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One of my students was practicing at the super-low stakes online games, and he came across a hand that ended up a lot more interesting than it seemed on face value. I have my own conclusions that I'll post later, but I'd like to hear your thoughts the hand first.

SB: Player9 ( $4.78 )
BB: Player1 ( $4.00 )
UTG: Hero ( $8.11 ) - VPIP 13, PFR: 10, 3B: 7.7, AF: 1.5
UTG+1: Player3 ( $4.60 )
MP1: Player4 ( $3.91 )
MP2: Player5 ( $3.00 )
MP3: Player6 ( $4.06 )
CO: Player7 ( $4.13 )
BU: Player8 ( $8.79 ) - VPIP: 12, PFR: 8, 3B: 1, AF: 7, Hands: 266

Player9 posts small blind $0.02
Player1 posts big blind $0.04

Dealt to Hero Q⋄ Q♠
Hero raises $0.14
3 folds
Player8 calls $0.14
2 folds

Flop: 7⋄ 2⋄ 8♣
Hero bets $0.25
Player8 calls $0.25

Turn: 7⋄ 2⋄ 8♣ 6⋄
Hero checks
Player8 bets $0.84
Hero calls $0.84

River 7⋄ 2⋄ 8♣ 6⋄ K♠
Hero checks
Player8 bets $1.26
Hero?

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Do we have a Spoiler tag like Gaming SE? I'd like to know what our Hero did, and what the result was, including the villains cards! –  Al G May 4 '12 at 16:23
    
@AlG: Hero ended up timing out trying to decide what he could beat on a board that looks so ugly at face-value. –  Jeffrey Blake May 4 '12 at 18:11
    
The board is not really wet... just saying... –  Radu Murzea May 5 '12 at 10:15
    
There are straight draws and flush draws and both get there. That's starting out wet and then turning into a flood.. –  Jeffrey Blake May 5 '12 at 12:49
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3 Answers 3

Assuming the opponent is a competent player, hero is over 200bb deep with this guy thus, I would imagine that the villain calling range is somewhat wider than at first glance.

I'd think this would include all pairs (22-QQ, 3-betting KK+), almost all suited connectors (23s-KQs, 3-betting AKs), some S1C's (46s-AQs), perhaps some S2C's (K9s, Q9s), quite a few Axs. Probably around 16% of hands call preflop, occasionally including some of the 3-betting range.

IMO, flop play is standard although it's likely I'll c-bet closer to $0.30. I disagree with the turn check as more often than not, I'd bet again, for value. Depending on my knowledge of this players tendencies to use various cards to bluff with (knowing he's an aggro AF: 7) if I felt it was more likely that he'd bluff or thin-value bet two streets with a worse hand rather than check-back or raise my turn c-bet, then I'd often check-call.

I'd call a turn bet or raise (depending on my own action of course) and most often bet-decide river or less often c/c a river bet on an uncoordinated card. It would be very important to me to know whether this player was capable of thin value betting/bluff-raising as I'd put a lot of significance on that info when deciding to call turn or river bets.

Missing the turn c-bet has obscured villains range somewhat and makes heros decision much harder IMO.

The types of 2 pairs available are few as only 8♠7♠, 8♥7♥ or 8♠6♠, 8♥6♥ or 7♠6♠, 7♥6♥ are possible. Only 6 combos. Sets are of course possible, but given this guys AF I'd assume he'd play them much stronger, earlier. A total of 12 combos but I'm discounting them. That leaves straights and flushes. 5♠4♠, 5♥4♥, or T♠9♠, T♥9♥. I'm discounting 95x almost entirely. Just 4 combos, and maybe 10 combos or so of likely flushes. Obviously he might have spiked a Kx. Again, I'd need to have a read on his thin value betting tendencies to predict his actions on that river card.

Getting to a possible showdown this way, I call.

Putting it all together... heros turn check, added to villains aggression keeps the opponents range wide enough to have a lot of bluffs in it. Well over the 30 or so value hands villain has (or so I believe!). You're not repping a flush, nor the Kx, which incidentally is a good card for him to bluff. Thus, you look weak, he is aggressive. Your pot odds are around 3:1 if I added correctly. GTO wise, I'd say hero is well within the top 75% of hands he gets to river with in this way accounting for pot odds. If you fold you're exploitable, and if you call you have to win about 25% of the time to breakeven. I'd say hero likely has favourable odds. Again, I call.

I can't say what I'd do in other scenarios as we didn't play it those ways.

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You and I have very different reasoning, but reached the same conclusion about every single street. Fascinating. –  Jeffrey Blake May 4 '12 at 1:39
    
I like that you're distrustful of stats. I think you might have gone a bit overboard on what hands to include for a player playing as tight as we see here, but on the other hand, I think I took it too much at face value. The one other criticism I have here is the assumption that a player at $0.02/$0.04 is a competent player able to adjust to deep stack dynamics. I have no doubt that this is absolutely not the case for 99% of the players playing below $0.10/$0.25 online. –  Jeffrey Blake May 4 '12 at 14:08
    
I actually agree that it's almost certain to be wrong to assume villain is competent, but if I don't make that point, I can't run an analysis. Decisions inferred from random data don't work so well ;) –  Toby Booth May 4 '12 at 14:56
    
I disagree that players this low aren't competent these days; seems like the .02/.04 players from today are the .10/.25 players from 3 years ago, who are the 1/2-3/6 players from a few years before that. Running 12/8 are pretty solid stats for full ring, if a little nitty, and that leads me to believe he's good enough to at least notice deep stacks and his position. –  Cory Kendall May 5 '12 at 22:12
    
I'm also not sure how the AF is calculated these days; I had thought the old algorithm was (bet or raise)/(call), which doesn't include folding, which means that we can't take it to mean "he always raises therefor he bluffs", we can only take it to mean "he raises rather than calling, therefor he plays draws quickly or not at all". But I may be dated on this stat. –  Cory Kendall May 5 '12 at 22:18
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Here's my thinking:

Villain is likely to 3-bet preflop with KK+. I think the right process for evaluating this hand is to decide what hands Villain could have here that make sense. So let's start with preflop and narrow down from there.

At 12/8, we know his average range does not include T9s. Specifically, 12/8 looks something like:

Plays: AA-22; AJ+, ATs+, KJ+, KJs+
Raises: 66+; AJ+; AJs+

Even if he opens his range up on the button when there is no raise in front of him, a player this tight is probably calling raises with a range similar to the 8% he is raising with. Possibly include all pairs. Possibly remove AJ/AJs.

I do not believe there are any hands in his range that make the straight. His flush potential comes from AJs, AQs, AKs, and rarely KQs, KJs. He could also have quite a few pocket pairs here. If we think there is a 50% chance that he 3-bets AA/KK, then we can include one and leave the other out. That leaves us with pocket pairs 22-KK (however since there is only one combo of QQ, we can remove it as unlikely enough to be irrelevant).

Our play on the flop is standard, though the bet is a touch on the small side. He is definitely continuing on the flop with 22, 77, 88, 99, TT, JJ, and KK. He is also probably continuing with the suited hands that hit a flush draw. I do not believe a tight player is continuing with a pair lower than 77 on this board against a tight UTG opener.

Thus, on the turn, we beat 99, TT, JJ and we lose to 22, 77, 88, KK, and any of the suited hands that he continued with on the flop. Note that AQs and KQs are out of his range now, since we hold Qd. Perhaps surprisingly, we have 57.5% equity on the turn, in large part due to our 4-flush to the Qd:

Board: 8s 7d 2d 6d

equity win tie pots won pots tied
Hand 0: 42.472% 42.47% 00.00% 598 0.00 { KK, JJ-77, AdKd, AdJd }
Hand 1: 57.528% 57.53% 00.00% 810 0.00 { QdQh }

With that in mind, I think betting the turn is the best play. If we did not have the Qd, it's a bit closer, but we still have 43.5%, so we should probably bet even then. Once we check the turn, we absolutely have to call his bet.

On the river, things are a bit different. But the fact that there are so few hands in his range means that we are still getting good odds to call a bet, even knowing that we only beat JJ, TT, and 99. Even if he only bets JJ in that range, plus the hands that beat us, JJ by itself accounts for enough hands in his range to make a call +EV based on the pot odds:

Board: 8s 7d 2d 6d Kh

equity win tie pots won pots tied
Hand 0: 64.706% 64.71% 00.00% 11 0.00 { KK, JJ, 88-77, AdKd, AdQd, AdJd }
Hand 1: 35.294% 35.29% 00.00% 6 0.00 { QdQs }

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I'm surprised at your preflop range; I wouldn't think it would be so top-heavy given stacks and both players positions. Possible though you are going off the fact that he is too inept an opponent to notice. –  Cory Kendall May 5 '12 at 22:14
    
My range is based on the stakes and the stats we have on how this opponent is playing. Players at this level are not adjusting their ranges based on stack sizes. Ever. His range could be wider on the button, but probably not by much - the super-low stakes online full ring games tend to lead tight players to play very tight vs a raise, and that's actually pretty profitable for them. –  Jeffrey Blake May 6 '12 at 0:11
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Hmm, seems like it's been too long since playing real money online (USA), and I'm overestimating the player. Carry on... –  Cory Kendall May 6 '12 at 4:51
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Grunch, aka I didn't read other responses.

Fold turn, 100% fold river. Why would you hero call in a full ring game with this river betsize, against this opponent? He's not floating the flop to make any of the draws which show up on the turn. His AF says he bets or raises rather than calling, it says nothing about the frequency he bets in relationship to folding. I don't think a penny-stakes opponent is meta enough at penny stakes to value bet an 8 on the turn and then turn it into a bluff when you don't bluff the river OOP on the overcard. He's valuing something here, fold.

EDIT: Apologies for my brief and direct response, I'm a little new to this site.

Preflop I take his 3B stat with a grain of salt due to small sample size. All I take from it is "he 3B less than usual". So I put his preflop flatting range from the button to something like 45s-KQs, 8Ts-AQs, A9s+, 78o-KQo, 22+, and a few random hands because it's penny stakes. This is ~15%+ of hands, which seems accurate. In a positionless vacuum we see 12 VPIP and 8PFR, and here I think villain should be flatting more like 30%+ given stacks, how transparent your range is, and the perceived huge IO you're offering, but because this is penny stakes and I don't give villain much credit, I expand his range slightly toward optimal play.

Flop I narrow that range to fully counted 56, 9T, 89, Axdd, discounted 77, 88, 78 (too deep play to be playing your perceived range correctly and flatting, he would probably just raise considering his AF), and discounted air (he could attempting to float+fire, but he shouldn't be doing this 100% of the time, nor against such a strong perceived range, thus I'm discounting). Of course air is also discounted against this player until we confirm he's really putting the pressure on positionally.

Turn his bet lines up nicely with all of his made hands, which seems to be the majority of his range, and push out almost all of his week hands, as I can't see him suddenly going full pot value with his "made" hands that beat you: 89/8T? A8s maybe? I'm not going to go as deep as combinatorics here, because I don't think it's necessary. His position advantage and deepness of stacks while you hold a reverse implied odds hand (and a mediocre one at that, an overpair) with a small sample size and no history against the opponent says fold to me. I would rather wait for information than battle OOP with a mediocre hand while there is another street and plenty of money to go. Plus I can't come up with a valid plan for the river. I can't hope to spike a diamond because I won't make any money on a 4 diamond board, and that won't happen that often. When the diamond misses, I'm OOP and at my opponents mercy, the same place I was on the turn but with a now bloated pot. I say lick your very minor wounds OOP and make your money in position.

Assuming you do call and get to the river, you are probably planning on calling his river bet, because I can't see another valid river plan you could have formed on the turn (other than praying for diamond or check behind). All of his made hands bet again for value (he's not afraid of the flush with his straight or set/2pair because it's penny stakes, and your top heavy range rarely has AKdd/AQdd/KQdd (3 combos) to your AA/KK/QQ/JJ (24 combos). He IS afraid with his hands he MAY value on the turn (though I doubt it, as stated above) that you beat (like the A8 or 8T), because now there's a king and he would probably just check behind for showdown value.

EDIT 2: Now I will go read other responses.

EDIT 3: Seems like I left out a significant portion of his range which may also play this way: 99-JJ. I think I would still fold on the turn given this, but only because of the positional advantage. Though this does give more credence to the "call with the plan of praying for a check behind" as opponent would do with 99-JJ and often check behind because the average competent opponent at this level isn't thin value betting most rivers given the board. However if that was your plan, the river fell and the villain bet (as what had happened), I would then feel happy about folding the river.

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Both my student and I agree that villain is not bluffing. However, that doesn't make this a fold. What hands is villain playing that he can bet for value? How do we stack up against those hands? –  Jeffrey Blake May 5 '12 at 12:52
    
Small point, but that's actually 19% of hands, not 15%. Position might make villain call wider than I allotted for in my answer, but it's not going to make him open up this much, especially against an early-position opener. Should it? Absolutely, especially given stack sizes. But thinking that an opponent at the lowest stakes will make that adjustment is a really bad assumption. –  Jeffrey Blake May 6 '12 at 0:18
    
Hmm, it appears I'm out of touch with players at this limit. –  Cory Kendall May 6 '12 at 4:52
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