5NL Top 2 with Royal Flush Draw facing Turn Bet

Villain is 76/0, but havn't seen him get out of line post flop in big pots.

No-Limit Hold'em, $0.05 BB (4 handed) - Hold'em Manager Converter Tool from FlopTurnRiver.com

BB ($5.07)
UTG ($19.85)
Hero (Button) ($6.17)
SB ($6.83)

Preflop: Hero is Button with Qhttp://www.flopturnriver.com/phpBB2/...miles/club.gif, Ahttp://www.flopturnriver.com/phpBB2/...es/diamond.gif
1 fold, Hero bets $0.20, SB calls $0.18, 1 fold

Flop: ($0.45) Ahttp://www.flopturnriver.com/phpBB2/...iles/heart.gif, Jhttp://www.flopturnriver.com/phpBB2/...es/diamond.gif, Qhttp://www.flopturnriver.com/phpBB2/...es/diamond.gif (2 players)
SB checks, Hero bets $0.30, SB calls $0.30

Turn: ($1.05) 10http://www.flopturnriver.com/phpBB2/...es/diamond.gif (2 players)
SB bets $1.20, Hero ???

i would peel the turn and fold on the river to a blank. its pretty likely he has a K or a flush (looks more like a K though). with so many outs its kind of hard to fold. then again, i'm a bit of a station.

easy call - raising is silly

make sure you get there

No points for a fold?

I put my equity around 25-30% depending on how many diamonds he held, and getting worse than 2-1 on the call. Just wasn't sure what the implied odds were, how much do we expect him to pay off on the river with 4 diamonds on the board?

EDIT NOTE: Numbers are all wrong - corrective post to follow

Well, generally we need to be able to find a fold with top two pair in these types of situations when the behaviour of our villain warrants it - but in this case we have Ad and I think that makes all of the difference.

Any ace or queen gives us a full house. That's worth stacking off with. Any diamond gives us the non-straight nut flush which is also worth stacking off with. So that's at least 13 cards worth stacking off with out of 46. We hit one of those 28.3% of the time. Problem of course is that sometimes we hit one of those cards and still lose to Kd (with 9d hitting) or 9d8d.

We are facing a bet of $1.20 so we need to win on average $1.2 * 46 / 13 = $4.25 for a call to be +EV. There is already $2.25 to be won, so we need to win on average $2 on the river if we make our hand to be profitable. There is $4.47 behind if we call and $3.45 in the pot so we have to be really certain he's willing to stack off for us to call for implied odds. And sometimes we're in a reverse implied odds situation where we put in the remaining $4.47 and lose to 9d8d.

Villain seems to be trying to get all the money in the middle (hence the slight overbet). It's probably safe to assume he loves his hand and wants to stack off. So he's committed, and the odds of him putting his money in on the river regardless what happens are pretty good. The worst hand I put him on at this time is Kdx for a straight with the K-high flush draw. Villain may at this time have 9d8d or Kd9d, but a lot of other flushes also justify the action.

If a K comes on the river the worst hands in the villain's range gives us a split, but I still don't think there's any bet that we can call. Any non-diamond, non-A and non-Q we have to fold. The only diamond card I'd feel sick about calling is 9d.

I think above all I want to put Kd in the villain's hand here.

Due to the presence of 9d8d and Kd9d in villain's range we need to be able to put something like 20+ hand combinations in the range that we beat if we hit for it to be clearly profitable to continue for implied odds. Add to that Kd (with any ace, queen, jack, ten, diamond and perhaps trash) in his range and 9d seems more like a card we should be looking to fold rather than stack off to if it comes and that doesn't help matters.

When we count on 9d not being an out and discounting the flush outs by about 1.5 or so as flushes are just so likely in our opponents range (we can reduce number of cards in the deck down 1.5 also of course) we have a slightly different calculation. Now we have 10.5 outs on 44.5 cards. $1.2 * 44.5 / 10.5 = $5.09. Now we have to win $2.86 on average with a pot size of $3.45 and $4.47 behind. And some of the time we go all-in and lose to Kd9d or 9d8d so we pay an additional $4.47.

If our villain is just smart but loose I think this is actually close enough to be marginal. I don't think folding to reduce variance is a big mistake if it is a mistake at all. A thinking villain's range for this behaviour has to contain quite a lot of hand combinations that we beat if we improve for it to be profitable.

But then - we also have to consider the villain. These are pretty low stakes and sometimes people have no idea what absolute and relative hand strength mean. On boards like this some people will play sets like they're the nuts because they don't understand how weak they are. Similarly sometimes people checking behind trips on the river on completely dry boards where we haven't shown any strength. So in this situation yeah - he likes his hand. But is he smart enough to understand the relative strength of his hand? At these stakes and with these stats, probably not. We probably have to call and call shoves, or shove over any A, Q or diamond (except 9d) rivers. 9d I might accept calling a small bet on, but I wouldn't shove on it. With 9d on the board I think we're behind enough of his range not to be favourites to win, but ahead of enough of the range that we can't just fold to a small bet. An open shove is a fold though imo.

Ok so I finished my post, shut down my work computer and walked to my car to drive home and on the way to the car I thought of a couple of things that made this even more marginal - and of course figured out that I'd applied my implied odds calculations incorrectly.

Let's correct the outright mistake first. I'll do that by using a simplified example of why my implied odds calculation works. Skip to Back to the hand if not interested.

Nothing to do with the actual hand
Let's say a pot (pre-bet) is 10 and you are facing a bet of 5. So you are looking to call 5 to win 15 that is out there already or the total pot of 20 once you've called. That right there is basically the difference between odds notations and equity notation (25% pot equity is 1/4 - pot odds are 3-1 against.) And that's basically the type of error I made. On to the generic explanation.

Let's say the situation is as I just described with no money behind. We can calculate that the portion of our call into the post-call pot is 25% of the pot which means we have 25% pot equity which means we need 25% hand strength equity (or more) for the call to be profitable. So with a simplified deck we could say that if there are four cards left in the deck and one of them makes us a winner and the other three makes us losers we are breakeven to call. That's back to the odds notation again. 3 winners, 1 loser => 3-1 against.

Let's fix the pot and bet sizes, give us 20% chance to be good (five card deck, 1 winner, 4 losers), say there is money behind and try to figure out how much we need to win on a later street for calling on this street to be profitable. Ok, in the 4 events where we miss we reckon we're losing and we're folding and giving up our equity. In 1 event we reckon we're winning and we're putting in more money. In all 5 events we are paying 5 on this street. The pot started at 10, is 15 with the bet that we call and becomes 20 with our call. We have paid 25 total so the 1 time that we are winning we need to win an additional 5 to be breakeven or more to be profitable. We calculate this 5 using either equity or odds. Another way of saying it is that we lose 5 four times and win 15 one time, so since 4*5 = 20 we need to win 5 more the one time that we win for it to be breakeven.

Equity: Bet / chance to win - post-call pot size: 5 / 0.2 - 20 = 25 - 20 = 5. Note that dividing by 1/5 is the same as multiplying by 5.
Odds: Bet * outs to lose / outs to win - pre-call pot size: 5 * 4 / 1 - 15 = 20 - 15 = 5

The main point I have in favour of using the odds notation is that the pre-call pot size is known (on some poker sites at least) without calculation. I find it quicker to mentally only have to do one calculation instead of having to first calculate the pot size that is relevant and then keep it in my head while I calculate the other particulars and then use it at the end. In hand history analysis we typically have to add the bet to the pot to get the pre-call pot size, but when doing hand history analysis we have time for it.

Back to the hand
Bottom line from my ramblings in the previous post was that I'll fold to a shove if the 9d comes on the river, but maybe call a smaller bet if I think the bet size makes me 0 EV or better against the opponents range (if it's wide enough to have sets, two pair, non-diamond kings etc in it). Not sure about the bet size but probably not above $2. So 9d is still not an out, and I'm discounting 1 flush card (no longer 1.5) because I think flushes (or Kd flush draws with straight and perhaps a flop pair) are quite big in the villain's range.

That means I'm now considering 11 cards as outs of 45 (the flush discount also counts here) with 34 bad cards.

$1.2 * 34 / 11 - $2.25 = $1.46 to be won on average on the river for calling to be profitable - if we have 11 clean outs.

In my previous post I focused a lot on 9d8d, Kd9d and Kdx with 9d coming on river and I guess we can extend that to 9dx with 8d coming on river as ways we can get in trouble. What I was thinking was that those hands mean we can run into a reverse implied odds situation when we improve, and the additional amount of money we lose ($4.47 in addition to the $1.2 we are looking at paying now - almost multiplies the risk by 5) means for each of the hands in the opponents range that beats us we need 5 hand combinations in the hand range that we beat. I pulled the number 20 pretty much out of thin air, and the number 10 is a bit better but also not perfect. The 'risk multiplied by 5' observation is not an EV calculation and the pot size also counts.

One way we can eliminate risk is to say that neither 9d nor 8d are outs (1.2 * 35 / 10 - $2.25 = $1.95) - the corrolary to that is doing an EV calculation for what happens when 9d or 8d hit and we sometimes win, sometimes lose and try to determine whether they should be considered outs or not. My instincts tell me that 9d will be -EV and 8d will be around 0 EV.

My problem with this 'risk multiplied by 5' thing is that it suggests that for each 9d8d we need to find 5 hand combinations that we beat - and while that's easy enough for 9d8d, what happens if the villain is truly playing any suited and can hold 9d7d, 9d6d, 9d5d, 9d4d etc. With any two suited there are literally 36 hand combinations. 8 are Kdxd, 7 are 9dxd, 6 are 8dxd and only 15 have none of those 3 cards that can make straight flushes. That's 14 combinations that make 9d a straight flush and 7 that make 8d a straight flush and it's the majority of the made flush range I thought was good for us. We still beat all but two of these hand combinations with a Kd (included in one of the two) or 7d- but still. Hitting 9d and 8d are certainly not hot prospects as literally the majority of the flush range becomes straight flushes.

Ok, so we may need to look beyond flushes. And now we come to my other problem that I started this post with. will641 said opponents play looked a lot like a K and while Kd is a special case that will be happy to stack off to us (on anything except 9d where we fold) I'm guessing by the way will641 said it he's thinking about non-diamond kings also. And this worries me. Non-diamond kings in our opponents range hurt our implied odds a LOT. Let's take Ks8s as an example.

Let's say he has Ks8s, we call, river is an ace, queen or diamond (not 8 or 9) he checks, we bet (shove probably) and villain folds. Oops - we need an average $1.95 or whatever on the river and a hand like this in our opponents range is going to give us on average $0 extra. With 4 to a flush on the board even straights can fold. The flush cards that make our hand are scare cards to any part of the opponents range that is not a flush. Flush cards may even be scare cards to 7d6d type flushes or Ks5d flushes. Our opponent may be willing and seeking to stack off on this street, but the rivers that we want him to stack off on are likely to be the rivers he is least likely to stack off on.

The irony here is that the villain may have a lot of weak hands in his range that are still ahead of us on the turn - and then when we improve on the river they are weak enough that he can maybe fold them. And we can't even check/check showdown and expect to win any reasonable percentage of the time when we miss.

The only real comfort is the part of the villain's range that is Kd. Like AsKd, KdQh, KdJc, KdTh etc. Luckily this range should be pretty wide and almost 100% willing to stack off on any river that hits our range. The back-door comfort is the non-diamond king with the raggy diamond which also hits a flush on the river and might be willing to stack off.

I think if we have a strong feeling that villain does this with 'any king' we have to fold. If villain does this with mostly Kdx and flushes we can call for implied odds.

That deserves a lot of respect Erpel.

1. Wrote a great post
2. Went back to your computer, after realizing some minor errors in first post.
3. Wrote an even better post.

People like you make my day great!

the heart outs are meh because they don't have any implied odds but he'll call if he has the king of diamonds
the boat outs have larger implied odds and we're going to get paid by a flush for sure and sometimes by a king
if he has k high flush on a 3 diamond board we could easily get all of his money