What is our percentage edge as Poker players?

[roGER]

Hello everyone,

What is our edge as poker players?

In a casino, every game has an edge. For example, playing craps, I've read that pass-line bets have a negative edge of 1.4% for the player. Baccarat is about the same.

A skilled Blackjack player has a positive edge of about 1.5% or more in a single deck game played under favourable rules and conditions.

But I've never read anything about poker players! Now obviously, poker players have different skill levels, and play different games at different limits.

To narrow down my question, let's assume we are talking about two limit Hold'Em players, one is rated as "OK" and wins at a rate of one small bet an hour, the other is rated as "Good" and wins one big bet an hour. Lets also assume the game conditions don't change much, and both players have been playing these games long enough for their hourly expectation to be accurate.

It seems to me we should be able to say something like:

"An OK Hold'Em player has a positive expectation of n%."

"A good Hold'Em player has a positive expectation of n%."

To the best of my knowledge, no author has ever come out with those statements.

Is it very hard to calculate accurately? It seems to me that on-line players with enough data (gathered with software like Poker Tracker etc.) should be able to arrive at this percentage.

My best guess, given from what I've read is that our expectation is small, perhaps very small. Something less than 3% for the good player, and perhaps as low as 0.5% for the OK player.

But I'm just guessing! Anyone ever done any research on this?

Any info welcome...

- roGER

[gonores]

You'd need to know how much he wagers on each hand or each hour, on average. Then it's elementary.

[DarkKnight]

I'm surprised by my results (thought it would be much lower)

From my pokertracker data (had to build an Access query)

2.52 BB/100 (1.42 / hour) over 9,500+ hands
Win Rate is 5.9% in a rake free game it would be 9.2%


DK

[roGER]

Absolutely!

But calculating that amount, or coming up with an accurate estimate is very difficult!

Here's the way my crappy non-mathmatical brain sees it:

Lets assume 35 hands are dealt each hour and there are ten players at the table. The one thing we can be sure about is the blinds.

At 10-20, each player must pay 3.5 big blinds ($35) and 3.5 small blinds ($17.5) each hour. So that's a minumum of $52.5 wagered each hour.

That's actually an important number, because it enables us to set some upper limits on expectation. If the good player is winning $20 per hour, then that means his expectation must be less than 38%, since $20 is 38% of $52.5.

The OK player is winning at at rate $10 per hour, so his expectation must be less than 19%, since $10 is 19% of $52.5.

OK, so far we've established that poker is less profitable for the OK player than Keno is for the casino. BIG DEAL!

But of course poker involves more than just wagering the blinds.

From certainties we quickly move into a huge gray area of assumptions, and this where solid data would be invaluable.

In the absence of solid data, here's my best shot at guess-timating how much money is wagered:

We can assume (I think) that a winning player plays about 15-17% of the hands he is dealt. At 35 hands an hour, that means he is playing about 5 or 6 hands each hour.

Lets now assume that of these 5 or 6 hands, he gets to see the flop for one small bet, but the flop doesn't fit for 3 of them. That means $30 is wagered.

Add the $30 to our blind wagers, and we get a figure of $82.5. Plugging this figure into our win rates, we reduce the winning percentages:

The good player is now down to an expectation of 16.5%, the OK player's edge is down to 8.25%.

Now lets try and guess what happens when the flop does fit!

Let's keep it simple and assume each time our player has to go to the river:

One one hand, lets assume our player has to pay one small bet to see the flop, one small bet to see the turn, one big bet on the turn, and one big bet on the river $10 + $10 + $20 + $20 = $60.

Lets plug in another $60 to our amount wagered:

$82.5 + $60 = $142.5

The other two hands are more expensive, let's assume he has to pay 2 small bets to see the flop, 2 small bets on the flop, 2 big bets on the turn, and 1 big bet on the river. $10 + $10 + $10 + $10 + $20 + $20 + $20 = $100 x 2 = $200.

So how much money has been wagered in an hour?

$142.5 + $200 = $342.5

So we have a good poker player with an edge of about 5.89%

The OK player has an edge of about half of that, about 2.9%

These percentages still seem too high to me, given the huge swings which we all experience from time to time which seem to indicate a low winning percentage, since the higher the percentage the more chance there is of emerging a winner...

I dunno what I'm missing - perhaps my assumptions are too conservative? Am I making fundamental errors?

Probably :-(

- roGER

[gonores]

I think your assumptions are conservative.

However, I don't think you'll find many players who would rather have 5% expectation on $200 wagered per hour than 4% expectation on $400 wagered per hour. There are too many playing styles, too many table textures, too many variables to figure out the proper numbers, especially considering that hourly expectation shouldn't be considered in poker decision-making, as it will skew your decisions conservatively.

[roGER]

Thanks for doing the query!

Your numbers are impressive, although not a million miles away from the rough guesstimate I did (see my other reply).

- roGER

[DarkKnight]

I saw your post. I was impressed by the accuracy of your guesstimate.

DK