Kelly Conundrum

Sonny said:
Technically it does, but the adjustment is made to the variance not the advantage. The reason BJ players use 76% Kelly is because of the higher variance. Instead of the standard “Bankroll * Advantage” formula we use a modified “Bankroll * Advantage / Variance” formula. This formula works better for most casino games because the payoffs are often not even money so the advantage has to be adjusted for the risk. For example, with a $2,700 BR and a 2% edge you would bet about $2,7000 * .02 / 1.33 = $40.60.

-Sonny-
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Before this thread turns completely into a tasty toad licking experience, let me surmise the following: Don't rely on Kelly for RoR as much as for proportional betting, and secondly, in the scenario you cite above, what would be my RoR with a $2,700 BR and a $10-40 bet spread? Still 13.5%.
 
bj bob said:
Don't rely on Kelly for RoR as much as for proportional betting,
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Yeah, the Kelly formula will tell you how to optimize your bet ramp so that you win money the fastest. After you have your bet ramp you can adjust your unit size to find a comfortable RoR. Your bet ramp shouldn’t change in terms of units bet at each TC, only the amount of money in actual $$$ that you bet at each TC.

bj bob said:
in the scenario you cite above, what would be my RoR with a $2,700 BR and a $10-40 bet spread? Still 13.5%.
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Right. As AM pointed out, betting full Kelly will give you a 13.5% RoR if you never resize your bets and never add any outside money to your BR. Basically, if you play on auto-pilot you will have a 13.5% RoR. I don’t know any people who actually play that way so it really becomes more of a theoretical number than an actual conclusion.

-Sonny-
 
sagefr0g said:
is there a link that summarizes the various formulas for the ideas such as advantage, ROR, kelly, trip goals, ect. ? inother words a summarization of most of the formulas useful for AP's. i guess i've reviewed most of them at one time or another but it all gets kind of lost in the mix and a summary of sorts would probably help keep it all in perspective.
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Sonny will do this in his book, when he writes it! ;)
 
EasyRhino said:
HE'S PLAYING RENO SINGLE DECK! Sooner or later, usually sooner, you're going to be stuck with negative counts playing single deck.

BTW, out of curiosity I did some basic sims with the restrictive "Reno" (D10) single deck rules... and the results were worse than I expected. Better than play-all in a shoe game, but worse than a decent doubledeck game with good penetration. And to think, when I was bumbling around Reno, I thought I was playing the cat's meow of card counting.
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The "typical" Reno D10, SD is no longer the norm as you well know by now. Your favorite venue (I shall not divulge) is DOA. Boomtown, and the Sparks houses are also, not to mention the "truck stop" which also alllows surrender and, BTW rumor has it that one of the well established stores on Va. Street is adopting surrender and DOA there as well.
So, while doing sims why not include those also and perhaps you can hear the 'ol cat starting to meow again! My figures show that with these conditions you're looking at a .14 HA even with H-17.
 
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Sure, there are the DOA places out there are, what... Boomtown, Siena, Rail City, Silver Club, and Alamo? And Alamo has LS too. Many of these places have $100 max bets, also.

Was the rumors Virginny St casino going to add LS but keep D10? That would be an unusual mix.

Also, I think it would be fun to go back to Siena and keep spreading 1-10, but use a unit that was ten times higher than when they backed me off. Just to see how long it lasts. :)
 
bj bob said:
Don't rely on Kelly for RoR as much as for proportional betting, and secondly, in the scenario you cite above, what would be my RoR with a $2,700 BR and a $10-40 bet spread? Still 13.5%.
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What Sonny said is true of course but what he didn't say is what happens if you want to spread 1-4 and get an advantage greater than what 4 times your bet would justify.

Or, if you're going to play all the hands, that that formula would say bet nothing in negative counts.

Anyway, any game and any bankroll has some spread that will yield a full-kelly ROR.

As I tried to say before, whether your 10-40 spread with $2700 constitutes full-kelly, or a fraction thereof, depends on the rules of the game, the penetration, your counting system, whether you play indexes, what cover you may choose to use, etc.

Like getting dealt 31 cards instead of 26 can make a big difference in how you would play the same bankroll even if if absolutely nothing else changed.

So the best thing is to get a sim and see how these are effected by how you most often play.

And, once you know what full-kelly is, like Sonny said, I think, it's really a pretty high-risk way to play. But each to his own.
 
sagefr0g said:
hey what ever works dude.
like we used to say in the 60's don't knock it if you haven't tryed it lol
:rolleyes:
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That would be the late 60's lol.

Anyway, here's a simple formula to figure ROR. The constant "e" of (-2/K) where K is your Kelly fraction. So, in Excel, it's just "=EXP(-2)" for a full Kelly fraction.

I think this is assuming an overall positive game with no re-sizing or time constarints. (Not 100% sure lol.)

Another one I like, and why I think I don't like betting full kelly, is no one asks anything other than ultimate ROR, like 13.5% for full kelly. No one seems to worry about the chances of being down a fraction of your bankroll at some point.

I think full kelly means you also have a 10% chance of losing 90% of your bankroll at some point.

So, I think "F^((2/K)-1)" where F is a fraction of your bankroll that remains and K is full-kelly or a fraction thereof, is a good one in helping to decide what swings you may expect.

Anyway, if I see one that seems simple enough, and, for me, it better be pretty simple, I stick it in a spreadsheet in case it comes in handy.

As for advantage, I don't think there's a way to know it except with a sim.
 
Kasi said:
That would be the late 60's lol.

Anyway, here's a simple formula to figure ROR. The constant "e" of (-2/K) where K is your Kelly fraction. So, in Excel, it's just "=EXP(-2)" for a full Kelly fraction.

I think this is assuming an overall positive game with no re-sizing or time constarints. (Not 100% sure lol.)

Another one I like, and why I think I don't like betting full kelly, is no one asks anything other than ultimate ROR, like 13.5% for full kelly. No one seems to worry about the chances of being down a fraction of your bankroll at some point.

I think full kelly means you also have a 10% chance of losing 90% of your bankroll at some point.

So, I think "F^((2/K)-1)" where F is a fraction of your bankroll that remains and K is full-kelly or a fraction thereof, is a good one in helping to decide what swings you may expect.

Anyway, if I see one that seems simple enough, and, for me, it better be pretty simple, I stick it in a spreadsheet in case it comes in handy.

As for advantage, I don't think there's a way to know it except with a sim.
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lol, i'll have to digest that for a while........ i suppose that 'e' is the natural logarithm used so often in science?

have you seen this? ====>>> http://www.bjmath.com/bjmath/kelly/kelly.pdf (Archive copy)

gonna have to read it and see what fraction i can make halfway sense of lol
 
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