Kelly Betting & Unsure Advantage

[blackjack avenger]

Originally Posted by sagefr0g

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/atta...1&d=1319059079) says 0.21%, no?

meh, bj ==>>

Play the other game!
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?

[sagefr0g]

Originally Posted by blackjack avenger

Play the other game!
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?

sigh
it's dead, i tell yah, dead, dead, dead dead.
thanks fer yer help

[blackjack avenger]

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

[sagefr0g]

Originally Posted by blackjack avenger

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

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.

[sagefr0g]

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?

[sagefr0g]

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

[blackjack avenger]

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.

[sagefr0g]

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?

[blackjack avenger]

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.

[blackjack avenger]

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.