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