# Kelly Betting & Unsure Advantage

Discussion in 'General' started by blackjack avenger, Oct 19, 2011.

1. ### blackjack avengerWell-Known Member

Given with Kelly resize betting:
Betting over double Kelly bankroll shrinks.
Betting double Kelly bankroll fluctuates with no long term growth
Betting 1.5 Kelly vs .5 Kelly both have the same growth rate, with 1.5 Kelly having much more variance.

So betting under Kelly is always preferred to betting over Kelly.

So one is facing a game/investment where they are unsure of the advantage or variance. Perhaps even a new player to a known game like blackjack with card counting, but are unsure of their skill or the validity of card counting. What should one do? Perhaps bet from 1/4 to 1/8 Kelly resizing* to protect the bank from errors in estimating advantage. As samples from playing come in if one is winning it is a weak confirmation that one does have an advantage and can bet more. If one is losing they bet less until wins proves a winning strategy.

In brief:
Underbetting; even by a large margin, is preferred to overbetting. However, its your money to bet as you want.

*For the aspiring or even established pro 1/4 Kelly resizing is quite conservative for blackjack with 1/6 to 1/8 Kelly being used for the unsure game.

2. ### sagefr0gWell-Known Member

gambling jargon

help me out here if yah can

i know my expected value...
EV = \$29
&
i know that in my quest to win the bets involved that i'm going to succeed 69% of the time

how would i use the calculator in this link?
http://www.albionresearch.com/kelly/default.php

..........
i can't figure out what odd's to enter in the odd's offered field...
would it be 30:1 since my ev is \$29?
errhh i'd be right to set up the estimate of probability of winning field as 69%, right?

3. ### blackjack avengerWell-Known Member

dont hold me to anything

I don't write the books I read them.

The calculator is cool but simple. There is no field for variance & you dont know the variance of your game? So its about worthless.

We can probably figure this from your results. The losses you have faced are probably not the largest losses you will face.

The payoff field is what you get back on a wager, BJ is mostly 1 to 1 as an example.

Your sample size is still to small to say much. What is the variance if someone plays 100 hands of bj but wins 70 hands? According to your calculator a 40% advantage. Seems the greatest game ever, but we know BJ is not that good consistently.

This might help us. Someone has figured out on their own card counting except they don't know the variance of the game. We know to account for variance, that instead of betting \$100 we should bet approx \$70. They bet \$100. What is their fate? If they bet Kelly resizing they are overbetting about 50%. Their bank will grow but with a lot of unnecessary variance. The variance will be so high they may lose confidence or have the bank lose a crushing amount. They would have been better off to have bet .5 Kelly, which would have offered the same growth rate.

So perhaps use the calculator and bet 1/4 to 1/8 Kelly. How does the variance feel? Are you getting paid or white knuckled waiting for multiple wins?

Underbetting is far preferred to overbetting.

4. ### sagefr0gWell-Known Member

oky dokey.....so.......

k, so that calculator is about worthless, lol ......
so but ok, more numbers help maybe?
say i have \$3000 for a roll, don't laugh, dammitt :laugh:
say i know my worst case day would be losing \$1,071.12 (very unlikely but could happen edit: on a really, really bad day)
say i know my daily EV is \$65.83
say i'm not sure but best i can tell at this point one standard deviation is circa \$256.27 (edit: hey, interesting four standard deviations would be \$256.27 * 4 = \$1,025.08 , pretty close to that worst case day number above)
can we surmise anything from that info?
could i use QFIT's calculators with this info?
edit: meh, see image below where i tried it........ not sure if what i tried is legit...
errh what i did was 'fudged' and imaginined a days play was like one hundred hands.... sorta thing.
oh, and i put a 69 for confidence probability since i'm relatively sure that my success rate with respect to this whole scheme is 69%

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5. ### blackjack avengerWell-Known Member

little confidence in confidence

Think your considering confidence different then Qfit. I think your considering winning 69 out of 100 hands? Think he is considering confidence of results.

Are you basing win rate & standard deviation on your results? Isn't this very weak information?

Given, if the info in the 2nd chart is correct; ror could be worse, a 21% ror is high if fixed or resizing bets, unless you can add to bank?

Think your ahead? If you can cut stakes your chances of overall success would go up greatly as far as ror and the chances of keeping winnings.

6. ### sagefr0gWell-Known Member

i think yer right, i believe i was misinterpreting the concept of confidence for Qfit's calculator and confusing it with a certain success level of this game.
i went ahead and used 86.5 for a confidence level on some new calculations (see below). i think that's the appropriate number, forget why though, lol.
standard deviation, yes, that's the best i can do. so yes, weak.
win rate, no, it's based on valid knowledge assuming one simple numeric assumption is correct, lol. so i guess not so weak, lol.
edit: hmmm, so being as SD is weak, could be interesting to do some 'what if's' with the SD numbers in the calculators, no?
errh ok, but correct me if i'm wrong, isn't the chart reflecting a 0.21% ROR?
well anyway pretty much it's fixed bets.
i worked up some new numbers with Qfit's calculators below.
yep ahead, errrhhh at least ahead, loan-wise, lol. bank is nearly trippled. (edit: amount ahead does agree with EV)
but unfortunately there isn't a real lot of wiggle room for cutting stakes.
perhaps some........
but anyway, far as using Qfit's calculators, makes a bit for lacking in confidence as well, maybe, no?
i mean, weren't they set up essentially with blackjack in mind? and this a'int blackjack we're talkin bout here. seems i read, how certain assumptions regarding Kelly theory and the nature of blackjack ie. (it's not even money payoffs, not necessarily flat betting, & there is splitting and doubling involved sorta stuff) were made so as to get Kelly to work better with blackjack, no?

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7. ### blackjack avengerWell-Known Member

its a mess

If your confident of advantage, then tweaking SD may give some insight.

Yeah, the calculators are for fixes bets.

Yeah, Kelly I believe works best/assumes small bets & even money payoffs. We can adjust it for other games

Does your game resemble VP? Perhaps those calculators?

If you have tripled bank through just play then your probably fine at current stakes moving forward. Especially if you never suffered a large loss.

8. ### sagefr0gWell-Known Member

meh, doesn't really resemble VP.
largest loss suffered so far \$518
largest possible loss \$1,071.12 ...very unlikely
but far as tripling the bank, errhh i left something out, there is another similar game involved that has less volatility, albeit a 'weakly' known SD as well, lol.
i guess i could read up in Bj Attack by Schlesinger and try and see if Qfit's calculators are only appropriate for blackjack, no?

9. ### blackjack avengerWell-Known Member

the swamp so far

You know your EV with reasonable certainty
Have an idea of SD
You have tripled bank?
Your ror is now; including bank growth?, 21% for flat bets.
The game offers little room to adjust bets up & down

Qfit calculators can cover more then BJ, if you know the fields. I think there would be concers involving games with large uneven payouts, they are not used for VP as an example as far as I know.

Can't find a nice little game of BJ? :grin:

10. ### sagefr0gWell-Known Member

yes
yes
almost, but another game is in the mix as well, with higher EV & lower SD albeit weakly known SD.
.
errhh no not including bank growth, but from an original \$3,000 bank, but come on bja, that (http://www.blackjackinfo.com/bb/attachment.php?attachmentid=8171&stc=1&d=1319059079) says 0.21%, no?
meh, it could be done, but probably best stay the same level.
hmm, kind of what i was concerned about, although it's not VP, errhhh any other kind of way to calculate ror, ect. with other formulas, references, sources, for games with large uneven payouts ?:fish::fish:
meh, bj ==>> :cow::violin::sleep::3rd:

11. ### blackjack avengerWell-Known Member

err umm

Play the other game!:grin:
You added a level of complexity. The higher EV lower SD game will improve things the more you play it. Even if the EV is lower, its a better game? given your ror

Ok 3g bank, 21% ror
So you tripled it from 1g?
Either you were lucky or the game is better then you think, even though limited trials.

Still don't like the fixed bets with; to me, is a high ror. Also, borrowed money?

12. ### sagefr0gWell-Known Member

sigh
thanks fer yer help

13. ### blackjack avengerWell-Known Member

sorry couldn't be of more help

You won, very good

You Mr. Frog, Definitely one of the more colorful & likable personalities. I really do try. My friends think I am one of the funniest people they know

14. ### sagefr0gWell-Known Member

oh, we a'int done yet

ty, ditto back at yah.
this here thang may go a loooong loong long time, (hopefully) and so probably gonna have lotsa data, definitely have more questions...........
circa 0.21% ROR ..... ca'pice?
edit: more on that ROR from Qfit's calculator, ehhmm tried it in excel using the formula ROR =((1-(F29/E31))/(1+(F29/E31)))^(3000/E31) in the image, agreed with Qfit's calculator pretty close.....
edit: got the wifey on the other game.

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15. ### sagefr0gWell-Known Member

worst case & data

i'm surprised there hasn't been any comments on consideration of a known value, ie. the worst case known value. but i haven't a clue for making a comment on that either, lol.
wouldn't worst case be a 'cap' on standard deviation? errhhh, but i guess problem is one doesn't know how often worse case might happen?
so but, worst case occurrences would be at the far, far, far, far.... bad side of the bell curve, no?
so can't one surmise a frequency of worst case (at least qualitatively) from that?
edit: guess maybe it would help to be able to enumerate all the other possible cases as well, work from there?

16. ### sagefr0gWell-Known Member

what sort of conjectures can one make

so one has some data for two games (albeit severely limited)
the EV is relatively certain, while the SD is derived from the limited data
graphs of the data are depicted below.

what sort of conjectures about the data, SD, earnings and graphs, is reasonable (albeit steeped in uncertainty)?

errhh, i'm not knowledgeable about stuff like normal distributions and all.....
but i think maybe some distributions can be skewed, maybe? ie. perhaps the bell curve representing the distribution may be not a perfect bell curve but fatter on one side than the other, sorta thing?

well anyway, far as the speculation, conjecture..... errhh (and i realize it's just that, speculation offa small sample size, uncertain SD, ect) ok, but what i'd speculate follows:

so far it looks as if maybe the bell curve 'could' be fatter on the 'sweet' side?
errrhhh, i mean, looking at the graphs, fluctuation is such that only one low 2sd has occurred, while high sd's are more numerous.

so is it reasonable to feel hopeful or lucky? or maybe both? or just happy to have a plus ev situation? or all three? lol :whip:

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17. ### blackjack avengerWell-Known Member

speculation

Let's say someone is going to play a coin toss game, they don't know it but the game is biased in their favor.

First flip they are favored to win.
As flips increase they are likely to win. The bell curve moves to the right.
However, the potential for big losses increases with flips. As an example one cannot lose 3 in a row until at least 3 flips have occurred. Of coutse as flips continue variance becomes background noise compared to EV. It's a bit of a errr Ummm situation.

So a big loss can occur but hopefully one is up enough that the EV overwhelms the variance

If you are winning & wins are increasing its a good sign.

18. ### sagefr0gWell-Known Member

just what if stuff, ie. what if the data was giving good info.

so from limited data
figured a not so certain SD
but EV is relatively certain...
went from there to let excel whip up some 'what if' values for plays made and plays into the future, not yet made.

blue line is expected value versus number of plays
green line is one standard deviation versus number of plays
red line is for low three standard deviations versus number of plays.

what can one theorize from the graphs?
oh the highlited in yellow numbers is where 23 plays passed and one standard deviation was equal to the expected value for 23 plays.
is that like N0 ? yes? lol
ok, also the low three standard deviation line, it cross's zero dollars at about the 188 plays point. gotta kind of neat curve to it coming up out of negative territory. seems to be heading up, up & away into positive territory.....
good sign, N0?
any thoughts, anyone?

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19. ### blackjack avengerWell-Known Member

projected

23 plays may be the N0 for this game;looking with BJ goggles, seems short? However, if the game is as well defined as this the variance seems very low.

I can't see any of the numbers from the graph on my phone, but no random walk? Virtually no variance on the graph itself? From what I can see the variance is lower then BJ?

If winning, continuing to win & % of wins increasing, your looking pretty good for an angry froggie.

Your basic ? Seems to be?
I think I am playing a winning game
I am winning
Should I continue?
The basic answer would seem to be yes.

As bank grows its confirmation of a winning game & ror goes down.

20. ### blackjack avengerWell-Known Member

ok, symetry of sessions

Each play is a projected session? Each session is made of multiple plays? The sessions are all so consistent that it seems that is what you should expect moving forward. If if your actual play results reflect your projections.

If you map out sessions like this for BJ, the results would be everywhere showing many more trials needed to have a clear handle on whats going on.

Oh, if I read correctly the penalty for being wrong on variance is higher then being wrong on EV, from a Kelly perspective. I'm sorry if that is not comforting. However your ror is .21% (1/3 fixed Kelly, cuz can't really resize bank?) and dropping with wins? That should be conservative enough?

Moving forward obviously if you take a loss bigger then you have experienced that changes everything.