I'm interested in the EV of giving (hopefully multiple) opponents reverse implied odds when I flop a big hand in a limped pot on a dry flop. It's not exactly slow-playing, but rather sizing small so opponents will call with any pair, giving them outs to improve to a second-best hand that they may not be able to fold (e.g., 5 outs to trips/two pair). This concept is most relevant to LLSNL b/c of the multi-way limped pots, so I decided to post here and get your insight.

Edit for those unfamiliar with the abbreviation: RIO = reverse implied odds

Hand example: My fourth hand at the table, so no history. I'm a 30-something white guy. Every hand thus far has been limped multi-way. Stacks are about 100 bb effective.

Hero is SB w/ 22.

4 limps, Hero in SB ($200) completes, BB checks.
Flop ($10 after rake/drop) Q52

I decide against a check raise b/c this game is so loose passive and it might check around even if someone has a weak-medium Q.

I tried to analyze the EV of Hero leading for $5 (one red chip) if that bet will be called by any pair, vs. the EV of Hero leading for full pot if that bet will be called by only top pair plus. I came up with a surprising result.
Reasonable assumptions: opponents can’t fold two pair plus on a dry, non-straight board; a roughly equal number of Qx and 5x are in a limping/BB checking range.

Say one opponent has 5x and Qy (different kickers), then the pot will be the same size going to the turn regardless of whether I lead flop for full pot or half pot. But in the case where I lead flop for half pot, there are 10 cards that can come on the turn that will theoretically allow me to get one opponents' stack.
If we are $200 effective, and we will get stacks in on the turn if he improves to 2-pair or trips, I calculate the EV of the player holding 5x simply seeing a turn card as:
$200 * (5/43) = $23.25 (but I have to multiply this by the percentage of the time that my hand holds up on the river against what is a 5.2-outer on average, so * 36.8/42) = $20.38

Am I missing something, or does leading flop for half pot in this case really have that big an EV advantage over leading for pot? Is there a flaw somewhere in my thinking/math?

You're thinking way too hard about this and it will end up getting you into a ton of trouble. There's a reason so many hands are being limped multiway and that's because people are playing hands you aren't expecting. So you bet your half pot against these limpers hoping to get called by people looking to improve to two pair. An ace comes, and huzzah! You're stacking off with ace queen! Or more likely you just got stacked by 34o which you gave unbelievable odds to draw out on you, or numerous middle pocket pairs that are still profitably set mining you.

If you just bet pot and only get 2 it's the same as if everyone came along. In the situation your describe lots of passive tables will still call with Qx and 5x type hands. Value missed is a hard thing to make up for, often. You never know what people will call you with.

Now if your example was say hero holds KK and raises pre and gets 4 callers and the flop comes KK6 or less extreme K 9 2 then betting small makes more sense because it's harder for villans to have a piece of that board.

Two flaws that I can think of:

1. Equal # of Qx/5x in limping ranges. We all like to think that our terribad stationy loose-passive opponents are playing ATC. But they're not. The vast majority of them are still folding complete rags. Open up PokerStove and look at the top 50%, top 70%, etc., of hands. I think you'll be shocked to see how many more Qx are in those ranges than 5x.

2. Ignoring geometric pot growth. When we're against an opponent with Qx, we win a lot more leading the flop with a PSB than with a 1/2 PSB when he doesn't improve.

The general question is a good one and I think it's a valid concept; this hand just isn't really the right situation to apply it.

To give an appropriate but extreme example: let's say we have 66 in the SB in a 5-way limped pot (at a loose-passive 1/2 table), and the flop is 6c6s3c. We're not going to get value from much, but we do want to set things up such that we're likely to stack someone if they hit a flush or straight. Stations will always call a $5 bet with a draw here. If they hit it and we lead the turn, they're going to think they're good, and it's much easier to win lots of moneys. If we had checked the flop, on the other hand, SPR on the turn is ~20 if we're 100bb effective, and even droolers won't automatically stack off with a J-high flush or something.

So, bottom line, giving opponents RIO has to be weighed against extracting max value from made hands.

Thanks for the feedback. I definitely concede that the Q52r wasn't the ideal example, but it was a real hand that I played that made me think about this concept. Yes, I realize that 34 and all pocket pairs were priced in, so I was giving myself RIO.
I don't get your point about stacking off w/ AQ. I have zero intention of applying this with one pair hands for obvious reasons.

Right, I know that top set on K83r, K82r, K73r, K72r, Q72r are the only sets that are truly invulnerable to a turn card (unless someone limped AA). The hand example with 222 was one that I actually played.

I guess it's possible that 5x hands might call a pot-size bet. But it would be basically a naked 5, except for backdoor draws. I just don't see many 5s calling a pot-size bet on the flop.

Targeting 5x and 99 type hands makes no sense to me. They're usually not continuing unimproved when you make a strong turn bet, regardless of how you size the flop... So we're talking about $5.

The question is how do I stack TPGK. And the answer is either pot the flop or check/raise. It depends how many of your 5 opponents you expect to bet/call with QT or better. 4 or more I'm definitely check raising. 2 or fewer and I'm definitely leading. You need to start building a pot asap.

1. I realize that a top 50% or top 70% PokerStove range has many more Qx hands. But from the perspective of a limp-happy $1/2 player, suited and connected cards look a lot better for a limp than Q7o. I guarantee that ~all average $1/2 players would prefer 54s to Q7o despite the fact that Q7o has much greater equity vs an average hand.

2. This is a good point. Often we are against only top pair and we lose a lot of value on the turn and maybe river by sizing so small in those cases.

Agree with all of this. I wasnt familiar with the term "geometric pot growth" until now but it's way better than "start building the pot asap." This is a critically important concept.

Thanks for the feedback. As I said to others, I posted the real hand that I played that made me think about this concept. Flopped quads, straight flushes and sets that are invulnerable on the turn are the most clear cut examples where you want to give opponents RIO.

Like you recognized above, letting flop check around can be a disaster so the $5 bet serves to both build the pot slightly and keeps the draws and weaker hands in.
Also, checking flop and then waking up and bombing turn and river looks scary to even the weakest players. On the other hand, no one sees their opponents at $1/2 lead-lead-lead with flopped monsters, so they might not believe you.

I understand that 5x is not continuing unimproved when I make a strong turn bet.
What I showed mathematically is that the EV of 5x simply SEEING a turn card is over $20. This is based on the very reasonable assumption that a $1/2 opponent will not fold two pair on a board with no straight or flush possibilities.

Yes, 38/43 times 5x will not improve and will fold to a turn bet. But the value is in the 5/43 times that 5x does improve to 2-pair plus.

You dont really give us much about the post Flop action in the previous hands ... bet/folds ... bet/multiple calls ... check through ... How long was the table going before you sat down (ie .. are you the new guy?)

But basically anyone leading out of the SB in a limped pot is going to get a lot of credit on a board like this. And with a pot this size a $4 bet is the same as a $8 bet IMO. Now if you start getting creative and betting out $15, then we have something to talk about. There are basically no RIOs in a pot this 'small' going 5 ways IMO. They are either going to call or not .. so $7 or $8 is fine, maybe $5 since it's just 'one chip'.

Your 'real' math doesn't start until the Turn when you see where you are at and how the action went down ... delayed calls ... insta-calls ... et and how the Turn card effects the board.

Most of these guys will give you credit for something .. any pair .. and wont continue regardless of your bet without something themselves .. being overcards, pairs and maybe Arag type of hands (certainly Qx) and 5x hands that have draws/good kickers attached to them. That's a pretty large range of hands, which makes sense in a limped pot.

You are just in the unfortunate position of not knowing the table very well .. so just shoot for a 'standard' c-bet when OOP type of bet .. being 2/3PSB+.

You don't want too many hands feeling priced in but yet you want max value, eh? That's the question every hand. Leading out here is very good .. then with multiple callers I go for the c/r on Turn. If HU keep firing away at the value bets and hope your opponent does improve to a 4-card type hand or better draw on Turn.

I just valued a guy right into a 9% Turn shove at 2.5 to 1 yesterday and he was extremely excited when he found out he 'out-played' me when he hit his 3 outer on the River.

Always make sure your opponents pay a -EV price to continue, then you can be confident that in the long run you will win out based on the math. If you let folks stick around, then you blame yourself and not variance for the lost chips. GL

Yes, I agree that this is essential in the case where you have one opponent with a strong Q. However, the example that I gave assumed that we have one opponent with a Q and one with a 5. In that case, there are two advantages to leading flop for half pot:
1. There are 10 RIO cards in the deck instead of 5
2. Our flop bet size makes us look weak and more likely to be called by a Q for three streets

We can't really answer my question fully without knowing the following for a typical $1/2 game. The % of the time that the following situations come up in a pot with 4 limpers and a BB that checks:
1. One opponent has Q, no one has a 5
2. One opponent has a 5, no one has a Q
3. One opponent has a 5 and one has a Q
4. No one has a pair
5. Uncommon cases with 3+ players with a pair

For may (admittedly imperfect, but real) hand example, we also need to know the number of pocket pairs and 34 combos for our RIO.

You can play around with Stove yourself to put in what you deem to be realistic ranges, and see what comes out. The biggest difference comes not in SCs/SGs (if they're playing 53s, they're probably playing Q9s too), but in random unsuited cards. Loose-passives play a LOT more Qxo than 5xo.

This is literally my 4th hand. I just sat. The table is four really old guys, two 40-something nitty looking guys and 2 other 30-something guys. I can't recall the post-flop action in each of the three previous hands, but it was a lot of checking, some calls, no raises. One old guy bet flop and shut down, lost to a pair at showdown.

I think $5 gets called b/c it's "just one chip" all the time. I see it viewed much differently than $8, which seems both large and like a thoughtful sizing.


I really want them to give me credit for one pair and stack off if they hit an overcard or two-pair plus.


No, it's the exact opposite. The real hand that I posted wasn't an ideal example b/c I was vulnerable to pocket pairs and 34, but I want everyone with a pair or an overcard to call so they can improve to a second best hand.

I was talking about hands you're stacking off against.

If they are all calling your flop bet with 5x, aren't they calling it with 66-JJ too? If that's the case your math should also account for the 2/43 times they turn a higher set and you get it in with 1 out.

How many reasonable combos of 5x are possible vs 66-JJ?

Are you sure all of your opponents going to the felt with 54 on Q5243 for example?

My bad. I see what you're saying. I would def stack off if the A fell, but I see A5 as more likely than either 34 or AQ given the preflop action.

As I conceded, the example hand I chose from my play wasn't ideal for a discussion of this as a pure concept b/c of higher pocket pairs and the 34 or wheel draws. I probably should have made up a hand like one of those mentioned above (KK on K72r).

Right, I should have made up an example hand without concern about higher PP or (edit) a possible straight.

I can't be certain that a given $1/2 player 100bbs deep will stack off w/ two pair or trips, but I think it's a reasonable assumption for doing the calculation. I can't imagine many $1/2 rec players folding two pair or trips on a dry board.

What I'm getting at the EV calculation you are doing just isn't very helpful on a 6 way flop with no reads. It's not a solvable situation, or even close. You have to make too many assumptions, and there are too many permutations of number of callers and board runouts to account for.

The math you're doing becomes increasingly powerful as you progress further in a hand (fewer permutations) and/or as you develop stronger reads on your opponents ranges (better assumptions.)

One other big problem in this example: you're hoping to target Qx and 5x, letting them improve to two pair or trips so they'll pay you off. But you're also inviting 67hh/cc/ss to draw extremely cheaply. And 64hh/cc/ss. And 63hh/cc/ss. And 68 or 78hh/cc/ss.

If you bet $5 and get three callers, a late position player will be happy to pay for another card with three to a flush and three to a straight/a gutshot. And that flips the entire scenario, because now you've invented an RIO nightmare for yourself.

This is pretty much what I am feeling here ..

We are trying to get 'max value' from the full range of hands we might be against. In a multi-way pot I am much more interested in V who have 2 card hands (pairs) that we dominate than allowing V with 0 card hands (that can become 5 card hands) in cheaply that will take our stack.

Bet 5 and get 4 callers .. $20 increase in pot .. but with potential to stack us.

Bet 8 and get 2 callers .. $16 increase in pot ... but less likely to get stacked AND more likely V continue to the River where we can 'make up' the 'lost' $4 in pot.

Crude math, but based on a $200 stack we risk winning $4 additional in chips against getting stacked 1 out of 50 times (200/4). Are we going to get stacked 2% of the time or more ... yes.

Granted there are ways to 'make up' these chips by being able to bet into a larger pot, 're-stacking' when we hit our boat and having these V stay until they 'miss' the River.

I just think OOP we need to play more standard and live with keeping only those players we truly dominate with less hope of catching up in the hand. The 'one chip' bets are for the HJ-CO-B players once things are checked through. GL

You are applying RIO completely wrong. You have RIO, not your opponents. Slow-play vulnerable hands and you only trap yourself. Heck last year I had TT with a T52 rainbow flop and managed to slow play myself into a trap (A4o got there on river).

Last week an opponent had Q3 on a 833 flop and she slow played and then went all-in when an 8 hit the river?? (I busted her with my 8)

Your best bet is to bet and hope someone raises the flop. But ultimately, sometimes you just aren't going to get any value from your hands because everyone misses the flop.