Shoving based on Hand Ranges + manufactured Pot Odds

chkmte

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After years of being a sub-average NLHE player, I've used this summer to study the game like a champ. My imagination and the advanced content at my disposal are forcing me to think differently than before. I'm trying to simplify the game but that's not easy because the game has become much more understood in recent years.

I'm going to run-down a situation, and you brilliant people should tell me if I have a correct understanding or not. Deal?

  • SB is in for 1. BB is in for 2. HERO opens for 6 with random cards. Everyone folds except for the DB, who raises to 18 with standard open range (via PokerStrategy.com). Pot is 27, HERO must call 12.
  • Without looking at his cards, HERO shoves the remainder of his stack (200), and is forcing DB to call 194 into 221 imputing 1.14-to-1 odds, which would require 87.8% equity (I think).
  • So, technically speaking DB is facing a -EV call no matter what their two cards, as AA will win about 85% of the time.
  • Additionally, it looks like when Villain folds over 49% in this spot, HERO profits (per Red Chip Poker Fold Equity Calculator).

It seems shoving and picking up 27 in this spot isn't such a bad concept. Again, HERO has no idea what two cards he has. I guess what I'm trying to understand and perhaps prove to myself is this: Playing the specific scenario as described is a more profitable path than simply playing my cards. Feel free to criticize and critique now.
 
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TheWhat

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"Whoever bets the most wins, cards just break ties." Is all that comes to mind. Really just here to see what the smart folks say.
 

upNdown

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One of the reasons I prefer tournament poker is that ICM makes these situations less clear. Translation, I can fold like Hellmuth and feel less bad about it. Further translation, see the comment above.
 

chkmte

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After giving this more thought, 1.14-to-1 odds can’t be 87.8 equity. That should be closer to 45-50%. But how to transform pot-odds to equity?
 

CrazyEddie

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Without looking at his cards, HERO shoves the remainder of his stack (200), and is forcing DB to call 194 into 221 imputing 1.14-to-1 odds, which would require 87.8% equity (I think)

194 + 221 = 415

194 / 415 = 0.4675 aka 46%
221 / 415 = 0.5325 aka 53%

Opponent needs to win 53% of the time in order to profitably call.

Every hand he raised with preflop will win more than 53% of the time against your random two cards. He will call every time and you will lose money, rapidly.

You need to read more about how to calculate odds and how to apply them, as you have made a fundamental mistake in your reasoning here.

Please continue your studies! Enjoy it, and best of luck!
 

DZPoker

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OP can correct me if I’m wrong, but I think the ‘2 random cards’ was used to take the focus away from his particular cards vs Villain’s.

Villain will be making his decision to call/fold by comparing his cards against what he assumes Hero has based on everything he currently knows, not just against ‘any two cards’. In my opinion this will likely lead to a fold very early but if the technique is tried repeatedly, that then becomes part of ‘everything Villain knows’ and at the right time, the call will be made that quickly reversed any earlier winnings by Hero. Therein lies the problem.

I’m by no means an expert though, so hopefully others will weigh in!
 

chkmte

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OP can correct me if I’m wrong, but I think the ‘2 random cards’ was used to take the focus away from his particular cards vs Villain’s.

Villain will be making his decision to call/fold by comparing his cards against what he assumes Hero has based on everything he currently knows, not just against ‘any two cards’. In my opinion this will likely lead to a fold very early but if the technique is tried repeatedly, that then becomes part of ‘everything Villain knows’ and at the right time, the call will be made that quickly reversed any earlier winnings by Hero. Therein lies the problem.

I’m by no means an expert though, so hopefully others will weigh in!

So according to Equilab, UTG with random cards has 42% equity vs DB with standard holdings from that position.
 

chkmte

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194 + 221 = 415

194 / 415 = 0.4675 aka 46%
221 / 415 = 0.5325 aka 53%

Opponent needs to win 53% of the time in order to profitably call.

Every hand he raised with preflop will win more than 53% of the time against your random two cards. He will call every time and you will lose money, rapidly.

You need to read more about how to calculate odds and how to apply them, as you have made a fundamental mistake in your reasoning here.

Please continue your studies! Enjoy it, and best of luck!
Can we walk through this if you have time - starting with the '415'. I'm coming up with '403', but I really want to learn this...
 

chkmte

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OP can correct me if I’m wrong, but I think the ‘2 random cards’ was used to take the focus away from his particular cards vs Villain’s.

Villain will be making his decision to call/fold by comparing his cards against what he assumes Hero has based on everything he currently knows, not just against ‘any two cards’. In my opinion this will likely lead to a fold very early but if the technique is tried repeatedly, that then becomes part of ‘everything Villain knows’ and at the right time, the call will be made that quickly reversed any earlier winnings by Hero. Therein lies the problem.

I’m by no means an expert though, so hopefully others will weigh in!
As I understand, UTG would have range advantage as that position is 'supposed' to be opening with a narrow/strong range.
 

DZPoker

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So according to Equilab, UTG with random cards has 42% equity vs DB with standard holdings from that position.

My point is that the math is only part of the equation. In reality, Villain is factoring more in, and in this specific situation that includes your betting behavior. If it becomes clear you’re shoving to buy the $27 over and over, you’ll hit the player who takes the calculated risk with the right cards to try to steal your $200 instead. Will he get it right always? Nope. But he’s what swings the math and the times he’s right, he swings it hard.

So against a computer programmed to play by the math only, I agree you win. But in reality, I believe you lose.

Again, just my thoughts...
 

Highli99

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I’ve been playing poker a Long time. My approach to the game is not really GTO and I can’t calculate the math as precisely as you did in your example. That’s not to say I don’t study game theory I’m just saying I don’t know it as well as you might. But in your example above I would be calling a certain percentage of time with a certain range. You’ll get away with it here and there but once I sense you are doing it too often I’ll get frisky. Many, many other players will call you off with any two cards because gambol. Can’t imagine there is a player who would fold aces pre. If there is, may God have mercy on their soul.
 

DZPoker

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I'll tell you what makes poker no fun, that's losing. I'm trying to correct that by making sound mathematical judgements.
Then switch to Limit :). 100% by the math works a lot better in Limit (IMHO)!
 

CrazyEddie

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>Opponent needs to win 53% of the time in order to profitably call.

Woops, sorry, got the wrong side of the bet. That's how often you need to win to make his call unprofitable for him. He only needs to win 46% of the time.

---

Also, opponent only needs to call 188, not 194. After your shove, the bet is 206 (your inital 6 plus another 200 from your all-in bet). Opponent has already put 18 into the pot this round, leaving 188 for him to call and add to the pot in order to match the 206 that you have put into the pot.

The pot stands at 1 + 2 + 6 + 18 + 200 = 227. He must call 188 in order to win 227.

The pot odds presented to him are 188 to 227. For every 188 he bets, he will win 227 on top of receiving his bet back, if he wins. That reduces to 188/188 to 227/188 which is 1 to 227/188 which is 1 to 1.2 .

You can see the bet he is being offered as a percentage as follows: 188 / (188+227) which is 188/415 which is 0.453 which is 45%. You can also see the same thing from the odds: his odds are 1 to 1.2, so as a percentage the bet he is facing is 1 / (1+1.2) which is 0.45 which is 45%. This is the portion of the pot after he calls represented by the amount of his call, i.e. the portion of the post-bet pot consisting of his bet. In order to profitably call, his equity in the hand must be that much or higher, i.e. 45% or higher.

In other words, by betting a huge amount into a tiny pot, you are offering him a nearly even-money bet, a coin flip - your LARGE BET + tiny pot vs. his LARGE BET. If his hand is more likely to win than yours - if the coin is weighted to his side - then you're offering him a good bet and he should take it. Since you're making this bet with any two cards and he's holding something like the top 10% or 20% of hands, his holding is much better than yours (on average) and much more likely to win (on average). You're offering him a bet of 45% and his equity is at the absolute minimum higher than 50%. He should take this bet.

That presumes he knows that you're betting with any two cards. I assumed he knew that since you said you didn't look at your cards. If he doesn't know that, then whether or not he will call depends on what he's holding and what he thinks you might be holding. That's impossible to know from your given scenario; it depends on his history with you, his read on you, how good a player he is, whether he's aggressive or passive, etc etc. Regardless, whether or not he does call, if he calls, he's going to win money on average, by the handful.

If you bet like that with any two cards, and he doesn't know that you're betting with any two cards, that's called a bluff. If he folds to the aggressive bet you made with random cards, you win the tiny pot. If he calls your bluff, his better-than average hand will more often than not beat your exactly-average random hand and you will more often than not lose your very large bet.
 

davislane

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I know my numbers are incorrect. I'm trying to get to the right numbers. :)
assuming utg and db started with 200 each plus blinds 403 is correct. 194 is incorrect as db had raised to 18 leaving 182 behind. thats is the 12 discrepancy.
 

CrazyEddie

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You're asking good questions. Lots of people get confused by calculating odds, which is one reason poker can be so profitable.

Keep studying, keep asking questions, and keep practicing.
 

CrazyEddie

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One way to conceptualize it is like this:

Odds are your bet vs. the rest of the pot.

Percentages are your bet vs. the entire pot.

There's 2 in the pot. Opponent bets 1. Now there's 3 in the pot, and you have to call 1 to stay in the hand.

Your bet is 1.
The rest of the pot is 3.
The entire pot will be 4 once you add your bet.

The odds are 1 to 3.
The percentage is 1/4 which is 25%.
These two statements mean exactly the same thing. They are always both true. They are merely restatements of each other. If you know either one, you can calculate the other.

If you call, you will break even if you win one time for every three times you lose (look at the odds), which is the same as winning 25% of the time (look at the percentage). If you win more frequently than that, then calling will be profitable. If you win less frequently than that, then calling will cost you money.
 

L3urntout

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Eddie simplified it really well, next step is to break it down into commonly seen scenarios so you know what percentages you are given/what you are giving your opponent!

Half is pretty easy, then 25, 33, 60, 66, 75, 80, pot , 1.25, 1.5, 2, 2.5, 3

Are all useful. If you know it makes it easier to think about other things (range, game script)
 

L3urntout

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Example scenario, Hero UTG, Villain on the button. Hero AcAh, raises to 3BB, folds to Villain who calls. SB and BB Fold.

Flop comes AsTs6h. How much should you bet to get value out of flushes? If you have a flush draw as villain we are talking approx 9 outs so a bit over 36% odds to hit your flush, so x / (1 + x) where x is your bet needs to be greater than 36%.

So solve for x if it was 36% ---> .36 + .36x = x ----- .36 = .64x ----> x = .5625 so around 56.25% of pot is the breakeven.

So you probably want around 60-75% pot, generally higher if you are OOP as you are giving up on info by acting first, so you generally want to play as if you're stronger, especially since your range is stronger as the PFR UTG and you have top set.

So let's say you bet .75 pot and the villain actually raises you, 3x your raise, so now you have a 4x original pot, and you need 1.5pot to call. In this spot with Top set, since he already has his money in the pot, just calling is actually more value in the Villain favor, so you again should reraise him and get additional value if he calls (you want him to all in). So in this case, his bet is already 2.25p, you have .75p in front, we need to recalculate how much you need to reraise to gain value again.

with y as your bet, (.75p + y - 2.25p) / (4.00p + y) = 36%

-1.50p + y = 1.44p + .36y

.64y = 2.94p

y = 4.59p

So with 2.25p for villain, you're raising to over 5.34p which is just under 2.25x

So I would raise to around 2.5x his total bet, depending how much there is much behind at that point you can look at just shipping it.
 

Legend5555

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Example scenario, Hero UTG, Villain on the button. Hero AcAh, raises to 3BB, folds to Villain who calls. SB and BB Fold.

Flop comes AsTs6h. How much should you bet to get value out of flushes? If you have a flush draw as villain we are talking approx 9 outs so a bit over 36% odds to hit your flush, so x / (1 + x) where x is your bet needs to be greater than 36%.

So solve for x if it was 36% ---> .36 + .36x = x ----- .36 = .64x ----> x = .5625 so around 56.25% of pot is the breakeven.

So you probably want around 60-75% pot, generally higher if you are OOP as you are giving up on info by acting first, so you generally want to play as if you're stronger, especially since your range is stronger as the PFR UTG and you have top set.

So let's say you bet .75 pot and the villain actually raises you, 3x your raise, so now you have a 4x original pot, and you need 1.5pot to call. In this spot with Top set, since he already has his money in the pot, just calling is actually more value in the Villain favor, so you again should reraise him and get additional value if he calls (you want him to all in). So in this case, his bet is already 2.25p, you have .75p in front, we need to recalculate how much you need to reraise to gain value again.

with y as your bet, (.75p + y - 2.25p) / (4.00p + y) = 36%

-1.50p + y = 1.44p + .36y

.64y = 2.94p

y = 4.59p

So with 2.25p for villain, you're raising to over 5.34p which is just under 2.25x

So I would raise to around 2.5x his total bet, depending how much there is much behind at that point you can look at just shipping it.
This example of course assumes you know your opponent has a flush draw, and it ignores stack sizes and implied odds.

Also, your opponent is calling a bet to hit on the next card. It's not as if the opponent gets to call this one bet and see both turn and river thus realizing his full 35% equity. So betting 75% pot is overkill in the sense that it is way more then enough to deny proper odds to hit a flush on the turn. Somewhere between 50%-60% pot sized bet is the break even point for the person to call holding a flush draw if they get to see both cards for this one bet. But it's only about 25% pot with one card to go.

This is why implied odds matter so much though. And why generally, the more draws there are on the board the more the "value hand" wants to choose a larger size. It charges the opponent's wider calling range more, and protects the value hand's equity in the pot.

What you will see very often from solver modeling is that we generally want to choose smaller sizes on the flop when the opponents range potentially contains more equity, and larger sizes on the turn when our equity increases. The greater your equity in the pot is, the more money you make by being larger and getting called.

But even then, you can't easily get tons of value on dry boards with hands like top set, or on monotone flops with hands like the nut flush. You just block all the value and calling hands from your opponent' range. So betting large won't work that well.

So betting to debt proper odds is useful fundamental to understand, but in practice when you are trying to balance your range against the opponents range, it's much trickier.

#pokeriscomplicated
 

L3urntout

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This example of course assumes you know your opponent has a flush draw, and it ignores stack sizes and implied odds.

Also, your opponent is calling a bet to hit on the next card. It's not as if the opponent gets to call this one bet and see both turn and river thus realizing his full 35% equity. So betting 75% pot is overkill in the sense that it is way more then enough to deny proper odds to hit a flush on the turn. Somewhere between 50%-60% pot sized bet is the break even point for the person to call holding a flush draw if they get to see both cards for this one bet. But it's only about 25% pot with one card to go.

This is why implied odds matter so much though. And why generally, the more draws there are on the board the more the "value hand" wants to choose a larger size. It charges the opponent's wider calling range more, and protects the value hand's equity in the pot.

What you will see very often from solver modeling is that we generally want to choose smaller sizes on the flop when the opponents range potentially contains more equity, and larger sizes on the turn when our equity increases. The greater your equity in the pot is, the more money you make by being larger and getting called.

But even then, you can't easily get tons of value on dry boards with hands like top set, or on monotone flops with hands like the nut flush. You just block all the value and calling hands from your opponent' range. So betting large won't work that well.

So betting to debt proper odds is useful fundamental to understand, but in practice when you are trying to balance your range against the opponents range, it's much trickier.

#pokeriscomplicated

Sure it is "way" more but implied odds are exactly what make it reasonable for a flush draw to call you and give up if the turn is bet again if they don't hit. You don't necessarily have top set, so you're not always going for 3 streets of value/protection, and villain doesn't know that. You could get a bunch of Ax combos, lower sets to call you down as well.

Also, OOP makes it easier to justify calling higher pot %, and acting behind i'm pretty sure it is a leak to fold EVERY flush draw here. I mean this also assumes that there isn't a gutshot as well...
 
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