! :-)
> The fixed 1/4 kelly bankroll can be considered the
> practical 0% ROR?
I'd write: "Betting 1/4 Kelly, without resizing, can be considered to have a practical ROR of 0%."
> Have I invented my own language? LOL
A little. See above.
> If I am correct on the above and you want to cut to
> the chase.
Yes, that would be nice! :-)
> I am considering the decision between these
> two choices.
> Wanting a 0% ROR
> Either bet fixed 1/5 Kelly. Which I understand has a
> shorter time horizon to long run.
Compared to what? How do you have shorter horizon to long run when you aren't betting anything?
> or
> Bet fractional Kelly.
1/5 IS fractional Kelly, but I get the idea. :-)
> Longer time horizon to long run
> but higher hourly EV.
Getting complicated.
> I was trying to nail down the concepts of long run and
> NO to help me with this very important decision. In
> the literature I have read it appears to be a more
> subjectivc vs objective decision.
> Does the long run and consideration of NO make playing
> fractional full Kelly impractical?
"Fractional full Kelly" is an oxymoron, and a cute one at that! :-) But, the answer to your question is yes.
> hmmmmmm Can you apply the DI formula to this question?
> Perhaps a subjective answer for if you want to play
> full fractional Kelly would be if you intend to play
> the required hours to reach 2 or 3 SDs?
> Perhaps a recreational or part time player should
> consider a more fixed betting approach while someone
> who plays professionaly or many hours should consider
> a more fractional approach?
> Don, thank you for your time.
> To everyone, I apologize for my ramblings and any
> potential headaches I may have caused. Perhaps you can
> take comfort in the fact that I make my own head hurt.
>
You're trying to understand, and you're being both polite and humorous about it, which is very much appreciated.
Here's my advice. Don't do a lot of resizing; it isn't a very good idea. Pick a FRACTION of Kelly that will give you a comfortable ROR if you were NEVER to resize -- say 1/2 to 1/3. Then stick to that, and, if you start to feel uncomfortable -- even with the fraction -- once you've lost, say, half of your bank, then consider resizing.
But, here's something that few people ever discuss: On the way down to losing half your bank, you didn't resize at, say, 3/4 of the bank lost, right? So, if you do resize at half lost, and you make a comeback, back to the 3/4 level, consider "restoring" to your original, full, stakes. After all, that's what you were playing on the way down, right? So, why not be playing full stakes on the way back up? How does your bank know in which direction you're going? :-)
Hope this helps.
Don
I just read an answer to a question where the poster, who is very knowledgeable, began with: "I will take the case of continuous proportional betting, where you are resizing instantaneously."
Notice, he didn't say, "fractional Kelly"! :-)
Don
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