Position, position, position (long)

[the shadow]

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)

[BradleyT]

The PokerRoom data is probably correct - Ed Miller references it in SSHE to derive some of his starting hand charts (along with his own stats of course).

Edit - that doesn't necessarily mean it's applicable to A) NL B) Tournaments like you stated.

I don't think some of the numbers correlate very well. In limit, 22 is an easy fold on the button after a tight players UTG raise because the implied odds aren't there. In a SnG if the raise was small and the implied odds were there this is usually a call.

[eastbay]

Isn't that data for limit?

eastbay

[the shadow]

Yes. As I noted,

[ QUOTE ]
A few caveats are worth mentioning. . . . 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.

[/ QUOTE ]

Please let me know if you know of any EV data for no limit games, esp. SNGs or other tourneys.

[SuitedSixes]

Don't you ever post anything non-useful?

[vindikation]

Wow great post THANKS!

[the shadow]

Position appears to be most important in three-way play. As my OP above notes, the slope (which measures the power of position on a hand's strength) of a probability-weighted average of the PokerRoom EV stats for all hands is greater at a 3-handed table than at any other table size. The slope's 8.2% at a three-handed table. That's over 3.5 times as steep as at a 10-handed table.

If position is most important at a three-handed table, its effect should be the strongest on the button. Because position is so powerful in three-way play, there should be more hands that you might otherwise fold UTG, in MP, or even on the button at a larger table that become playable on the button once it's down to three players. To identify those hands, I ran the following screens on the PokerRoom EV stats for 3 players:

First, I looked at only those hands that have a positive EV on the button. That cut 169 possible hands down to 80 hands.

Second, I looked only at those hands that have a negative EV in the SB. That cut 80 hands down to 37 hands.

Third, I then looked only at those hands that had an EV >= 0.08 on the button. That cut 37 hands down to 16.

While any cut-off is arbitrary, I wanted to exclude hands that were negative EV in the SB and just barely positive EV UTG. For example, T8o is -0.16 in the SB, -0.10 in the BB, and only 0.01 on the button. I figure I won't get rich by playing T8o on the button three-handed, but, knowing me, will probably bust out.

To exclude marginally positive EV hands, I used 0.08 as my cut-off. I used 0.08 because it happens to be the same EV as 55 or A7s, which are two hands that I might play on the button at a full-table. I figure that if I'm willing to play xy on the button at a full table, I should be willing to play ab in the same position at a short-handed table, so long as its EV is the same or greater as xy's in the same position at a full table.

I took the 16 hands above that survived my 3 screens, added one hand, and came up with the following list of 17 hands:

A8
K9o + K7s + K5s + K4s + K3s
QTo + Q9s + Q8s
JTo + J9o + J8s
98s + 97s
87s
76s
44 (a/k/a "the Dali" [img]/images/graemlins/smile.gif[/img])

The one hand I added was Q9s. While it fell outside my screen because it is marginally positive EV in the SB (0.01), it fits in nicely between QTo and Q8s.

(Note that this list leaves out K6s. I'm not sure why, but K6s is an anomaly. On the button, the EV is 0.10 for K3s, 0.15 for K4s, 0.09 for K5s, and 0.15 for K7s, but only 0.03 for K6s. That could just be variance, but the EV of K6s is also lower in the SB than K5s or K7s. In the BB, K6s is -EV, while K5s and K7s are marginally +EV.)

So what exactly is this list? It's a set of hands that are -EV in the SB but more than marginally +EV on the button. In other words, it's a list of hands that you might otherwise fold that may worth playing in last position once you're in the money. As a group, you will be dealt one of these 17 hands about 8.3% of the time, or roughly 1 out of 12 times. The probability-weighted EV of these hands as a group is 0.13. By way of comparison, that's about the same EV as playing A8s in the SB (0.14) and a bit more than playing K9s in the SB (0.10).

Needless to say, it's not a complete list of all of the hands you might want to play on the button once you're in the money. It's just a list of hands that you might be folding that you might want to play on the button against two opponents.

I'd like to hear whether you think that this group of hands makes sense to play on the button three-handed and what your experience has been with them.

The Shadow

[eastbay]

I'm still confused about why you are discussing this in the SnG forum where almost everyone plays NL.

eastbay

[the shadow]

There's no publicly-available NL EV data I know about and you haven't pointed to any. My assumption is that looking at the limit EV data may give some useful info about NL play. My thinking is that position is probably more important in NL than limit. If so, then looking at the limit numbers may give a perhaps useful and maybe conservative starting point for the effect of position in NL.

Rather than simply dismissing this data because it's from limit tables (as I had noted in my OP), I'd be interested whether you think the observations from the limit EV data apply to NL. For example, the PokerRoom stats suggest that position becomes more powerful as table size decreases, and is greatest in three-way play. Do you agree or disagree that the same is true in NL?

As you often put it, "Discuss." [img]/images/graemlins/smile.gif[/img] I'm just trying to get a further discussion going of the effect of position.

[eastbay]

[ QUOTE ]
There's no publicly-available NL EV data I know about and you haven't pointed to any.

[/ QUOTE ]

It's quite irrelevant to the question of whether what you're trying to derive from the limit ring game data makes sense for NL SnG games.

I don't have much reason to believe it does, as tactics and strategy in limit ring and NL SnG are vastly different.

[ QUOTE ]

For example, the PokerRoom stats suggest that position becomes more powerful as table size decreases, and is greatest in three-way play. Do you agree or disagree that the same is true in NL?


[/ QUOTE ]

I don't know what "more powerful" means, or even how you are defining position, since in a NL tournament almost all action 3-way is preflop, so in many ways SB is "better position" than button 3-way in a SnG. Obviously this is completely different from a ring game where button acts last for 3 of 4 bettings rounds. There's no such advantage in a NL SnG. This is one of many reasons why I think the limit ring data is of dubious value for drawing conclusions for NL SnG.

Tread carefully, if at all.

eastbay