Top pair and 4th pair on dangerous river
 

Button is 55/9/0.8 over 45 hands, MP2 is 49/8/1.6 over 61 hands, and SB is 59/0/0.5 over 17 hands.

I need a sanity check on my play, because I've been making a lot of wrong moves in similar situations lately.

Paradise Poker 2/4 Hold'em (9 handed) converter

Preflop: Hero is CO with A[img]/images/graemlins/diamond.gif[/img], T[img]/images/graemlins/heart.gif[/img].
<font color="#666666">3 folds</font>, MP2 calls, <font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises</font>, Button calls, SB calls, <font color="#666666">1 fold</font>, MP2 calls.

Flop: (9 SB) J[img]/images/graemlins/diamond.gif[/img], T[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(4 players)</font>
SB checks, MP2 checks, <font color="#CC3333">Hero bets</font>, Button calls, SB calls, MP2 calls.

Turn: (6.50 BB) 8[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(4 players)</font>
SB checks, MP2 checks, Hero checks, <font color="#CC3333">Button bets</font>, SB folds, MP2 folds, Hero calls.

River: (8.50 BB) A[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">Button bets</font>, Hero calls.

Final Pot: 10.50 BB

I don't like my flop bet. I don't figure to be ahead, and opps will have at least 10:1 odds here. Not sure that there's anything to accomplish by a bet.

In some ways it's easier to start with the river call than the turn check/call. Here's my thinking: Button is very loose, and would call but not 3 bet, preflop, and then bet the turn, with any of these hands:
Hand Ways
AQ 8 (2 As X 4 Qs)
AJ 6 (2 As X 3 Js)
AT 4 etc.
KQ 12
KJ 9
KT 9
QJ 12
QTs 3
JJ 6 maybe should discount, might 3-bet preflop
JT 6
TT 1
99 2 heavily discounted for calling flop, betting river
88 3 50% discount for calling flop
This adds up to 81. Of these, I'm ahead only against KJ KT JT, totaling 24. So I've got a bit worse than 3:1 odds against me, but am getting 9.5:1 to call. This gives me plenty of leeway, even if my estimates of button's play is significantly off.

On the turn, I didn't like my prospects at all after all 3 opps peeled the flop. As for my call of button's bet, I think that's close, but correct. I need about 5 1/2 outs with 7.5:1 odds. There are superficially 9 (3As, 4Qs, 2Ts) but discounting is needed. The river analysis above indicates that if an A comes on the river I'm only winning about 1/4 of the time (81:24 against), so I'm only counting the 3A outs as 0.7 outs. If a Q comes I'm splitting the pot to AQ AJ AT (18 times) so the 4 Q outs are factored by (81-18)/81 leaving 3.1 outs. A T wins against all but JJ, so I count that as 2 full outs. This adds up to 5.8 outs, which is enough to call with, but only marginally +EV.

Does this reasoning seem okay? Should I consider button's mild postflop passivity more? At the table of course I didn't go through all this calculation, and frankly on the turn I didn't see the problem with my A outs until one actually hit on the river. Hole-pokers appreciated.

Re: Top pair and 4th pair on dangerous river
 

I agree with your assessment of the flop. THere are really no hands you want to fold that would conceivably fold, except MAYbe for a weak jack. Except even those aren't a problem since you aren't really planning on seeing a showdown UI.

The turn call is pretty marginal. With maybe 1 ace out, 3 queen outs, and 2 ten outs (give or take an out or two on each count) you're just barely getting the odds to call, and I don't think implied odds are working in your favor. Button's not passive, but I'd still be more inclined to go further in the hand if he was a little bit more aggressive.

Once you get to the river though, I definltey think this is a donk/fold. You're probably losing this pot more than 50% of the time, but he'll call a bet from you with a worse hand a lot more often than he'll check through a better hand.

Re: Top pair and 4th pair on dangerous river
 

Check the flop and pray for a free card.

As played, fold the turn.

Re: Top pair and 4th pair on dangerous river
 

Thanks for the help. The river donk hadn't occurred to me at all. At the table, I was sick as I realized how bad a position hitting my A had left me in.