A Good Semi-Bluff Gone Bad. (Or the other way around).
This article is about a pretty common situation that comes up in NL ring - when you make a move with a draw or some kind of semi-bluff and get played back at with an all in from your opponent. Dan Harrington describes a great system for dealing with these kind of situations in tournaments - Structured Hand Analysis.
Dan’s approach is far more in-depth than what we’ll use for this article, and I, as always, strongly reccomend his books. We’re going to run through an example that offers a quick and dirty version of Dan’s model that you can use at the table [with a little practice] to help you decide whether or not to call the all in.
First of all, I saw my opponent do this a few hands earlier.
No Limit Holdem Ring game
Blinds: $2/$4
9 players
Stack sizes:
UTG: $182.80
UTG+1: $246
MP1: $317.82
MP2: $411.30
MP3: $495
CO: $708.50
Button: $90.50
VILLIAN: $392
max_pot: $490.98
Pre-flop: (9 players) max_pot is BB with 6c 4h
UTG folds, UTG+1 raises to $8, 5 folds, VILLIAN raises to $25, max_pot folds, UTG+1 calls $17 (pot was $35).
Flop: 6d 8h ah ($54, 2 players)
VILLIAN checks, UTG+1 bets $20, VILLIAN raises to $40, UTG+1 calls $20 (pot was $114).
Turn: as ($134, 2 players)
VILLIAN checks, UTG+1 bets $30, VILLIAN calls $30 (pot was $164).
River: 8d ($194, 2 players)
VILLIAN checks, UTG+1 bets $60, VILLIAN folds.
Uncalled bets: $60 returned to UTG+1.
Results:
Final pot: $194
Then came this hand. I hadn’t been raising very much at all preflop and decided to try and pick up the button and maybe the pot.
No Limit Holdem Ring game
Blinds: $2/$4
8 players
Stack sizes:
UTG: $726.70
UTG+1: $90.50
VILLIAN: $297
max_pot: $470.98
CO: $182.80
Button: $345.50
SB: $407.30
BB: $491
Pre-flop: (8 players) max_pot is MP2 with 6s 8s
2 folds, VILLIAN calls $4 (pot was $6), max_pot raises to $17, 4 folds, VILLIAN calls $13 (pot was $27).
Flop: 9h 9d 7c ($40, 2 players)
VILLIAN checks, max_pot bets $30, VILLIAN raises to $60,
I saw a repeat of the behavior from the previous hand [the dink CR bluff] – I thought it was likely that he was putting me on AK and trying to represent the 9. I decided to clarify my hand for my opponent and raised, trying to communicate that I had an overpair.
max_pot raises to $155,
Then it got a little sticky.
VILLIAN raises all-in $280,
At this point it wasn’t really relevant any more what hand I was ‘representing’ – now the hand shifted to a cold calculation of whether or not I had the odds to call. It’s hands like this that sort of make me hate playing online – give me an extra minute and I can make a much better decision.
I had to call $155 more at this point for a $445 pot. I was pretty damn sure he didn’t have a 9 – I put him on an underpair, a 7, or maybe 10 10 – I figured there was also a small chance that he was just on 2 overs. Here’s how I asses of the likelihood of each hand:
Underpair: 20%
Seven: 50%
Overpair: 5%
Overs with no draw: 10%
Overs with gutshot / redraws: 15%
Note that these estimates are obviously backward looking and possibly skewed, but what I haven’t yet done is calculate my chances against each hand, so I’m not ‘fixing’ the estimates to get me the conclusion I want. I’m not sure that this was a good call yet, although I’m leaning that way. [Note: I can hear you. How can I be so sure he’s not holding a nine? You’ll find an alternate set of numbers below that attempt to satisfy that question]
That’s right, I called. It’s a little under 3-1.
max_pot calls $155 (pot was $445).
Turn: tc ($600, 1 player + 1 all-in - Main pot: $600)
River: th ($600, 1 player + 1 all-in - Main pot: $600)
Great turn, terrible river, but it worked out. This time, anyhow.
Results:
Final pot: $600
MP1 balance 0 lost 297 5d 5h
max_pot balance 770.98 bet 297 collected 597 net 300 6s 8s
Now how about that math? I don’t think my estimates for his holdings are all that crazy, so let’s see how it breaks down.
Underpair: 20% - Against 55 I win about 42% of the time, any lower I win about 53%
Seven: 50% - Here I win about 36% of the time against A7, win about 25% against 78, win about 40% against 76. My worst case scenario is that I’m a 3-1 dog.
Overpair: 5%. If I’m up against 10 10, I’m in trouble at 16%; against QQ I win about 30%.
Overs with no draw: 10%. I’m about even money here to KQ, AJ etc
Overs with gutshot / redraws: 15% - I’m thinking like J10; I’m about 35% to win.
The loose conclusions is that since I’m almost always better than 3-1, I have to call. Here’s my scrub math
20% [Win $445 44%, lose $155 56% / W = 195.8 L = 86.80] +109 = 21.8
50% [Win $445 33%, lose $155 67% / W= 146.85 L = 103.85] +51.82 = 25.9
5% [Win $445 20%, lose $155 80% / W = 89 L = 124] – 35 = -1.75
10% [Win $445 50%, lose $155 50% / W = 222.5 L = 77.50] +148 = 14.8
15% [Win $445 35%, lose $155 65% / W = 155 L = 100] +55 = 8.25
Looks like a positive expectation of about $69.
How certain would I have to be that he had a nine to fold? Let’s swap out one of my best situations – an underpair – for A 9. I’m still going to argue that there’s a very slim chance that my opponent is holding the nine based on how the hand played out, but I’m curious. I’m about a 3-1 dog to A9, J9 and 98; the worst case scenario is about 7-1 if he’s holding 10 9. Let’s call me 4-1
20% [Win $445 20%, lose $155 80% / W = 89 L = 124] +109 = -35
50% [Win $445 33%, lose $155 67% / W= 146.85 L = 103.85] +51.82 = 25.9
5% [Win $445 20%, lose $155 80% / W = 89 L = 124] – 35 = -1.75
10% [Win $445 50%, lose $155 50% / W = 222.5 L = 77.50] +148 = 14.8
15% [Win $445 35%, lose $155 65% / W = 155 L = 100] +55 = 8.25
That cuts down my expectation to about $13. Still positive. If I swap out the overcards with a scenario where I’m drawing dead, that swings it to about a -$20.
To put it very roughly, I’d have to assume that he’s holding a nine or stronger almost 30% of the time to make a fold correct here.
I’m a little surprised by this conclusion; maybe I did the math wrong somewhere. The call seemed a lot more borderline to me at the time, but it looks pretty automatic in the review. And that’s the moral of the story – this hand is just another example of how one or two seemingly harmless assumptions about ‘correct’ play – especially when calling all ins – can be eating away at your bottom line without you even knowing it.
