Donkey Test

[JPajamas]

I know the answer should be 88, you all seem to agree with me, BUT, now here's where the DONKEY part of the test comes in...88 isn't the "correct" answer, which makes me leery of some of the other choices that are theoretically correct. If someone can justify AK, please do so...

[JPajamas]

Wait till we get to THIS ONE!....whoooboy!

[thoman8r]

[ QUOTE ]
I know the answer should be 88, you all seem to agree with me, BUT, now here's where the DONKEY part of the test comes in...88 isn't the "correct" answer, which makes me leery of some of the other choices that are theoretically correct. If someone can justify AK, please do so...

[/ QUOTE ]

I was the one who picked AK, and here is my reasoning.

If we are called, we are very likely to be behind no matter which of those 4 hands we have. Therefore, we want the hand that has the most equity against villain's range.

Poker Stove results:

Text results appended to pokerstove.txt

2,613,600 games 0.031 secs 84,309,677 games/sec

Board: Ts 6d 2c
Dead:

equity win tie pots won pots tied
Hand 0: 20.849% 20.85% 00.00% 544900 0.00 { QJs, QJo }
Hand 1: 79.151% 79.15% 00.00% 2068700 0.00 { 99+, 66, 22, ATs, KTs, QTs, JTs, T2s+, ATo, KTo, QTo, JTo, T2o+ }


---

2,613,600 games 0.016 secs 163,350,000 games/sec

Board: Ts 6d 2c
Dead:

equity win tie pots won pots tied
Hand 0: 11.600% 11.54% 00.06% 301670 1506.00 { A9s, A9o }
Hand 1: 88.400% 88.34% 00.06% 2308918 1506.00 { 99+, 66, 22, ATs, KTs, QTs, JTs, T2s+, ATo, KTo, QTo, JTo, T2o+ }


---

1,015,740 games 0.005 secs 203,148,000 games/sec

Board: Ts 6d 2c
Dead:

equity win tie pots won pots tied
Hand 0: 09.676% 09.65% 00.03% 97998 285.00 { 88 }
Hand 1: 90.324% 90.30% 00.03% 917172 285.00 { 99+, 66, 22, ATs, KTs, QTs, JTs, T2s+, ATo, KTo, QTo, JTo, T2o+ }


---

2,613,600 games 0.062 secs 42,154,838 games/sec

Board: Ts 6d 2c
Dead:

equity win tie pots won pots tied
Hand 0: 19.512% 19.51% 00.00% 509975 0.00 { AKs, AKo }
Hand 1: 80.488% 80.49% 00.00% 2103625 0.00 { 99+, 66, 22, ATs, KTs, QTs, JTs, T2s+, ATo, KTo, QTo, JTo, T2o+ }


---

So as you can see it's pretty close between AK and QJ. However, if villain is capable of calling you without a pair (possible given your history and the ragged board), and include hands such as AJ+ in his range, AK is clearly the best choice.

2,744,280 games 0.031 secs 88,525,161 games/sec

Board: Ts 6d 2c
Dead:

equity win tie pots won pots tied
Hand 0: 22.111% 21.45% 00.67% 588518 18261.00 { AKs, AKo }
Hand 1: 77.889% 77.22% 00.67% 2119240 18261.00 { 99+, 66, 22, ATs+, KTs, QTs, JTs, T2s+, ATo, KTo, QTo, JTo, T2o+ }

---

1,087,020 games 0.016 secs 67,938,750 games/sec

Board: Ts 6d 2c
Dead:

equity win tie pots won pots tied
Hand 0: 13.732% 13.71% 00.03% 148983 285.00 { 88 }
Hand 1: 86.268% 86.24% 00.03% 937467 285.00 { 99+, 66, 22, ATs+, KTs, QTs, JTs, T2s+, ATo, KTo, QTo, JTo, T2o+ }


---

2,772,000 games 0.031 secs 89,419,354 games/sec

Board: Ts 6d 2c
Dead:

equity win tie pots won pots tied
Hand 0: 20.738% 20.74% 00.00% 574851 0.00 { QJs, QJo }
Hand 1: 79.262% 79.26% 00.00% 2197149 0.00 { 99+, 66, 22, ATs+, KTs, QTs, JTs, T2s+, ATo, KTo, QTo, JTo, T2o+ }

[OrangeKing]

[ QUOTE ]
I know the answer should be 88, you all seem to agree with me, BUT, now here's where the DONKEY part of the test comes in...88 isn't the "correct" answer, which makes me leery of some of the other choices that are theoretically correct. If someone can justify AK, please do so...

[/ QUOTE ]

AK or QJ are both better if your all-in bet is called. If you move all-in, do you expect a skilled player to call you with anything less than top pair? If so, how often do you expect to improve with 88 to suck out?

AK and QJ both have 6 outs against a modest hand, while 88 has 2. QJ also has the backdoor straight draw and is slightly less likely to be dominated. I think AK and QJ is an interesting decision, but 88 is clearly wrong, as demonstrated in the post above.

[ QUOTE ]
pretty much, he could be holding any random cards.

[/ QUOTE ]

However, the key is that the hands he will call you with are NOT random. If he folds, we don't care what we have.

[crashzzz]

I guess I have to revise my answer...

let's see. The villain is loose-aggressive, so it doesn't mean he has a top pair because of his c-bet. So you can put him in the top 21% of hand with his raise pre-flop. He may be loose, but I doubt he's wild enough to raise PF with 2-6, T6, or T2

Board: 2c 6d Ts
Dead:

equity win tie pots won pots tied
Hand 0: 50.907% 50.68% 00.22% 713499 3153.00 { 88 }
Hand 1: 49.093% 48.87% 00.22% 687975 3153.00 { 66+, A4s+, K8s+, Q9s+, J9s+, T9s, A9o+, KTo+, QTo+, JTo }

Hand 0: 53.098% 50.57% 02.53% 1604000 80235.00 { AKs, AKo }
Hand 1: 46.902% 44.37% 02.53% 1407490 80235.00 { 66+, A4s+, K8s+, Q9s+, J9s+, T9s, A9o+, KTo+, QTo+, JTo }

Hand 0: 23.760% 21.62% 02.14% 715903 70690.50 { QJs, QJo }
Hand 1: 76.240% 74.10% 02.14% 2453276 70690.50 { 66+, A4s+, K8s+, Q9s+, J9s+, T9s, A9o+, KTo+, QTo+, JTo

Hand 0: 36.901% 34.19% 02.71% 1134678 89890.00 { A9s, A9o }
Hand 1: 63.099% 60.39% 02.71% 2004022 89890.00 { 66+, A4s+, K8s+, Q9s+, J9s+, T9s, A9o+, KTo+, QTo+, JTo }

Hence, re-evaluating our situation, indeed, holding AK would hold a slight advantage in equity over pocket 8s.

[JPajamas]

Thanks, at least now I can see why AK would be a viable answer...well done!

[gedanken]

whoa, this didn't even seem tough. IF CALLED we're going to want the big guns, (not those 88s!).

Plus, we haven't invested $40, we paid $130 when he 3bet us. Pay attention, ya donkey Pot is $460, and worth bluffing at.

QJ is a little interesting, but runner-runner straights don't add much value, and AK has half a chance to hit one anyway. Plus, whatever he calls with, our AK will have higher high-card value than his hand, and that's the only consideration, I think. We're just as likely to run into JT as AT, so reverse-domination isn't a factor.

[ QUOTE ]
AK and QJ both have 6 outs against a modest hand, while 88 has 2

[/ QUOTE ]
this is precisely what I'm thinking.

edit: JP, easy there on giving out the "answers." 9am-1:15pm is not long enough for me to get to look at things! (especially after a long holiday in the thread) Lucky for my confidence I missed your giveaway until after writing this.

[willyc]

[ QUOTE ]

QJ is a little interesting, but runner-runner straights don't add much value [...]


[/ QUOTE ]

When you factor in the backdoors straight possibilities (1.5 outs for QJ, 0.5 outs for AK), QJ is about 15% more likely than AK to improve to a hand that beats a pair of tens (7.5 outs vs 6.5), which I think is significant.

Edit: By 15% more likely I mean QJ has about a 32% chance to improve and AK has about a 28% chance, and 32/28 ~ 1.15.

The chances to win for each hand are smaller than the chances to improve because of redraws/reverse domination possibilities, but I still think QJ is better than AK.

[DWarrior]

Yeah, AK is the best answer. You're guaranteed to have 2 outs with 88 if called, AK has 6 outs over most hands. Also, AK takes 1 A and 1 K out of the deck, which gives him less chance to have AT, AA, AK, KT.

[Davdob]

This was a fun exercise. I would love to see the "key"