In real estate, the saying goes that the three most important features of any property are "location, location, and location." Maybe position, position, and position aren't the the three most important aspects of any poker hand. Even so, most players would likely agree that position is one of the most important aspects of any hand. Given its importance, it seems to me that it might be worthwhile to take a closer look at position.
While I may be missing something, I'm not aware of anyone who's attempted to quantify the relationship between position and a hand's EV. The question's how to do so. Computer simulations would be difficult, may be unrealistic, and, in any case, are beyond my ability. An analysis of my own hand histories wouldn't be representative. There's little publicly available data.
In fact, the only available data that I'm aware of are
PokerRoom's EV stats. PokerRoom has posted tables of each starting hand's EV. According to the website, the statistics are based on approximately 122 million pair of pocket cards dealt at real money tables. The unit for EV is average profit measured in big bets. There are separate tables for different table sizes, ranging from 10 players down to 2 players.
A few caveats are worth mentioning. First, aside from what's posted on the PokerRoom website, I have no idea how the data was collected or calculated or whether it is correct. Second, the EV stats are based upon limit hold'em tables, ranging from $1/2 to $25/50 tables. I'm sure that EV differs between limit and no limit games -- I just don't know how. Third, the stats are based on ring games, not tournament play. Because chip EV (CEV) differs from dollar EV ($EV) in tourneys, these stats may be unrepresentative of the effect of position upon a hand's EV in tourney play.
With all those qualifications, attempting to use the PokerRoom EV stats to try to figure out the relationship between position and a hand's EV reminds me about the the drunk looking for his keys under a lamppost. (A cop walks by and asks the drunk where he had last seen the keys. The drunk points toward a dark alley. "Why aren't you looking there?" asks the cop. The drunk looks up and replies "cause the light's better here." [img]/images/graemlins/grin.gif[/img]) That said, let's start looking under the lamppost.
What I did was to download the PokerRoom EV stats by table size into an Excel spreadsheet. I created 9 separate worksheets ranging from 10-handed tables to 2-handed tables. Each worksheet has separate rows for each hand from AA to 32o. Each worksheet has separate columns for each table position (1=SB, 2=BB, etc., up to the button, e.g, 10 at a full table). Each cell shows the EV of a particular pocket cards at a particular position at a particular table size. Using those worksheets, I then used the Excel functions to calculate a best-fit linear regression line between position as the independent or x variable and that's hand's reported EV as the dependent or y variable. That yielded an intercept (the point at which the best-fit linear regression line intersects the y-axis) and a slope for each such hand. While I'm not sure that I found my keys, I did find a few things that look interesting.
[img]/images/graemlins/spade.gif[/img] First, as common sense suggests, there's generally a positive relationship between position and a hand's EV. In other words, as table position increases from SB to BB to UTG to MP to the button, a hand's EV generally increases. Let's take a look at a 10-handed table. I calculated the average slope for each hand's EV by table position. I weighted each hand's slope by its probability of being dealt. The average slope for all possible hands is 2.3%.
To illustrate what that means, let's look at 77. The slope of its best-fit linear regression line is 2.4%, almost the same as the overall weighted average. Using the calculated intercept (-0.04) and slope (0.024 or 2.4%), the predicted EV of 77 UTG is 0.03 (= -0.04 + 3*0.024) [img]/images/graemlins/confused.gif[/img]. In other words, pocket 7s are barely break-even when dealt UTG at a full table. However, the predicted EV of 77 at the button is 0.20 (= -0.04 + 10*0.024). To put it differently, because it gets to act last, the EV of 77 at the button (0.20) is just about the same as AQo UTG (EV=0.22).
[img]/images/graemlins/spade.gif[/img] Second, as many players would expect, there's generally an inverse relationship between slope and table size. In other words, as table size decreases from 10-handed to short handed to the bubble to 3-way, the power of position upon a hand's EV increases. To put it differently, all things being equal, the effect of position upon an average hand's EV is greater at a 3-handed table than at a 10-handed table.
I calculated an average slope for all hands, weighted by the probability being dealt, for tables with 10, 9, 8, . . . , 3 and 2 players. Those numbers are:
10 2.3%
9 2.8%
8 3.2%
7 3.8%
6 4.5%
5 5.5%
4 6.9%
3 8.2%
2 6.4%
As these numbers show, slope (which shows the power of position upon a hand's EV) increases as table size decreases. Once again, while I'm no statistician, the effect appears to be strong. The coefficient of correlation between table size and that table's weighted-average slope is -0.9, or a strong inverse correlation. In fact, when I exclude heads up play from the calculation, I get a R squared of -0.97, or a nearly perfect inverse relationship between table size and slope.
[img]/images/graemlins/spade.gif[/img] Third, the effect of position is not the same for all hands. It appears that position is more powerful for ok hands than for great hands. To illustrate this, let's look at pocket pairs. The slope for AA at a full table is 3.0% while at a 3-handed table it's about the same at 4.0%. However, the effect of position is stronger for mid- and low pocket pairs. For example, the slope of 99 at a full table is 0.8% while at a 3-handed table it's much steeper at 8.0%. Similarly, the slope of 22 at a full table is 0.8% while at a 3-handed table it's 7.0%. This observation would appear to confirm the common-sense view that mid- and low pocket pairs improve as players get knocked out.
[img]/images/graemlins/spade.gif[/img] Fourth, position is less powerful heads up than 3-handed. As noted above, the weighted-average slope for all hands is 8.2% at a 3-handed table, but only 6.4% heads up. I found the same effect for pocket pairs. The average slope of pocket pairs generally increases from 1.8% at a full table to 6.3% in 3-way play, but drops down to 1.4% when it's heads-up. I have some guesses of my own, but invite any speculation as to why position is less important when it's heads up.
I may have some more observations as I play around with the data. If anyone wants to take a look at my work in progress, PM me your email address and I'll email you my spreadsheet.
The Shadow (who knows what cards lurk in a player's hands)