I read the poker math that matter book recently, and that book based all it's assumptions on villain hand ranges.

My problem is though, to be able to compute the numbers while playing, the hand ranges cannot be huge, which they most often are. How does one shrink or estimate the villain hand range to small enough sample that f.e equity can be calculated mid game?

Yes, experience and study will allow you to become 'automatic' over time .. some Players take longer than others and only you can determine if you need 'more' study during this process.

Each poker hand is a story. You are telling your opponents a story and they are also trying to convey their story to you. It's up to you to decide which of these stories makes the most sense before moving to the next chapter (street of play). Unfortunately some 'readers' (Players) just don't comprehend what you're trying to tell them!! GL

While the solvers give equity to the nearest 0.1 or even 0.01%, being able to calculate your equity to that degree of accuracy is not really that critical. Most players cannot do so. What is important is to have an approximate idea of what your equity is and how that affects your decision making.

Just to give a simple example, this is from a $1 buy in tourney I played. I was BB and folds to button. Button was short stacked and shoved for 2.5 BB. I had 97o. A quick risk reward calculation - If I call I risk 1.5 BB to win 4BB (his 2.5, the 1BB I posted plus SB’s 0.5). I need 1.5/5.5 = 27.3% equity to call. Do I have it? He’s shoving wide in this spot, so give him any pair, any ace, plus most Broadway combos. Against 22-66 it’s about 50%. I’m about 30% vs 77-99, and maybe 15% vs TT+. I’m probably about 40% on most of the rest of his range other than A9 or A7 combos.

The point is that while I don’t know my exact equity, I do know that it’s greater than 27% against the majority of his range. I called. I realized he didn’t understand this type of thinking by his reaction. He showed 44. I caught a 7 and busted him, and he lost it. He called me a fish and swore on and on about how the site was rigged and “How could you make such a dumb call; you had to know you were behind?”. Of course that’s the whole point — I did know I was behind, but I had the proper equity to make the call anyway.

maybe give an example where you have to look at your cards before calling?

Agreed. It was an easy decision and ATC would have called. The principles involved with the equity calculation are the same for a more difficult decision, though. I thought that working through the equity calculation would be more helpful to OP than just saying “Call with ATC.” The calculation explains WHY you call with ATC.

Right on que I see a hand from a SnG on PokerGo where PHell semi-tank folded A7o (face up) from the BB against B shove of 8.5 BB and the table lit into him. He said he saw the Ace and got excited, but he didn't like his 2nd card so he folded.

The best comment was that 'every' poker player under 30 would've snap called after seeing the Ace, not caring what the other card was and then getting a sweat after the chips were in the middle.

The point is 'any' Ace has equity against that shoving 'range'. Probably not 'ahead' all the time but the Ace holds plenty of equity if you get to see all 5 cards come out.

You should almost never be able to play a session of PLO and not hear this type of table talk at the lower levels. It's very hard to not have equity in PLO, so you can see a lot of decisions that may look very questionable at Showdown. If you are HU in PLO the worst odds you can have are 2 to 1, so all you need is 33% or better to continue. So if you put your opponent on AA (any over-pair xx holding) and hit at least one pair on the Flop you will find yourself getting the right price to call a shove baring any 'extreme' straight or flush texture that completely misses your holding. Of course the AAxx guy is going to go nuts at Showdown when you hit a 3 on the River for two pair .. GL

I am one that doesn't know about how all this equity business goes but i do know it's important. I have read a little, but still find the concept hard to grasp. BUT i do freaking love the way you explained your thought process and I want to learn that more than ever!!!

It’s a pretty simple concept really. Many beginners just say “I am behind, I should fold”, but depending on the situation that may not be the case. Even if you’re behind NOW, that doesn’t mean you cannot win the pot. Equity is just your chance of winning the pot. If you have enough equity, it can be correct to call a bet even if you know your opponent is ahead.

Simple example: you are on the flop with AThh. (Assume a live game), your opponent accidentally exposed his cards and he has KK. Flop is Kh Qs 6h. He bets $10 into a $40 pot. You and two others call. 2d on the turn. He bets $20 into the now $80 pot. The two players ahead of you fold so it’s heads up. Do you call?

You know you’re behind, but it’s a clear, easy call. You have 10 outs — 7 hearts (note that the Q and 2 are not outs) plus the three jacks that aren’t hearts. You know 8 cards, so there are 44 left in the deck. Your equity is therefore 10/44 = 22.7%. How do we know if this is enough to call? A simple formula is risk/(risk+gain). If that value is less than your equity, call. In this example calling risks $20 to gain $100 (the $80 already in the pot plus the $20 your opponent bet). The formula then gives 20/(20+100) = 16.7%, which is less than your equity so you call.

It won’t always be so straightforward; you obviously won’t generally know your exact equity since you don’t know your opponent’s hand. You can approximate it reasonably well though. Also the risk/reward calculation I gave is valid, but incomplete. In my example, (unless the bet put you or your opponent all in) there can be further action on the river. If you hit one of your outs, you could bet and possibly get more gain from calling than what was figured above. If you miss, you obviously will fold, so you aren’t increasing your risk by calling. This it’s often ok to call even if your equity falls short of what the risk/gain formula indicates. This concept is called implied odds, and it’s often the reason you can call draws.

I love your statement !
There are way to many players in low level live games like 1/2 that play so Incorrectly sometimes its hard to tell where they are at. They are just stupid enough to be dangeous.
I cant tell you the number of times I see some clown call a sizeable 3 bet pre flop with something like A3 off suit and they had 2 guys behind them.
I think most guys here would agree that given the situation that is a Terriable call.