Let's use the probability that half the time they'll have trips/boat and half the time they'll have pairs or missed flushes or high cards. And we'll assume when they have trips/boats you'll call a $35 bet on the river, and when they have missed flushes or medium/small pairs they'll check it down and won't bluff (I honestly don't think either of them will have the courage to bluff into two opponents who've called down to the river).
50% of the time you'll put in $10 and win $70 which is +$35. 50% of the time you'll put in $10 + $35 and lose $45 which is -$22.5. So calling on the turn has +$12.5 EV.
It's not quite that simple but I think you have the right idea. You aren't considering river action here. If it were $10 for a guaranteed showdown then yeah I think all of us call all day long. I'm pretty sure we will win more than once every eight cracks at this. But that isn't the case.
I also think 50% is too much but we can quibble on this all day. I don't think anyone in this thread will disagree that there is indeed a significant chance that we do indeed have the best hand but there is a significant and I think I would argue at these limits greater chance at least one of them will have us beat. I seriously doubt they both have us beat. I would have a very hard time at putting our odds of having the best hand right now at
any less that 25%. It's probably higher. So...
Case 1A: We are up against TJ/77/22 and AsQs. We call and a blank falls. I agree with paulson and others...we are by no means obligated to call a river bet because we called a turn bet. We check..the TJ will bet confident of having best hand since flush was avoided, flush draw goes away. Do we call this? Probably not because I doubt he's going to bet very small. If he does bet small I think we have to look him up. Why? Because the odds he has 88/99/JJ/QQ/A7 are too high. We lose the $10 bet + whatever he bet on the river (say $20-$40). You can't tell me that with this action a JJ/QQ isn't going to have reason to think they have the best hand.
Case 1B: Up against the same two hands but a spade falls.. Well in this case we will probably see a bet and a raise and possibly a reraise. Very easy fold, river costs us nothing.
Case 2A: We are up against some combination of UI pp's and flush draws. A non spade falls that doesn't set anybody, we probably just see a check down and we win the pot.
Case 2B: Same as above except either a spade falls or someone makes a miracle boat (or both). We check and fold to the action that ensues.
Case 3: An Ace falls. If we are up against any good hands T/boat/or made flush.. we could stack one OR BOTH of them. Small chance but the reward is so huge it has to be considered.
So..all this has been said in one way or another already. I think the pot odds + the significant possibility we are actually ahead here make this call worth it. Saying if we call this we are obligated to call a river bet is not true imo. If I call this and a blank comes on the turn AND one of them bets small yes I will feel obligated to call. If one of them bets and another raises or one bets huge and another folds then you can go ahead and muck it and it only costs $10. If you spike the ace you could win a gigantic pot.
Personally (been thinking about this one a bunch since yesterday) I'm wondering if you should have checked the turn. Checking the turn + the action that followed gave you no useful information and looks a whole lot like you have AK encouraging lesser hands to act with more confidence.
I still don't mind the fold but I like it less as I think about it more. I think I dislike the turn check more... A JJ/QQ type hand is really encouraged by the check and would be extremely cautious with another bet. OTOH someone slowplaying the T or boat would want us to bet it so maybe checking is best. If we bet out though and are just flat called twice again we could check fold the river cheaper than calling $10 + calling the river bet of one of these hands and that wouldn't encourage the JJ/QQ types to bet out on the turn thinking you have AK I guess is my thinking.
I think I'm trying to convince myself that calling is the right move as well here. I'm really on the fence on this one.
/wow this post ended up long