### Doing Business

Last night I got in a quick one hour session at some place in New York that is not Salami or EBB. I was very tired and stressed after an action packed week at work with little let up on Friday, but had a little time to kill before the KATM got someone to open up his leg shackles at Big Firm to come out and have a drink.

So I figured I'd get a few hands with a view to playing extra cautious given that my mind remained a bit addled. I got the last seat at the 2-5 and sat with 500 (had forgotten max was 600, but only two stacks at the table had more than 500 anyway).

No super obvious fish after two orbits, and there was one solid aggressive player I've known way back from Playstation and Aquarium, a nice guy with a thick New York accent in his late twenties who appears to be making a living at the game or at least supplementing one. I was a little apprehensive at being on his right, but with two players in between I wasn't overly concerned, that plus the facts that rightly or wrongly (shut up Kid Dynamite), he seems to respect my game so might not see me as an mark to be tested and moreover he had only 300 in front of him as he seemed to be having a bad session. Some of the other table talk, however, led me to believe I wasn't necessarily dealing with a shark tank.

Played extremely tight, four hands in first dealer push, three limps for the minimum and one late position open raise with premium suited connectors which got me heads up against the small blind.

An ace flopped and I took it down on the flop with a continuation bet. That sequence confirmed my suspicion that notwithstanding my very tight play, at least one guy was not paying attention as he we willing to call me preflop completely out of position for 28 more, very likely to be heads up (I'll call him Mark).

I continued to fold a lot, and actually considered getting up with $5 profit as I was really not focused. Then, mid conversation under the gun I looked down to see those pretty pretty little As. Somehow, I managed to finish my sentence without skipping a syllable (danger of talking while looking at your cards) and, without pausing in my conversation, bet out 25. I was very happy that an aggressive player two to my left raised it up to 75 with about 325 behind, and even happier when two players after him, Mark, with 400 behind, made it 175 to go. It folded around to me and with a hand that was playing itself, I had the joy of pushing my one full stack of green beauties out in front, facing the other two shorter stacks with a decision to call for all their chips.

The first guy hemmed and hawed for while, (correctly) stating that boy didn't it suck but he probably had the third best hand (turned out he had tens). For some reason, this was a difficult fold for him but he did manage it. Then Mark goes into the tank, deciding to whether to call a 225 raise into a pot of 657. He ended up calling with queens.

I actually think this is a fairly easy fold given the action before hand. Sure he is getting great pots odds, better than 3:1 (need 25.5% to win), but unless he can put me on a hand other than AA or KK, he can fold—against those hands he's more than a 4:1 dog (18%). Even if you somehow throw in AKs into my range (maybe he read my last post!), his chance of winning only goes up to 27%. Only when you add in AKs, QQ and JJ does the call become clearly correct, and I just can't see how he can put me on that wide a range there. It's actually ironic given the numbers—he raised pretty close to the exact amount that did not pot commit him against my likely range (if I rereraise) and yet he called anyway. I'm sure this mirrors his thought process exactly—not so much.

Given my tired state, I did not really want to get my aces cracked before meeting KATM—not really fair to him to have his Friday night ruined by my moaning. Before the hands were flipped I offered business, that is we could run it with three full boards splitting the pot into thirds for each board won. He asked what I had and I told him, and the some on table were stunned I offered business this far ahead in a hand. How could I give up such a solid chance at a huge pot?

This line of questioning highlighted just how brilliant was the table—yes I was giving up an 82% of winning a $900 pot, but I was avoiding an 18% of losing that whole pot (netting -400 or so) in exchange for a ~55% of still winning the whole pot, something like a ~5% chance of “winning” $300 (it's significantly less than just calculating the chances of hitting 18% of the time in of 3 tries (about 7%) since that does not factor in the dependence between the three boards—i.e., his by far most likely win is hitting a Q and if he hits one on one board it's significantly less likely he'll win one of the other two boards), a something like a ~40% chance of winning $600 and an all but 0% chance of losing on all three boards.

As it happened, I cleanly won the first two boards, but he spiked a Q on the turn on the third board, but I spiked an ace on the river for set over set and a clean sweep.

I have had this discussion of whether or not it is a good idea to "do business". I think, and please anyone that has really thought about this and has a different thought, chime in, that from a flat EV point of view, it makes no difference. I have heard only one substantive argument that doing business might affect EV—that is that if people know you'll give it, you'll invite more marginal calls. That may be so, but I'm not sure in NYC games that makes much of a difference. In very deep stack games with better players, some of whom may be at the limits of their bankroll, I might concede the point that you may be giving something up here.

But thinking about my situation last night, I came up with one thought how doing business is actually plus EV for both players—if you accept the math that on a per hand basis, doing business has the same EV result as not doing business, all that doing business does is reduce risk for the same EV. In the world of financial products that I work in (and in others), anything that reduces risk without changing expected return is an asset—in fact, people will definitely give up some expected return in exchange for reducing that risk (that's why people pay money for hedges and insurance). The amount someone is willing to pay to reduce risk is in insurance terms a premium. Since it is clearly established that entirely rational people are definitely willing to pay premiums to mitigate risks—particularly large risks—we can deduce that in reducing risk for free as one does when one agrees to do business, one is capturing the value of the implied premium. It's free as in free beer free money.

Anyway, on a side complete note, one of my professional pet peeves has come to life. Ever notice in some contracts when they write out a number, they put it in Arabic numerals right beside it or vice versa, like fifty(50)? As a drafting technique, this is intended to increase clarity and certainty. But it's just plain stupid as it risks just the opposite: what happens if for some reason the English word doesn't match the Arabic numerals?

Well, I just received this important message from Ms. Gloria Edwards, (Lottery Coordinator/Director) for LOTTO Rheinland-Pfalz. and I'm afraid just such an error may come back to haunt her. You see, she wrote me:

"You have been approved for a payment of ₤100,000,000 (ONE MILLION EURO) which is deposited with a Finance and Security Company."

I fully intend on pursuing my full 5F5E100 (0101111101011110000100000000) claim to the last 10

^{-2}Euro.

After some consideration, I did think matching the currency sign in the first term with the spelled out Euro number in the parenthesis and thus demanding the amount in pounds sterling may be a bit overreaching.

Wow, maxed out the geek factor!

## 11 Comments:

Hey Sox. I never run business, but after your analysis, I might change that. You have some well thought-out ideas here. Thanks.

The way you describe, running business best approximates your EV. If you ran the whole deck out, in five card increments, you'll win pretty close to your EV in the hand. I wouldn't say that it is +EV for either player, but is variance minimizing.

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Hey, it was nice meeting this weekend! Sorry I thought you were Jordan, but if it's any consolation, you could have kept it to yourself and I would have told the story of your having to take a mad crap as if it were him instead.

I agree with David's comment.

And if that's your goal, why not just split the pot by pot equity? you can take 80% and give him 20%.

Did you see the High Stakes Poker hand last season where Phil Hellmuth paid a 10% insurance premium to Barry Greenstein to insure his hand? Basically, Phil had 80% EV or something, and he took 70% of the pot - because he's a giant douchebag.

anyway - i would suggest that you never finalize "BUSINESS" until you see your opponent's cards with your own eyes. I have seen some fucked up things happen where people mis-represent their hand.

Gary Carson has a post up about simulating hands that will shed some light on thinking about business.

Definitive proof that online poker is rigged. What the online poker sites DON'T want you to know.

See the Proof Online Poker is Rigged Here!

Clearly running it 3 times is different from having situation occur 3 times at 1/3 stakes due to not being able to spike a Q 3 times vs. .8% chance it can happen with 3 different hands.

But difference between 8 out of 1000 vs 0 of 1000 seems neglible for making decision.

Crux of decision is you are reducing variance by artificially creating 3 "occurences"

Not so clear in fact. I think your math is a bit off, it is exactly the same; you are not accounting for the effects that hitting or missing has on the remain deck.

For example, imagine a short deck with only three cards, one of which is a queen.

The probability of draw a queen in on try is 1/3. Equity thus equals 1*1/3 or 1/3.

If you do business twice, the equity of drawing a queen using the same deck without replacement is:

1/2(1/3) + 1/2(2/3 * 1/2) = 1/3

(On second try, the 2/3 is the chance you missed on the first try since you can't hit it twice and the second term now 1/2 since you've removed a card).

If we do it 3 times, the equity remains the same:

1/3(1/3) + 1/3(2/3 * 1/2) + 1/3(1/3 * 1) = 1/3

If we add another card to the deck, the equity remains same for 1 draw (1/4) versus 3 draws:

1/3(1/4) + 1/3(3/4 * 1/3) + 1/3(2/4 * 1/2) =

1/12 + 3/36 + 2/24 = 1/4

This will hold no matter many cards we put in the deck and no matter how many times we do business. What does change is the chance that your actual result is greater than zero. In the last example, 1/4 you hit at least once with 1 draw, and 3/4 you hit at least once with 3 draws.

The probability of draw a queen in on try is 1/3. Equity thus equals 1*1/3 or 1/3.

If you do business twice, the equity of drawing a queen using the same deck without replacement is:

1/2(1/3) + 1/2(2/3 * 1/2) = 1/3

Three card deck, with a queen. The probability of catching the queen on the first card is 1/3. The probability of catching the queen on the second card, given that you missed the first is (1/2)(2/3), so the probability that you catch the queen when you run business twice is 1/3 + (1/2)(2/3) = 2/3. You need to think of it in terms of the cumulative distribution.

What does change is the chance that your actual result is greater than zero.And by zero-sumness, it changes the chance that your actual result will equal the whole pot.

Actually, now that I've figured out what you wrote, you make the point that doing business best approximates your EV (equity in the pot).

Not sure if your comment is intended to correct my last comment. I do not disagree at all with your calculations of the probabilities of hitting at all, but note that in my comment, I am calculating equity not chance of hitting.

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