I think I need a boost...

[Zybomb]

If you're saying damn now, You should have seen him b4 this past month....

[Windbreaker]

Oh, almost forgot about this:




2 player SnG, top 1 itm.

return on investment : 15.0%
kelly criterion : 15.79%

return on investment : 10.0%
kelly criterion : 10.33%

return on investment : 5.0%
kelly criterion : 5.22%


Cliffnotes on kelly criterion for those unfamilar:

The formula specifies the percentage of the current bankroll to be bet at each iteration of the game. In addition to maximizing the growth rate in the long run, the formula has the added benefit of having zero risk of ruin; the formula will never allow a loss of 100% of the bankroll on any bet. An assumption of the formula is that currency and bets are infinitely divisible, which is not a concern for practical purposes if the bankroll is large enough.

[Talking Poker]

I need to read more about this, but this is very interesting - I think the bold above is what I should be focusing on (we all should, in theory).

Thanks. +Rep.

For those interested:

[Windbreaker]

Should note the disadvantages....in the wiki link.

The optimum bet for the greatest growth of bankroll is making the full bet suggested by the Kelly criterion, but this produces a volatile result. There is a 1/3 chance of halving the bankroll before it is doubled. A popular alternative is to bet only half the amount suggested which gives three-quarters of the investment return with much less volatility. Where money would accumulate at 9.06% compound interest with full bets, it still accumulates at 7.5% for half-bets.

[Talking Poker]

I can not get over these numbers. I keep going over it different ways, and I keep coming out with results that tell me I am a puss.

If I am reading this right, let's say you have a $1000 bankroll. If your HU SNG ROI is 10%, what this is saying is that you should be betting 10% (I'm going to round all numbers down - this almost exactly covers the rake anyway) of your bankroll to maximize your growth rate, or in this case, playing $100+5 matches. By doing so, there is a 1/3 chance that you will halve your roll to $500 before doubling it to $2000 (implying that there is twice as good a chance of you doubling your roll before cutting it in half).

Can that be right?

Taking it a step further, many people prefer to bet half of the optimal Kelly numbers, because doing so will yield 75% of the return, but with much less volatility. So, in our case of Mr. 10% ROI and $1000 roll, he should play $50+2.50 matches to be conservative.

That STILL amazes me.

Another example for the low-rollers: You have a $500 roll and a 5% ROI in HU SNGs (you play while sleeping, in other words). Kelly says you should be playing $25 SNGs, but to be ultra-conservative, you play in $10 ones, with virtually no chance of busting your roll.

Running my numbers (only counting my "virtual" bankroll - what I have online), Kelly says I should be playing $2k SNGs for optimal growth. The more conservative approach would be to play $1k ones.

Can that be right?

One thing not factored in here is that my actual ROI when playing at $1k or $2k limits would likely be MUCH less than the number I am using in these calculations - in fact, it could very well be a negative number, which throws everything out the window. If your ROI is negative (losing players), the optimal bet for you is of course $0.

Still though, everything about this tells me I should move up.

If I'm misinterpreted anything in the math or what it means, some please point out where.

[Windbreaker]

I think your logic is correct.

Although I wouldn't necessarily interrupt everything the same way.

- You have no idea what your ROI is at the $500 level, because you haven't had a significant sample size at that level. So you won't know what your "ideal" bankroll should be.

- Technically, since your bankroll changes as you play (either + or -), you should be changing levels as you go. So if you're on a downswing, you technically should be going to a lower level.

- Also this method is volatile. If you keep the same bet size: your bankroll will halve before doubling 1/3 of the time. That may not be a very good thing if you tilt.

Also your statement -

"By doing so, there is a 1/3 chance that you will halve your roll to $500 before doubling it to $2000 (implying that there is twice as good a chance of you doubling your roll before cutting it in half)."

Isn't quite true. According to KC, you should never bust your roll....because your Bankroll changes, thus your bet size changes. (Not really practical in poker because your ROI isn't constant, and players may not be willing to grind microlimits if it came down to that). That statement says, 1/3 of the time you're going to halve your bankroll before you eventually double it. It doesn't mean you will double 2/3 of the time before halving your bankroll.

I think it means that your bankroll will always eventually double - assuming the following to be true:

- ROI is constant
- Your bet size is = to the KC all the time
- And that your bet size can be small enough where you can continue to place the bet.

***I don't know if everything I wrote is necessarily correct.

[Talking Poker]

Good stuff.

[Talking Poker]

So, I decided to set up a little Kelly Criterion calculation in Excel. I went the conservative route with all of my numbers:

For my bankroll, I didn't use all of it, but have it based on my 2008 HU SNG winnings plus a bit (less than that total I have online).

For my ROI, I used my 2008 number, and included that ridiculous run of turbos I played that knock down my non-turbo ROI a few percent.

Both my bankroll and ROI update automatically, so everything is recalculated after every match I play.

Then, rather than going with the straight KC number, I rounded it down (this coincidently will match ROI for HU play), and set high and low tolerances for where I think I'd be comfortable playing. I'm pretty sure going straight KC (losing half my roll 1/3 of the time) is would be too much variance for me to stomach, so I picked 20% KC and 50% KC for my low and high limits, intending to play within that Buy In range.

Now here's the funny thing, and I couldn't make this up if I tried. The numbers it spit out for me:

Low - $199.81
High - $499.53

Well, isn't that ironic?

Going by the letter of the law, my next match should be a $200 one and if I win that, I should immediately move to $500 (the numbers will adjust up slightly). Of course, that doesn't count the juice, which needs to be counted.

Funny thought how it came out basically saying I should be at the crossroads I feel like I'm at.

[Invigilator]

*Invigilator gets out the popcorn and beer*

[Talking Poker]

I know how to read graphs, thanks.

And yeah, he's playing at a level that I don't think I would ever be comfortable with. I'd love to chat with him sometime about this HU SNG progression. Hook it up.