KQs vs. ATo

[private joker]

My friend was playing 4/8 in New York last night and an interesting argument came up. My friend (he'll be Hero for this example) had KQs in the BB, and a late position player (Villain) open-raised. Could be a blind steal, could not be. Hero called the raise along with a third player (not sure if it was button or SB, but it's not relevant in the following calculations). Villain turned out to have ATo. After the hand (which Villain won), Villain scolded Hero for playing KQs against a raise, and Hero responded that it was a good hand against an obvious blind-steal, and it turned out that indeed, KQs is a favorite over ATo in a 3-handed pot.

Wha?! It's true. Heads-up, obviously we all know ace-high is better than king-high, and indeed Hero would be a 56-44 dog if it were HU. But the point of this post is to show how drastically situations change once that third player is in the pot. I came up with these calculations PF:

K /images/graemlins/spade.gif Q /images/graemlins/spade.gif: 37.7%
A /images/graemlins/heart.gif T /images/graemlins/diamond.gif: 30.4%
8 /images/graemlins/club.gif 8 /images/graemlins/heart.gif: 31.8%


K /images/graemlins/spade.gif Q /images/graemlins/spade.gif: 37.1%
A /images/graemlins/heart.gif T /images/graemlins/diamond.gif: 31.6%
J /images/graemlins/club.gif 9 /images/graemlins/club.gif: 28.4%


K /images/graemlins/spade.gif Q /images/graemlins/spade.gif: 35.2%
A /images/graemlins/spade.gif T /images/graemlins/diamond.gif: 35.6%
9 /images/graemlins/club.gif 8 /images/graemlins/club.gif: 29.2%


K /images/graemlins/spade.gif Q /images/graemlins/spade.gif: 35.7%
A /images/graemlins/spade.gif T /images/graemlins/diamond.gif: 32.3%
5 /images/graemlins/club.gif 5 /images/graemlins/heart.gif: 32.1%


K /images/graemlins/spade.gif Q /images/graemlins/spade.gif: 28.9%
A /images/graemlins/heart.gif T /images/graemlins/diamond.gif: 20.7%
A /images/graemlins/spade.gif Q /images/graemlins/heart.gif: 50.5%


Wow. So in virtually every case, Hero is ahead of Villain. Even when Villain's ace is Hero's suit, Hero is only at a slight disadvantage when player 3 has two live undercards -- but when player 3 has a pocket pair, Hero is a small favorite over Villain even when Villain has the A /images/graemlins/spade.gif.

Even more fascinating is that when they are both dominated (I gave player 3 AQo in the last example), Hero stands up far better against domination than Villain -- and that's with the A /images/graemlins/spade.gif in the dominator's hand!

All of this to show that Sklansky is right to put KQs in Group 2 and ATo in Group 6. But I thought it was worth pointing out (and pardon me if HUSH is the wrong forum) that although you want ace-high over KQ when it's heads-up, add a third player in the mix and you do not want ATo against KQs.

[Entity]

Though I'd probably rather have KQs in a lot of scenarios than ATo, it actually isn't a favorite overall against ATo in a 3-handed pot, from what I can see:

Hand 1: 22.4061 % [ 00.22 00.01 ] { random }
Hand 2: 39.3824 % [ 00.39 00.01 ] { ATo }
Hand 3: 38.2115 % [ 00.38 00.00 ] { KQs }

[private joker]

[ QUOTE ]
Though I'd probably rather have KQs in a lot of scenarios than ATo, it actually isn't a favorite overall against ATo in a 3-handed pot, from what I can see:

Hand 1: 22.4061 % [ 00.22 00.01 ] { random }
Hand 2: 39.3824 % [ 00.39 00.01 ] { ATo }
Hand 3: 38.2115 % [ 00.38 00.00 ] { KQs }

[/ QUOTE ]

But why assume it's a random hand? Against a raise, I put player 3 on a range of hands and put that range into my calculations. Player 3 isn't going to enter with 24o or J3s. Pretend he's a reasonable human being in the real world, and play it out with small pocket pairs, suited connectors, etc.

[Entity]

[ QUOTE ]
[ QUOTE ]
Though I'd probably rather have KQs in a lot of scenarios than ATo, it actually isn't a favorite overall against ATo in a 3-handed pot, from what I can see:

Hand 1: 22.4061 % [ 00.22 00.01 ] { random }
Hand 2: 39.3824 % [ 00.39 00.01 ] { ATo }
Hand 3: 38.2115 % [ 00.38 00.00 ] { KQs }

[/ QUOTE ]

But why assume it's a random hand? Against a raise, I put player 3 on a range of hands and put that range into my calculations. Player 3 isn't going to enter with 24o or J3s. Pretend he's a reasonable human being in the real world, and play it out with small pocket pairs, suited connectors, etc.

[/ QUOTE ]
I know. You were just stating that as a blanket statement, KQs is better than ATo in a 3-way pot. I was saying that it isn't, but it's about dead even.

Here's another run:

Hand 1: 30.2158 % [ 00.27 00.03 ] { AA-66, AKs-ATs, KQs-KTs, QJs-QTs, JTs, AKo-ATo, KQo-KTo, QJo-QTo, JTo }
Hand 2: 35.5993 % [ 00.33 00.02 ] { ATo }
Hand 3: 34.1849 % [ 00.33 00.01 ] { KQs }

[private joker]

[ QUOTE ]


Here's another run:

Hand 1: 30.2158 % [ 00.27 00.03 ] { AA-66, AKs-ATs, KQs-KTs, QJs-QTs, JTs, AKo-ATo, KQo-KTo, QJo-QTo, JTo }
Hand 2: 35.5993 % [ 00.33 00.02 ] { ATo }
Hand 3: 34.1849 % [ 00.33 00.01 ] { KQs }

[/ QUOTE ]

Yikes. This does change my mind. So why is this a Group 2 vs. Group 6 situation? Because in a full game KQs is better?

I still agree with Hero's call from the BB against a probable blind steal. There are far worse hands than ATo that LP could be stealing with (QJs, for example, which Hero dominates). The flop in this hand, BTW, was T9x, giving Hero overcards and a gutshot, so the line went bet-call, bet-call, check-check. When Villain ended up winning with flopped top pair, he got mad that Hero forced him to play it so passively. That's his problem, baby.

[private joker]

For the record, I made a mistake. Hero had actually 3-bet his KQs from the BB, which is why Villain slowed down with his ATo.