That is correct. So if we're good 54% of the time, we can call down.

What if we're good 53% of the time?

Fold turn, slightly EV-.

Great thread. This hand I was in recently vs a TAG reg is probably a great example of RIO in action since with the action I only really want to put one or two small bets in but there's a significant threat of a triple barrel shove by the river. http://forumserver.twoplustwo.com/17...ation-1509225/

OP what would your math have to say about this?

There is a relationship between your implied odds and your opponents' reverse implied odds (and between your reverse implied odds and their implied odds). RIO is not just villain-dependent, it's hero-dependent.

It's not just starting hands. Your implied odds go up when your opponents play worse post-flop. Your reverse implied odds go up when your opponents play better post-flop. They also go up when you play worse.

Sometimes, hands are trouble hands because you have post-flop leaks, not because you are playing too many hands. "Fold pre" is overly simplistic advice that isn't always completely correct. Of course, sometimes, it's absolutely correct for players who over-estimate their post-flop abilities.

Still reading through the thread but fantastic COTM. Thanks for the great OP and all the thoughtful responses.

So I'm finally coming to the end of this and my contribution will be brief for a few reasons.
1. I'm on my lunch break and anyone who reads my edit comments knows how I feel about my phone.
2. It's more in depth than I hope to go and I'm lazy.
3. I don't want to encourage anymore discussion that could jeapordize my position in the COTM run off.


Without going into any math:

Just about everyone overvalues their implied odds. It leads to playing OOP (see SB debates). It leads to really bad set mining. It leads to really bad drawing habits. The bad thing about it is that since you're not losing tons of money all at once you don't really understand just how fast you're leaking.

On the flip side. Just about everyone undervalues their reverse implied odds. It also leads to playing OOP too much. It leads to chasing non nutted draws and super crappy spots with one pair hands (see my last two weeks of play for reference).

If this thread even begins to get you to think about these spots when others aren't then it has done you a great service.

loool!

Sorry it's taken this long to reply. Lot of good replies in here.

I saw this hand when you posted it. I think the flop is a textbook case of RIO. For those that haven't looked at the thread, Hero has raised preflop with QJ and now Villain has led out on a flop of

Q77rb (Hero has a backdoor club draw)

The pot is 45 and Villain has bet 30.

What makes this a RIO spot is Hero's read that Villain is going to continue to fire on the turn, no matter what he has. This is a significant factor in the question of "how often do we have to be good here to call?" The answer is not 28.5% as our 5:2 pot odds would suggest, because we know there's at least one more bet coming. In fact, Hero says that he called and faced a $60 bet on the turn.

The thing is, we knew that a bet like this was coming when we called the flop. We didn't know the exact size, but we knew there was going to be a bet. So really, when we decide to call the flop with another bet coming, we can't fold the turn. The only logically consistent plays are to call both bets or fold the flop--otherwise we are just handing Villain an extra $30 before folding.

As far as the math goes, if we could somehow know that the turn bet would be $60, then really, with RIO, we aren't calling 30 to win 45 and then 60 to win 165--we're really calling 90 to win 135, which is odds of 3:2. So already we have to be good at least 40% of the time if we want to be able to justify calling the flop. Furthermore, this does not mention river action. If we don't know our opponent's tendencies on the river, this can get even worse!

The point of RIO is that you have to know, or at least have a good sense of, how the hand is going to go down before you put that flop call in. If you don't, you'll be stuck in spots where the fact that you put in dead money earlier means you're making marginal decisions to protect your dead money, and throwing good money after bad (or however that expression goes).

The only times it makes sense to fold turn after calling flop are:

1. We aren't sure whether Villain will bet again. In other words, we think Villain has enough hands we beat that he'll shut down on the turn with that it is OK to call one bet and fold to future action.

2. We realized in the middle of the hand that calling the flop was a mistake, and we're folding the turn so as not to compound that mistake.

Reason #1 actually leads me to this:

This (the underlined) is a statement that is very often true about a lot of situations in LLSNL. A lot of times people will bet a relatively weak range, then on future streets they'll shut down with the weak hands and continue betting the strong ones. As this happens, the strength of their hand rises with the size of the pot, and this creates the inverse relationship between the pot size and our hand equity.

What I'm trying to say, though, is that while this statement is often true, it's not RIO. It's actually the opposite. And in fact, the worst RIO spots are the ones where this is not true, or where it's true in a weird way.

Let's use the above hand as an example, broken up into 3 parts.

1) Let's suppose that in that flop spot, Villain's leading range is AQ/KQ/QT/Q9 (ignoring QJ to simplify the math). Then let's suppose that on the turn, Villain checks QT and Q9 and only bets AQ and KQ.

Clearly on the flop, we are good half the time, and on the turn (ignoring the times we improve), we're good never (if Villain is betting). So what's the right course of action in the scenario I just outlined? Obviously it is to call the flop and fold the turn if Villain bets again. Half the time, Villain checks and we win 75 (or more if Villain calls a value bet from us). Half the time, we lose 30. This is a case that would validate Willy's point that as the pot size goes up, our equity goes down. It's also a spot where we can call and then fold later because the situation has changed in a predictable way. That means this is NOT a RIO spot. Our true odds are exactly our pot odds because we can confidently fold the turn if facing another bet and we're confident we won't face another bet from a hand we beat.

2) Now let's change it by assuming that Villain has a range of AQ/KQ/QT/Q9 and we know that he double barrels all these hands and always checks the river (and let's assume that we won't see a J, T, 9, or 2 clubs on later streets). That means that as the pot size goes up, our equity does NOT go down. It would seem to go against Willy's point. And yet, this IS a RIO spot because our flop pot odds are 5:2 but our true odds are 3:2. It is a RIO spot where the correct play is to call two bets and see the showdown, but it is a RIO spot nonetheless.

3) Finally, let's look at a case that makes it weird. What happens if Villain continues on the turn with AQ/KQ/QT and shuts down Q9? So first of all, obviously this is a spot where there's an inverse relationship between your hand equity and the pot size. On the flop we have 50% equity; on the turn, it's 33.3...% when facing a bet. However, if we again assume Villain checks the river with his whole range, the correct play is once again to call down, right? If the turn pot is 105 and the bet is only 60, we're getting odds of 165:60, way better than 2:1. So we can call the turn, since when we get to the turn, we'll win the existing pot of 105 25% of the time, lose 60 50% of the time, and win 165 25% of the time. All told, that's an EV of 67.5-30=37.5.

Since we called 30 on the flop, our total EV on the flop call has to be 7.5 since we're calling 30 to make an average of 37.5 later on. So here, as with case 2, we should call down.

But now let's compare the 3 EVs:

Case 1, where we call flop and fold turn, playing perfectly: we win 75 half the time and lose 30 half the time. Our EV is 22.5.

Case 2, where we call down because Villain's range doesn't narrow: we win 135 half the time and lose 90 half the time. Our EV is 22.5. (By the way, it should not be surprising that this is the same as the first case, since compared to that case, the only difference is a bet going in at 1:1 odds with 50% equity.)

Only in Case 3 does our EV go down. It doesn't go down enough that it's -EV to call down, but the fact that now our turn bet is going in at 33% equity instead of 50% slashes our EV.

My point, I guess, is that the negative effects of RIO do not correspond with how much our equity drops from street to street. When our equity drops a ton (in this example, to 0) on the turn, RIO barely applies (in this example it doesn't apply at all) because we know we can safely call one bet to fold to future action. Only when our equity goes down part of the way, so that the turn decision is closer, does RIO really mess with our EV. It can also impact our EV in other ways, but to me this is the weirdest.

Still reading, but I noticed in the discussion between samo and CMV we used a "guess and check" method of getting to the 53% breakeven point. Just for your reference, I think we can use algebra to solve it as well.

x = % we are good
-$400 represents the $100 (turn bet) + $300 (river bet) we call and lose when we are beat
+$500 represents the $100 (current pot) + $100 (turn bet) + $300 (river bet) we call and win when we are good and V shoves river (50%)
+$200 represents the $100 (current pot) + $100 (turn bet) we win when we are good and V checks back river (50%)

EV = 0 = (1-x)*-$400 + x*(.5*$500+.5*$200)
0 = -$400 + 400x + 250x +100x
$400 = 750x
x = 53.3%

Technically the solution is not complete until you can prove that calling turn/folding river is always -EV when you're good less often than that, but if we take that as a given (and it's also not hard to show), then 8/15 (the fraction that 400/750 reduces to) is the same answer I got when I worked it out before posting it.

Finally finished. The hand equity vs pot size discussion with the three scenarios was very eye-opening.

Doesn't it also make sense to fold turn if we think the turn card improves a significant portion of Villains range vs ours? (i.e. a card that completes a flush draw, straight draw, and could give a dominated hand two pair)

Not in the specific example of the super-dry Q77rb flop. But in general, yes, that's definitely part of the story.

Awesome post. Thanks for the quiz questions. Without the quiz questions I would have read the post and moved on, but since I couldn't answer the quiz question on the first try I'm going to re-read a few times. Thanks again

Hi guys. I hate to sound like a "lazy" student but could somebody please simplify the main points of RIO and how to utilize them best in a game. I tried but I'm far behind grasping this properly at this time. Thanks!

The idea that you can hit your hand, and still not win, yet have a hand strong enough that you pay off Villain and/or have what seem like good odds to draw, except that you haven't considered Vs likely future bets..

Easiest applications:
1-TPmehK gets bet into on the flop: You have to consider his future bets, as well as your current pot odds, or you'll pay off a bunch of bets with a second best hand.
2-Drawing to a small flush, or the low end of a straight: What if you hit and a V hits too?

More common applications: Really dig in to the OP. You can trust him on the math, but really look at what RIO does to expected value.

thank you

Thanks Vernon!

I have been hoping there would be a thread on RIO. I always thought I didn't get the whole picture. Turns out I understood some of this already but didn't know it was RIO. Also, some new stuff I hadn't considered.

Thanks y'all!

Been thinking about this some more. Much of the thread discusses RIO situations where it is not profitable to call the turn/river. Or even to avoid certain hands preflop that can get us into RIO situation.

One thing I'm realizing is that raising is a viable alternative to folding in RIO situations. i.e. If you have TPWK on a draw heavy flop and a tight villain cbets where his range consists of TPTK and draws. Calling is probably the worst option there, folding is probably fine, but there very well may be a case for raising being the most +EV move.

My hypothesis is that when facing an RIO situation, you should often be deciding between raising and folding. (Calling in RIO situations usually only makes sense imo when a very aggro player will barrel away with worse but will fold worse hands to a raise.)

Consider the scenario where you have position and the tight villain will bet his made hands on the turn to charge draws (as well as his draws that get there) and check his draws that don't hit, hoping for a free card.

I decided to really study this COTM & am having a difficult time with it. I was reading it & got to the RIO on draws, which is what I had a lot of interest in & I do not understand the figures you're coming up with, even though I understand [at least I think I do] the math behind it.

I do not understand what your statement: "$170 came from our stack", has to do with your math, when $200 * .8545 = $170.90, which is only slightly off from your $171.80

If you came up with this figure the same way you did in #1, then $200 & .7338 = $146.76, $23+ more than your figure.

$200 * .9221 = $184.42

This is easy to do, once I understand why my figures are off from yours.
I just don't understand what I'm missing here.

Classic post

I didn't look deep into the math but the $170 comes from Hero's contribution to the pot ott. Yeah Hero put in $10 pre and $20 otf, but that's a sunk cost so when those streets are over, it's dead money.

You raise to $20 pre, get called. Flop ($40) X X X, you bet $40, call. Turn ($120) X X X - X, you bet $100, guy shoves $200 eff. Yeah, you put in $20 pre, $40 otf, and $100 ott, but that's all in the pot now. The pot has $420 in it and you can fold or call another $100. The $160 you put in already is gone, you're calling $100 to win $420, your price is 100/(420+100) = 19.2% or 4.2:1 if you're into the whole odds things.

Thanks, but that doesn't help.

In the 1st example [5s3s vs. AA/KK/AK on a flop of KsTs8c] Vernon says 5s3s has 85.45% equity when the 8s comes on the turn & gives an EV of $171.80

I'm lookin' to find out how he got that figure & the figure for the other 2 examples.

Bingo!!

Yours truly figured it out on his own! Wonders will never cease!

$400 in the pot * .8545 equity = 341.80 - $170 = $171.80 - matches Vernon's numbers!

$400 in the pot * .7338 equity = $293.52 - $170 = $123.52 another match.

$400 in the pot * .9221 equity = $368.84 - $170 = $198.84 another match.

When I multiplied $200 * .8545 & got $170.90, which is damn close to Vernon's $171.80, I didn't even consider doing the math based on [$400 * equity] - $170.

Great post Vernon!!!