To Call or Not to Call, That is the Question

I’ve seen a lot of amazingly bad call decisions playing a few million hands of poker over many decades, and suspect that many of them are because the caller isn’t really thinking about the actual pot odds they are being offered relative to their actual odds of winning, or, are over collapsing their opponent’s range based on some kind of hunch to just a few bluffs, when many strong value hands are obviously in range also.

So I thought it might be fun to just post several specific scenarios over a number of days, looking mostly at spots where you face an all in bet, and ask whether it is nobler to suffer the slings and arrows of outrageous run outs with a call, or to take arms against a sea of troubles… yeah, yeah, ok already: should you call or should you fold?

Before getting on to the first examples, though, it’s probably good to add a bit of a disclaimer: these spots are all about loss reduction. You really mostly don’t want to be in a situation where you have to decide only between calling or folding, as these defensive lines have almost no hope of showing a profit against anyone except the most bluff heavy opponents. But still, better managing loss reduction lines is an important skill.

Spot 1: It is late in a tournament, and blinds have climbed to $1,000 and $2,000, with no ante on a 6 max table with 4 players now seated. You are the big blind with 7h4c. The cutoff folds, and the button, who has only $5,400 left, jams all in. The small blind in front of you folds. You are in the lead at the table with $32,500. The pot is now $8,400, and it costs you $3,400 more to call.

Context: this player is usually very tight, but seems to have some awareness that having a really short stack should make them raise with more hands, but you think they understand “more hands” to mean, instead of shoving with just aces, they will now shove with any pair, AQ+, all suited aces, and maybe a very small number of other hands, like KQs, QJs, and JTs (so their shoving range is still much tighter than their situation in the tournament warrants).

Do you call or do you fold?

Spot 2: 6 max cash game table with blinds of 200k and 100k and 5 active players. You are the small blind with $9,800,000. HJ folds, CO raises to $500,000, button folds. Both the CO and the big blind have you covered. You have Qh9s should probably fold, as the big blind is aggressive, and prone to make 3 bets. You call anyway with a masterful plan to outplay both players post flop even out of position. The big blind 3 bets to $1,800,000, the CO calls, and you call again.

The flop comes Th9d3d. You check, the big blind bets $2,000,000 (a bit under half pot), and the cut off jams all in for $25,000,000. It costs you $8,000,000 to call and you will win $19,600,000 if you somehow win here.

Context: both players are aggressive pre-flop and post-flop. You think the big blind’s 3 betting range will be something like AA-TT, ATs+, AKo, KQs, A5s and 87s, and the cutoff will mostly only 4 bet with AA and KK, and will call with AQ+, all suited aces, K9s+, suited gappers down to 86s, and suited connectors down to 54s, and also 53s. On the flop, you think the big blind fires this small continuation bet with most of their very strong range, while the all in over bet from the cut off is quite polarized with only sets, 2 pair type hands, and a variety of high equity bluffs. You think they will make this bet some of the time with around half of their highest equity draws and occasionally with a few weaker ones. You also think that 2 pair type hands, while in range, maybe only take this line about 1/3 to 1/4 of the time.

Call or fold?

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Spot 1

No, I wouldn’t call. In that situation i.e., being in the big blind, the $2k is a part (or price) of playing poker. And, it wouldn’t influence my decision to call esp. with a 7h4c hand. You can only hope for a pair (a low pair at that), 2 pair or a straight but what are the odds of that happening.

My thinking would always be … why provide a short stack with more chips when you have a poor starting hand?

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1 Is pretty straight forward since you specified his jamming range. You just check how your hand performs in aggregate against it. Though the math for this is too complicated to do in real play under time constraints without having tools available or previously memorized hand charts. I just estimate my equity as being 25% against his range. The pot odds require ~30% equity. There’s value in eliminating a player late in a tourney. I assume this is post bubble and at the point where each player removed represents a pay jump. So I use this as justification for calling what is probably slightly -EV.

2 I don’t understand how I would work out the math against two opponents ranges without any tools available in a real play situation without getting the clock called on me. I would just intuitively fold against even two wild players and even getting a bit over 2:1. Assuming the “average” case is CO has a draw and BB has an overpair (since he’s calling after two shoves he must be very strong), this isn’t so attractive. Some of your Q and 9 outs are dirty against COs draws. CO may also have two live overcards which makes this even less attractive. The good scenarios seem too unrealistic for the price. It just feels like a losing spot. I would be surprised if the math said this was +EV

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The first one seems pretty close to me. You probably have 2 live cards, and are getting a good price to call if he doesn’t have a pocket pair. Then again, there’s a good chance he does have a pocket pair, and you’re in rough shape against most of them if he does.

I’m a defender, but even if we round off and say you need to defend there with the top 2/3 or even 3/4 of your range, 74o is probably a reluctant fold for me. The chips I might lose there are worth more than those I can win, so time to go to mucksville.

The reason I think it’s pretty close is because there is value in knocking the guy out.

Spot 1 was intended to show a class of situations where I think many tournament players dramatically over fold. You are seated at the big blind against 3 other players with blinds of 1k and 2k and have $32,500 in chips. The cutoff folds, and the small stack at the table, the button, goes all in with their $5,400 chips. You look down at your cards to see 74 off.

Lets first examine your equity against different types of ranges.
• Range 1- AA-TT and AK: you have 22.1% equity
• Range 2 - A 50% range consisting of most suited cards, all pocket pairs, all aces, K8+, Q9+, J9+, T8+, 98 and 87: 34.3% equity
• Range 3 - Against the range described (all pairs, AQ+, all suited aces, KQs, QJs, JTs): 29.06% equity

One way I like to use for calculating if a play is profitable (I somehow find this easier than the traditional approach): multiply your equity times the amount you will win, and your opponent’s equity times the amount you will lose (how many additional chips you have to put into the middle to make the call).
• Range 1: 22.1% x $8,400 = $1,856; 77.9% x $3,400 = $2,648.60
• Range 2: 34.3% x $8,400 = $2,881.2; 65.7% x $3,400 = $2,233.80
• Range 3: 29.06% x $8,400 = $2,441.04; 70.94% x $3,400 = $2,411.96

Note how, except against the super tight range 1, we win more chips than we lose. Note also that 74o is still behind literally every hand in range 3. There is not one holding it is a favorite against. And we also lose the vast majority of the time. But when we win, we win more than the times that we lose, and so even in this case a hand as weak as 74 off shows a profit calling the shove (and the situation has been constructed so that ICM considerations shouldn’t alter that evaluation).

Spot 2 is an obvious fold, inspired by a hand I’d seen that same day where the player lost all of their chips (and most of their bank) with a hand with even less equity (probably tilt). Against a single very aggressive opponent, you might need to think briefly about folding, but having to beat two ranges most of the time here should just make this a snap fold.

Feel free here to plug in your own range assumptions to see if you get a different result. Obviously if the cut off is super bluff heavy and you think the big blind is tight/weak, and will fold after you call a high percentage of the time, you can construct ranges where calling here can be profitable, but those would be outside of the parameters of what was described in the context section.

• Hero has Qh9s
• Flop cards are Th9d3d
• It costs $8 million to call
• You win $19.6 million if your hand holds up
• BB range: AA-TT, AKo, ATs+, KQs, A5s, 87s
• BB calling range: AA-TT, AdKd, AdQd, AdJd, AdTd, 8d7d
• CO jamming range: TT, 99, 33, Td9h, Ts9c, Tc9s, QdJd, 8d7d, QhJh, 8h7h, AdTd

Let’s start by examining a simple case, where the big blind always folds, even with the nuts, just to see if we have the equity we need against the CO range alone…

On this board, Qh9s has 17.13% equity against the CO range we’ve listed. Chance to win of 17.13% x $19.5m = $3,357,480; chance to lose of 82.87% x $8m = $6,629,600. Even in a best case were the BB folds after we call even with TT, we lose far more here than we win against a polarized range consisting of strong value and high equity bluffs. As the big blind starts calling also with hands that are far ahead of us, the situation just gets that much worse.

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In the first hand, I think range 1 is too tight. I would think something like 88+, AT+, A9s+, A5s, or something like that. Ranges 2 and 3 don’t seem realistic given that he’s a “very tight” player. I don’t have the software to calculate the equity.

I also wouldn’t discount ICM implications. Hard to say without more details though. OK, you’re the chip leader at your table, but how many left? How many pay? How does your stack compare to the average stack and the chip leader?

Truth be told, I would think it’s a close fold, then probably call anyway. LOL

Spot 3 is an actual hand from August 28th. It is a 9 max table with 8 players seated. Blinds are 100k/200k.

EP limps under the gun with a stack a little under $22m, after which it folds around to the hero on the button with Ac3c and a stack of $22,742,253 before limping behind. The small blind, with $13,651,213, makes a small 3 bet to $600,000, which is called by the big blind with a stack of $34,455,000 before making the call. The EP limper folds, and hero closes the action with a call.

The flop is Jc2c3d, with a pot of $1,940,000 after the rake is removed. The small blind passes on making a continuation bet and checks. The big blind also checks. Hero, with Ac3d, fires a roughly pot sized bet of $2 million, and the small blind, after a short pause, shoves all in. The big blind folds.

Context: the small blind is a top 20 player with an unorthodox style, and makes occasional bluffs with unusual holdings, but overall seems to have a pretty good balance of value and bluffs. I suspect their larger bets tilt more toward value, and that they bluff more frequently with smaller bets (certainly not GTO, but something that can definitely work as an exploit against those that over fold to small bets). It costs $9,151,213 to make the call, and you will win $15,091,213 if you hit your nut flush without a set redrawing to a boat, or in any other way end up with the best hand after the river.

Do you call or do you fold?

Yeah, I agree. Range 1 seems silly tight, and even range 3 would be too wide for some of the tight players out there (though it was the range presented in the original question). Range 2 is certainly wider than you’d expect from a tight player, but was included to show that against a fairly appropriate raising range from someone about to be blinded out of the tournament, you have a hugely plus EV call.

I also agree that it is a pretty close call with 74 against the range presented in the original question. The intent though is to show that when you are facing a small all-in bet, close the action and aren’t putting your tournament life at stake, you should call with a much wider range than a lot of players do.

Spot 4:

Heads up play as the button with blinds at 100k, 200k. You min raise with 8d7d, and your opponent 3 bets to $1,600,000 and you call. You started with $40,000,000, and your opponent with $30,000,000.

The flop is Qd4c2d, your opponent fires a small continuation bet of $1,000,000 into the $3.2 million pot. You raise to $6 million, and your opponent shoves all in.

Context: your opponent is hugely tough to play against heads up, with a ruthless mix of bluffs and value. You think there are many bluffs in range (many even with little equity), but also many strong hands like over pairs, sets, and 2 pair hands (and some middle strength top pair or middle pair hands with some extra equity).

Do you call or do you fold?

Spot 3 is a snap call unless you’ve only ever seen Villain do this move with sets, in which case it would be a fold.

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Would you also agree that chips lost there are worth more than chips won? I think that makes it closer still.

To me, there’s another factor that isn’t addressed by the math: the impact on your table image. People seeing you call that light might make adjustments, and the ones they are likely to make work against you. This is especially true in tournament late stages, when I have to assume those left are paying more attention.

I do make a lot of calls in that spot, but there are times I let it go too.

That’s one way of expressing that chips won don’t increase your expected winnings as much as chips lost generally do. Note that in the situation described, I’ve deliberately tried to minimize (and even reverse) that effect, though I’ll have to admit that I don’t feel I understand ICM enough to be able to quantify this effect well.

I’m not too worried about table image in this spot. How can I be exploited? If they reduce their raising range to something overly strong, there is profit from not having my blinds stolen often enough. If instead they raise with a wider range, the call just becomes more profitable.

Well, i would think people would raise or jam wider, putting me in more tuff spots. I like to avoid hard decisions where possible.

If their wider ranges contain more 7s and 4s in this particular spot, that can’t be good.

I do want to thank you though. It’s nice to have an occasional thread about poker on a poker forum.

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My first instinct was that Spot 4 should be a fold unless Villain goes really wild on the low equity bluffs. However, I’m not sure.

Here are my “back-of-the-envelope” calculations. Let’s say you have 45% equity against Villain’s bluff range (that’s probably too optimistic even against many low equity bluffs, especially since Villain has many better flush draws in that range). Against Villain’s value range, Hero has at best about 35% equity with the flush draw (we should subtract some equity due to Villain’s sets). If Villain has 50% bluffs and 50% value, we have about 40% equity. With more conservative estimates of 40% against Villain’s bluff range and 30% against Villain’s value range, this drops to 35%.

You need about 22.4/60 = 37.3% equity. So yeah, if Villain bluffs significantly more than 50% and with sufficiently many low equity bluffs, it could be a call. I’m curious to see what you think about this spot.

3 I dislike the hero overlimping the button with a suited wheel ace. If the SB tends to overlimp a lot then I assign a tighter range to their raise. Otherwise I would view it as representing a normal opening range for their position. But the SB check/jam is suss AF.

Again only doing the math in my head as I would be forced to do in a real game, the pot odds require ~40% equity. (Calling 11 million to win 28 million combined)

Let’s assume since they’re a top player if they have a postflop check/jam strategy it’s suitably balanced. The problem for me is having the Ac in hand blocks a lot of their potential equity bluffs. Would a top player check/shove a non-nut flush draw? You’re also holding the 3c which eliminates all pair+FD bluffs.

I give SB as a value range AA, KK, QQ, and AJ, JJ 33 and 22. I give SB overpairs since you described them as unorthodox.

Even against this range alone the call is justified.
AA (6 combos) 40% equity
KK (6 combos) 50% equity
QQ (6 combos) 50% equity
AJ (12 combos) 50% equity
JJ (3 combos) 30% equity
33 (1 combo) 30% equity
22 (3 combos) 30% equity

On the fly you can simplify the analysis by dropping AA because it’s 40% which is close enough to our equity requirement. There are more combinations you have roughly 50% against than you have 30% against, which averages out to over 40%. So this clearly +EV.

Throw in the potential for a few random wtf moves from an unorthodox player, such as overplaying TT-66 you start including combos that are pushing you well into +EV.

tl;dr Easy call

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Spot 3:

The actual player in this game called with Ac3c on the board of Jc2c3d and ended up losing to KK, but lets look again at 3 possible ranges villain may have had.

• Sets only, and all possible combinations (though I think they wouldn’t have full combinations of 33 or 22, having raised in the small blind over 2 limpers)
• AA-JJ, one combo of 33 and 22 each, KdJd
• Hands above, QcTc and all combinations of 74 (inside joke that some of you will likely get, which covers the scenario with some strange bluffs)

The equity here is 30.15%, 45.79%, 63.86%, and roughly 37.5% is the break even point. You can see the situation is a bit grim against sets only, as you’ll come out quite short with only 30% equity, but it may be surprising to some that what is now only a pair of threes has over 51% equity against both KK and QQ, and while, as @unskilld pointed out, your hand blocks a lot of the natural bluffs, the hand also has ridiculously high equity against most of them. I tend to also think villain is unlikely to have full combos of 22 in range, and so we’re left in my opinion with a hand that is probably the favorite to win and a must call (I’m guessing overall equity against villain’s real range is around 55%).

Spot 4:

This is an imaginary hand inspired by heads-up play in the past with some of the more aggressive top ranked players, where I felt a bit out of my league, pushed into defensive lines more than I would have liked. With these players it was usually difficult to get any feel for how they constructed their ranges, as they seemed to be constantly making a variety of adjustments.

Here I’m going to start by assuming a relatively normal, if wide heads-up 3 betting range. Yes, some of these players would often raise much wider than I’m describing here, but they’d also have stretches where they would play more carefully.

• I’m assuming they will almost always 3 bet a min raise with AA-88, AQ+, ATs+, K9s+, Q9s+, JTs-54s, and J9s-53s
• Mostly 3 bet AJ, Axs, K8s-K7s, Q8s-Q7s, J8s-J7s, T7s-63s, KQo and 44+
• Fairly often 3 bet K6s-K5s, Q6s-Q5s, J6s
• Sometimes 3 bet K2s+, Q4s, J5s, T6s-T5s, 95s-73s, 42s, 32s, 22+, KJo and QJo

On the flop of Qd4c2d, after hero’s raise with 8d7d, it costs $22.4 million to potentially win $37.6 million. I don’t think the small continuation bet changes villain’s range too much, but the large all-in raise at the end gets rid of a lot of the middle parts of the range. Since I don’t really have major insight, I though again it might be good to see how 8d7d fairs against a few different ranges.
• Somewhat tight (33.03% equity): AA-QQ, 44, Qh4h, AdKd, AcQc, 5d3d, 5c3c, 4s2s
• Some surprises (33.78% equity): everything above plus AcKc, Ad4d, Ac2c, KcQc, KdJd, KcJc, QcJc, JdTd
• Thinner value with more bluffs (35.86%): everything above plus all pocket pairs down to 77, all diamond flush draws and many gutshot (or better) straight draws with back door flush draw, JTc (with some combinations reduced to reflect the parts of their range not always 3 bet)

At least for me, with the way I constructed these ranges, it just doesn’t quite work out. Even in the last, best case range it is:
• 35.86% x $37.6m = $13.5 million on the plus side
• 64.14% x $22.4m = $14.4 million on the minus side

I think the main problem is that we have poor equity against most of villian’s potential bluffs, and there just aren’t enough combinations of bluffs that actually have low equity against our hand. Admittedly, adding a 4th range that adds in 8c7c and 7c5c almost gets us to break even, and one more super low equity bluff would get us over into +EV territory (around 37.5% equity is enough), but I think the 3 betting pre-flop just thins out the low equity bluff candidates too much for this call to be +EV.

Spot 5 is the first hand where I was actually involved, and happened just moments ago, knocking me out of a tournament. With a relatively small stack relative to the blinds (12.5 big blinds), I make a small raise of 2.25 big blinds from the high jack with 99. 2 players have me covered, and one of them raises all in from the small blind after the CO and button fold. It costs me $21,344 to call, with just over $30,000 in profit if I win (it’s roughly a 2 to 1 over bet of the pot).

Context: As I raised I thought to myself, “this hand is good enough here for me to call a jam from anyone except Rusty…”. I had very few notes on him, but had not seen him 3 bet at all in a few dozen hands at the table. It didn’t seem like an adequate sample, but I wasn’t sure at the time that he would 3 bet all in like that with anything but relatively high pairs. Again, I don’t have a good sense at all of what his real 3 bet jam range there is, but: was it a call or a fold?

If he doesn’t 3bet much I would say the worst hand he has you’re ahead of is AK. I read the context as making him passive, so AQ- or TT- are likely flat calls from him. There are 24 combos of JJ+ and 16 AK. You’re drawing thin to 60% of his range and flipping against 40%. Seems like a fold intuitively for less than 2:1 and leaving yourself 10bb to fight another day. That’s if my read of his range is correct given the small sample.

Yeah… I think it really does just get down to what kind of range does he make that move with. I find it comic that even as I raised I told myself that it was ok to call a jam from anyone but him. You’d think I’d be able to better listen to my own advice. Of course just because he ended up with KK doesn’t mean his range is necessarily super tight, but I think I should have just gone ahead and relied on what evidence I had.

I always try and look at how many outs I have. Even with A-K off suit you have 58% preflop equity and a 45% chance you will rake the pot. A-K suited is not much better so all in at preflop ? If I don’t have an over-card pair i don’t even think about it. Sometimes just by watching a players play you can tell if they are bluffing etc. It just really all depends,