Tuesday, January 2, 2007

The Fallacy of Bad Beats

"A child of five would understand this. Fetch me a child of five."

As I wrote in my inaugural post, I've been consistently getting the heave-ho from tournaments lately by getting all the money in with a higher pair than my opponent, or some other dominating hand, only to see them hit their set (or even quads), their four flush, four to a straight. Sometimes, we'll play a pot for all the bacon when I sneak in with the smaller pair and hit my set. But (it seems) inevitably the evil opponent will catch their two outer set, or their runner-runner.

Sometimes (often?), I donk off all my chips with medium pair. Ahem. Never mind.

There are infinite variations, but the same story: Some mind-blindingly bad junk happens and I'm all done, despite my blindingly effulgent poker skills, which are both "sick" and "madd".

I've started asking myself, though: ARE these really 'bad beats'? If my all-in gets called by somebody who only has 8% of it pre-flop and he sucks out, is that actually a bad beat?

The people I play sure seem to think so when I suck out on them. They'll type things like this.


"OMG. So ghey."

"**** u ur a luck"

"This ****ing site is ****ing rigged u doknkey awlys sucks!!11!!!!!!1"

"***** ***** of a ****** RiverStars monkey***ers"

"Every TIME!!! Every ******illet *other***ongle TIME!!!"

Ah, to be fair . . . that last one was me. Last week.

But are these actually bad beats? Do bad beats even exist?

I'm drawing a line in the sand. I'm going to say no. It's a myth.

This may be easily refuted by anybody with a math degree or an IQ in triple digits. It may be a completely obvious thought that has been writen about before, and better, and here I'm treating it as profound and original. But I think that if you get your chips in with 92% of it, and you win the pot, you didn't hold up. No, bubba, you just got lucky.

Behold. Here's the Fallacy of Bad Beats in MTTs.
Proposal #1: The goal of a poker tournament is to get all the chips, every last one of them.

Proposal #2: In a non-rebuy tournament, everybody starts with the exact same number of chips.

Proposal #3: With evenly distributed cards, and with completely even talent, winning a tournament is essentially a process of doubling and redoubling your chips, for as many re-doublings are necessary until all chips are yours.

Proposal #4: Every time you double your chips, you are incurring a level of risk somewhere between 0% (you're holding the mortal nuts) or 100% (drawing dead).

Proposal #5: All things being equal, your level of risk for each attempt to double through should approach 50%, the popular coin flip. Skill is the factor that tends to lower this risk -- by making good reads, good bluffs, good lay-downs, and by managing bets, flop texture, and innumerable other factors to win larger pots with smaller bets. Incompetence is the factor that raises this risk, through poor card selection, failure to calculate pot odds when chasing draws, and over-valuing marginal holdings.

Proposal #6: All things aren't equal. Sometimes you are wrong, sometimes the pot odds or implied odds recommend a call with the worst of it. Sometimes you just need to take a stand before the blinds gobble you. You're sometimes going to get into the money with the worst of it. Your average risk for a double-through is not going to equal 100%. Even the very best players, catching the very best cards, can't hope for an average risk lower than 10% -15% (just making up numbers here, but that sounds about right).


OK, hopefully all that makes sense and doesn't make me sound like a baboon or a pedantic dink.
Having said all this, the question is begged: How many times do you have to double through to get all the chips? Answer: It depends on the size of the field.

Let's take the last tournament I played, which had approximately 1300 entrants.

I started with 1500 chips, which represented one (1) buy-in. My goal was to represent approximately 1300 buy-ins.

The first time I doubled through, I officially had 3000 chips and represented two (2) buy-ins. The next time I doubled through, I had 6000 chips and four (4) buy-ins.

If I continued like that, I would next represent eight buy-ins, then sixteen, then thirty-two, then sixty-four, then 128, then 256, then 512, then 1024, at which point I would only need to add about 30% to my stack to get the rest of the buy-ins. I'd be heads-up with a commanding chip lead. So let's make it simple and say 1024 is the promised land.

That's ten double-throughs.

Say I am correct that getting an average of only 10% risk for each double-through is a best case scenario for even a very good player (and if you disagree, ask yourself how happy you are when you're called by somebody who is only getting 10%).

You are 90% ahead. Which means that you'll lose one time out of ten. And you have to do this successfully ten times.

So, in a field of 1024 or more, you have to do better than being way, way, way ahead, or statistically, you're going to lose. You have to be, on average, better than that when you risk your chips, or you can't really call yourself unlucky.

It's something I intend to remember when I push with cowboys, get called by Jacks, and watch the Jack hit the river to end my night. That was the one time in ten.

Variance, then, is the property that says: Sometimes your opponent will hit his 2-outer on the river, but not always: sometimes, it will be on the turn or even the flop.

But your opponent will indeed eventually hit that 2-outer, but only if you're good enough.

I realize that I'm describing a closed system of nothing but all-in shoves and double-throughs, and that this theory doesn't take into account the delicate dance of bluffs, semi-bluffs, positional steals, and the rest of it that makes this a far more complex equation. There are other things you can do to get chips, other tools in your kit to give you an edge.

In the final wash, though, the goal is to get chips. To get them, you must risk them. It comes down to chips and cards, and with what combination of the latter you choose to risk the former. So the next time your Aces hold up against those pocket sevens, feel very lucky. You missed the one in ten.

"Every time I get in with rockets against Jacks, a Jack hits the flop. EVERY TIME!"

Well, of course every time. That's expected. That's normal.


Am I saying, then, that it's all luck? Skill not a factor?

Just the opposite.

I'm saying you need skill to even hope to get lucky. A player without skill could start with 10x the starting chips as the rest of the field, and rarely get lucky enough to find the final table. Try this: take note of the chipleader about a half hour into a large-field tournament. When it's done, see what place they went out. Was it even in the money?

Skill gets you to luck's front door, then you hope that luck is home when you knock. She's usually out on a date. Sometimes, she's home, and will invite you in and scramble you some eggs for breakfast. You need that 'good' kind of luck, which, like the 'good' kind of cholesterol, is necessary in small doses for healthy living.

"Good" luck is when your favorite doesn't lose. "Bad" luck is when you suck out, and it will clog your arteries if you get too used to living on them. Suckouts are like the Big Macs of poker. They taste so good, you want another.

So the next time I'm bounced despite a good play with a good read, I'll try to keep it in perspective, and wait for some scrambled eggs.

A little advice: When you hit YOUR two outer on the river, your victim doesn't seem to want to hear your theories about how it's supposed to happen.

They become so rude.


Alan said...

Holy cow... no comments on this awesome post? I love your analogy of "bad" luck to big mac. So true... I guess I shouldn't spoil myself with so many suckouts then... :)

Goat said...


Thanks for the kinds words. This is actually my favorite post to date, but my blog was about 2 days old and the readership was utterly nil when I posted it, so it's kind of been lost.

Or . . .



Glad you enjoyed it.