Should We Be Calling Stations?

[Phoenix Wright]

It is shocking how little math we poker players actually know for the most part. We can memorize a few formulas like how to calculate outs and estimate the rest on the spot if we aren't math-people. However, I had a pot odds question that confuses me a bit. I'll detail my reasoning and hopefully someone can highlight where I went wrong in my conclusion if I did...

Most of the time, I think players understand pot odds in the vague sense of if they should call off a River bet etc. but seldom consider what odds their bets are giving the opponents. So if I understand this correctly, then...

Let us assume we are on the River. There is exactly 1,000 chips in the pot (nice round number isn't it? Almost as it it was chosen for simplicity ). We are now heads up and Villain bets 500 chips (half of the pot). We now risk 500 chips to call that bet to potentially win 2,000 chips (1,000 in pot + their 500 bet + the 500 we add to call). Therefore, we are offered 3:1 odds and need 25% equity to continue (call). I think most players understand this concept but that is where my concern begins...

25% equity isn't so difficult to have, so does this mean we should all be calling stations? Let us take pocket 9s for example (say 9s9c, but it doesn't really matter what suit). According to Equilab's free calculating, 9s9c versus a random hand has 72.06% equity to win. This means that if my opponent were to show me their "premium hand" of 99 and I got any random hand, then I should call with these odds because 27.94% equity (100 - 72.06 = 27.94)? This doesn't feel right at all. I feel like I'm overlooking something here.

I suspect one could say that a "random hand" (say I didn't look at my hole cards) could be anything; it could be trash like 72o or the renowned AA, but this "random hand" doesn't work here because players use ranges and don't play 100% of the hands. Fair enough, but without knowing the opponent hole cards for certain, then are we still calling down almost everything?

Another consideration I have to my troubling conclusion might be that we all know pot odds are NOT everything in poker. It is merely a factor in our decision-making progress because naturally a thinking Villain wants to give us good odds to continue with worse hands and pay off their value bets (basically the core thought behind GTO strategy). However, how much are we betting to get Villain to fold? Usually raising x4 their bet does the trick, but what is the math strictly saying? No emotions, but simply how big must we realistically go to force someone off a hand? If we shove a pot sized bet, then they only need 33% equity to call. If we shove 2x the pot (how often do you do that?), then they can continue with about 40% equity! Are we ever able to force players off a hand or is it strictly about ICM and applying pressure based on effective stacks?

Hopefully someone can correct my thinking because I don't want to be a calling station Okay sure, I'll call if I'm getting odds to call, but by my thinking process I'm finding it really difficult to fabricate a situation where I should fold. Help anyone!

 

[Collin Moshman]

Welcome to limit hold 'em! The dilemma you're describing applies even more to limit games where you're always getting great odds.

Here are a few thoughts:

1. Like you said, we have a specific hand instead of random cards. With 72o, we shouldn't call vs 99 getting 3:1 pre-flop.

2. Equity isn't everything. For example, pre-flop we could be getting 3:1 odds to defend the big blind and still decide correctly to fold a junk hand that still has 28% equity against our opponent's range. The reason is that we're OOP and too unlikely to realize that equity. We need to think about whether future betting helps or hurts us.

3. A lot of the time, yes -- You're correct to make wide calls based on odds. This is particularly true in all-in or river situations. If you have 27% equity and you're getting 3:1, you're (usually) correct to call at the river, in an all-in, or at any point earlier in the hand if future betting is neutral or in our favor.

 

[Nafor]

However, how much are we betting to get Villain to fold? Usually raising x4 their bet does the trick, but what is the math strictly saying?

If I'm not completely off with my math then raising a pot of 1000 chips to 4000 would require your opponent to have 75% equity to make a profitable call. But poker is never this straightforward

 

[Phoenix Wright]

Welcome to limit hold 'em! The dilemma you're describing applies even more to limit games where you're always getting great odds.

Here are a few thoughts:

1. Like you said, we have a specific hand instead of random cards. With 72o, we shouldn't call vs 99 getting 3:1 pre-flop.

2. Equity isn't everything. For example, pre-flop we could be getting 3:1 odds to defend the big blind and still decide correctly to fold a junk hand that still has 28% equity against our opponent's range. The reason is that we're OOP and too unlikely to realize that equity. We need to think about whether future betting helps or hurts us.

3. A lot of the time, yes -- You're correct to make wide calls based on odds. This is particularly true in all-in or river situations. If you have 27% equity and you're getting 3:1, you're (usually) correct to call at the river, in an all-in, or at any point earlier in the hand if future betting is neutral or in our favor.

Thank you for this; I was questioning whether I miscalculated or something - seemed like in so many situations I could fabricate, there seemed to be odds to call - just to be on the safe side conveying my point, I had to say something we all agree isn't objectively good like 72o

 

[Phoenix Wright]

If I'm not completely off with my math then raising a pot of 1000 chips to 4000 would require your opponent to have 75% equity to make a profitable call. But poker is never this straightforward

Yeah I considered raising super big too to make the odds less favorable to a call as well, but I don't think raising a 1k pot to 4k is a commonly correct situation nor a safe strategy.