So higher the CE (plus) the better?
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I've read up on the subject but find the material is either oversimplified or the math is just too complex. I think I have a vague understanding of kelly. This sort of betting maximizes the logarithmic growth rate of the br, whatever that means.Originally Posted by DSchles
Ok so I think you are talking about expected growth where as I was talking about EV. Where I'm experiencing confusion is how expected growth comes into play with fixed betting which assumes NO resizing of unit.EV might be greater with 100% ROR also, no? Don't you understand that your bankroll grows as a function of TWO simultaneous concepts -- both e.v. and variance -- and not just one of those functions?
What happens if you start off betting 13.53% RoR but then your BR shrinks such that RoR is now 33%? If one is still using the same size wagers then will expected br growth still be optimal? I could be wrong but at this stage in order to maximize bank growth (for 33% RoR) wouldn't you have to resize unit?
The reason I'm playing to such a high RoR is because it is the only way I can get down a reasonable bet spread given the table minimum.
Thanks for any clarification,
MJ
They are the same thing. N0 and its proportional reciprocal c-SCORE factor in variance and EV. This will tell you how much you are actually gambling and how much you are being an AP. If your N0 is high which would mean your SCORE is low it will take a really long time before your play starts to tame variance, the square of standard deviation. Time, or more precisely rounds played tames variance because EV grows linearly as related to rounds played but standard deviation grows by the square root of rounds played. This means if E is EV and S is SD for 1 round:
After 100 rounds:
EV = 100*E
SD = 10*S
After 10,000 rounds:
EV = 10,000*E
SD = 100*S
Eventually E = S and you are at n0 or N-zero, which is the number of rounds it takes for EV to equal SD.
If n0 is 5,000 rounds you will have a high certainty to make money after 20,000 rounds (4*n0 chosen somewhat arbitrarily). If n0 is 240,000 rounds you are basically gambling because you won't reach the same degree of certainty until you have played 960,000 rounds (4*n0). Basically due to the uncertainty of BR growth the swings are highly likely to eat your BR before you have made enough to reduce the chances of busting out to something more reasonable. Of course I have left out BR size which is a very important component of the chances of busting out.
If you search the archives you will find posts by people like Bjarg that speak of using a massive BR to play a small edge with really high n0 that is extremely tolerant of huge bets. I am sure he leaves key parts of the play out because the info is sensitive but these team players write of winning and losing hundreds of thousands of dollars a session. Their BR is so large that losing such sums is a trivial matter. Obviously if their BR was a million dollars or less losing such sums would be devastating. So the size of BR swings relative to your BR is very important. That is what SCORE, n0 and CE try to help you manage. Counting cards is easy. Making money counting cards is hard because you need to be a master of BR management, game selection, adapting styles of play to different situations, comportment in the casino that allows you to play for more than a short time before being told you can't play anymore and many other things that have nothing to do with counting. RoR is an important stat. 13.5% RoR gets you maximum BR growth. Any more and you BR grows slower with ever increasing risk of busting out. Any less and BR growth is slower but the risk of busting out is reduced. Obviously if you aren't playing the optimal 13.5% ROR the latter is far better.
You may have such a meager BR that you have to play at a high RoR but your plan should be crafted to outrace ruin as quickly as possible. It gets a bit complicated I like the analogy of the guy walking a dog on a leash. The guy walks a straight line or path of EV. The dog is actual results and is on a leash related to variance or SD. The dog will run within the range of the leash. The mans position at a given time going forward can be viewed were the dog is for possibilities moving forward. You are trying to shorten that leash from a point that the dog is far above the path of EV. That will lower the chances the dog can hit the electric fence that will kill it, the zero BR line. At 33% RoR your dog dies one third of the time. If the dog strays closer to the fence he is even more likely to die. If the dog strays from you away from the fence you can go over to the dog and shorten the leash some and proceed from that spot down the new EV path with a shorter leash.
OP: "Ok so I think you are talking about expected growth where as I was talking about EV."
Tthree: "They are the same thing."
No, they most certainly are not. The more you bet, the greater your e.v. Period. But, if you overbet Kelly by more than double, you eventually go broke. Sound like a contradiction? It isn't.
When e.v. is stated, it is the aggreagte result. So, if millions of people overbet, virtually all of them go broke, but one lucky bastard wins every hand and now owns all the money in the world. Divide that by all who started, and you get the e.v.: higher than if everyone had bet less! When you bet more sanely, the distribution changes, and more and more people earn the average e.v. of the whole group. But, it is less than for the group that bet 'too much."
Do you understand the distinction?
Don
I like to think of EV as hourly earnings. Expected growth rate refers to the logarithmic growth of the bank. So, as Soon pointed out, one can have a positive win rate with an expected negative growth rate.
Does expected growth rate apply to a fixed size bettor? Wouldn't CE be meaningless for this style of play?
Don, should one focus on minimizing N0 or maximizing CE?
Correct me if I'm wrong, but I believe this would indicate you are massively overbetting your bankroll. For instance, imagine a game where you have a 25% chance to win, but you are paid 6:1 (3:1 would be a break-even 0 EV game)....and you're betting 80% of your bankroll. The N0 will be low, EV will be high. I don't know what the exact figures are for ROR or CE, but I imagine CE might be negative.
But remember, part of CE is based on your own risk tolerance. If you and I both had the same net worth, but I was much more conservative and had less tolerance to risk while you were okay with risk, the CE for me would be a lower value than to you. But a negative CE game should NEVER be played. You can't adjust the figure based on your risk tolerance, because your risk tolerance has already been used when calculating the figure.
CE is probably the best way to analyze plays and determine which are good/playable, which are bad/unplayable, as well as which is better than the other. In laymans terms, it's basically the risk-adjusted EV of a play, or at least it can be thought of like that.
"Everyone wants to be rich, but nobody wants to work for it." -Ryan Howard [The Office]
Thanks for the correction Don. A poster used the term Expected Growth and I asked him to define what he meant. His definition was the definition of EV. I had never heard the term Expected Growth and assumed his definition was the correct one. My bad. He may have said Expected Gain. My feeble brain errantly made the connection either way.
Some like to maximize BR growth, by maximizing CE, while others like to reach the long run faster, minimize n0. The two are related so one will tend to follow along with the other. Better is a matter of opinion or perhaps personal preference is a better term. I try to consider EV, n0 and certainty.
Last edited by Three; 05-18-2017 at 06:48 PM.
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