Fish at the table, friend or foe?

Okay, so you hear a lot of things lately about how you want fish at your table. I agreed, in some circumstances. I disagreed that you want a LOT of fish at your table. People didn't seem to be thinking about the equity that you lose for every calling station that sits and chases. If you don't know what I'm talking about, read on and learn with me.

For those who don't pay attention, I play my micro limit cash ring games pretty exclusively now at Full Tilt (see the ad over there? Click it and get it now! Okay, advertisement over). Why? I have found that there are less fish in the micro limit games at FT than at any other sites. How do I know that? I use PokerTracker to datamine. When I rate players, the Full Tilt dB has the least number of people that are rated above Semi-Loose Passive-Passive (go look at the site to see what this means if you don't know). I consider anything worse on their scale than this as a fish, other than a few players who play a LAG style very well. So you have more serious players at the site, and less fish. Was I right in my thinking? Read on and let's learn together!

First of all, I used pokerstove for all these calculations. If you don't have it, go get it now. I can wait.......

Got it? Good. Now let's play with some numbers. First of all, what happens to your AA when you are up against a completely random hand? What's your equity? Well, according to the stove, you have 85.2037% equity. So for every dollar that is put in the pot with this hand, over the long term, you should see 85 cents coming back. This is the best chance that you have against any random hands. You are still +EV as for every dollar you put in, you will get 1.70 out with one caller. Here's the pokerstove output:

2,097,572,400 games 2.468 secs 849,907,779 games/sec

equity (%) win (%) tie (%)

Hand 1: 85.2037 % 84.93% 00.27% { AcAd }

Hand 2: 14.7963 % 14.52% 00.27% { random }

So that's just one fish at the table that will call with any two cards. A lot of sites now are known for having a lot of "fishy" players. What happens when you draw a table with more? Let's see! (A word of caution....If you want to try this yourself, I'd recommend that you move pokerstove to a Monte Carlo mode and get time on a parallel processing system. The stats I'm about to give took several hours to run on my Athlon XP 3200+ processor. User beware!)

When you end up vs two random hands, you lose another chunk of equity. How much? AA vs two random hands drops the AA to 73.4352% equity. So now every dollar in the pot nets you just 73 cents. However, you now get back 73 cents x 3 (two callers) = $2.19 for every dollar that YOU put in. With three you drop a little more to (rounding here) 64 cents for every dollar in the pot, giving you $2.56 out for every $1 you put in if you get all three to call. Here's the Pokerstove output:

1,894,107,877,200 games 3806.625 secs 497,581,946 games/sec

equity (%) win (%) tie (%)

Hand 1: 73.4352 % 73.21% 00.23% { AcAd }

Hand 2: 13.2824 % 12.92% 00.36% { random }

Hand 3: 13.2824 % 12.92% 00.36% { random }

11,107,035,128 games 31916.750 secs 348,000 games/sec

equity (%) win (%) tie (%)

Hand 1: 63.8345 % 63.61% 00.22% { AcAd }

Hand 2: 12.0549 % 11.59% 00.46% { random }

Hand 3: 12.0561 % 11.59% 00.46% { random }

Hand 4: 12.0544 % 11.59% 00.46% { random }

What about AK? You start at 67 cents for every dollar in the pot, netting you $1.34 for every dollar when you are heads up. If you get two callers, you get about 49 cents of every dollar put in giving you $1.47 for every dollar you put in.

It's pretty tough to get to a point where this becomes -EV for you against random hands. So overall, more fish should be better for you. Sure, you will see big swings in your BR, but overall you should be a winning player.

When I first started this little journey, I thought for sure that I would find that more fish at the table made things worse for you. In fact, when I first started writing this I was thinking about the equity being the amount of return you get for YOUR dollar (and the original post name was "the fish tax"). I neglected to take into account that for every dollar you put in, each caller has to put that dollar in with you.

So now I have to change my tune. I was only looking at the short term variance and fluctuations in my roll when I played at some of the "fishy" sites. That was a mistake by me. I am still going to limit myself when I go out to some of these places, but you might see me dipping my toe in the water again now that I'm convinced in the math. I hope that you learned something with me in this journey.

I'll see you at the tables....