IRC Poker Quiz #6 - Pot Odds Edition

In NLHE we're heads up on the turn, the pot is $15 and our opponent bets another $10. How much equity do we need against his range to call?

another mindfuck, huh?

0%

Assuming we want the call to be profitable...

The breakeven point for calling is:

10/(10+25) ~ .29

Therefore we need at least ~29% equity to call.

In this example stack sizes were left out, so depending on how deep we are, and how likely villain is to pay off future bets, we could call with a hand that has less than ~29% equity - however, we need to make up for it on the river.

If calling closes the action, then all that matters is your pot odds, as there is nothing left to gain due to no future betting rounds. If villain will not pay off any bets on the river, then we have no implied odds and cannot call without the minumum ~29% equity.

Originally Posted by Micro2Macro

Assuming we want the call to be profitable...

The breakeven point for calling is:

10/(10+15) = .4

Therefore we need at least 40% equity to call.

In this example stack sizes were left out, so depending on how deep we are, and how likely villain is to pay off future bets, we could call with a hand that has less than 40% equity - however, we need to make up for it on the river.

If calling closes the action, then all that matters is your pot odds, as there is nothing left to gain due to no future betting rounds. If villain will not pay off any bets on the river, then we have no implied odds and cannot call without the minumum 40% equity.

ok say the board is 5678
we have TT
villain is bluffing 40% of the time and WILL BLUFF AGAIN ON THE RIVER but by shoving because the $10 bet is to make him have exactly a PSB on the river
60% of the time he has a straight and plays it exactly the same
should we call if he's bluffing 40% of the time on the turn?

10/35ths ? to call just the turn... more if we take into account the bets on the river

reason for edit: i had river on my mind.

Originally Posted by iopq

Originally Posted by Micro2Macro

Assuming we want the call to be profitable...

The breakeven point for calling is:

10/(10+15) = .4

Therefore we need at least 40% equity to call.

In this example stack sizes were left out, so depending on how deep we are, and how likely villain is to pay off future bets, we could call with a hand that has less than 40% equity - however, we need to make up for it on the river.

If calling closes the action, then all that matters is your pot odds, as there is nothing left to gain due to no future betting rounds. If villain will not pay off any bets on the river, then we have no implied odds and cannot call without the minumum 40% equity.

ok say the board is 5678
we have TT
villain is bluffing 40% of the time and WILL BLUFF AGAIN ON THE RIVER but by shoving because the $10 bet is to make him have exactly a PSB on the river
60% of the time he has a straight and plays it exactly the same
should we call if he's bluffing 40% of the time on the turn and 40% on the river?

Um. 50%?

Originally Posted by Micro2Macro

Originally Posted by iopq

Originally Posted by Micro2Macro

Assuming we want the call to be profitable...

The breakeven point for calling is:

10/(10+15) = .4

Therefore we need at least 40% equity to call.

In this example stack sizes were left out, so depending on how deep we are, and how likely villain is to pay off future bets, we could call with a hand that has less than 40% equity - however, we need to make up for it on the river.

If calling closes the action, then all that matters is your pot odds, as there is nothing left to gain due to no future betting rounds. If villain will not pay off any bets on the river, then we have no implied odds and cannot call without the minumum 40% equity.

ok say the board is 5678
we have TT
villain is bluffing 40% of the time and WILL BLUFF AGAIN ON THE RIVER but by shoving because the $10 bet is to make him have exactly a PSB on the river
60% of the time he has a straight and plays it exactly the same
should we call if he's bluffing 40% of the time on the turn and 40% on the river?

Um. 50%?

wait 40% is not even right it's 10/35 = 28.5%

Yeah just realized I forgot to add the bet+pot when doing the calc edited.

Originally Posted by bigspenda73

0%

that's the least we need, the most we need is 50% if we can play an unexploitable strategy on the river
if we can get exploited on the river, we need 100% vs. his range just to be sure

I wonder when Spoon thinks of these things, must be tough to find the time in between taking pictures of racist church signs and banging 14yr. old redheads.

Originally Posted by spoonitnow

In NLHE we're heads up on the turn, the pot is $15 and our opponent bets another $10. How much equity do we need against his range to call?

You don't need any equity, just click the damn call button if you have at least $10 left

But seriously, on the assumption that we won't have any further bets to call on the river, we're calling $10 to win $35 so we need something like 30%.

If we think our opponent will bet on the river, this obviously changes. Assuming we call $10 and our opponent then bets $x on the river, we need our equity against this range to be at least (10+x)/(35+x) to make a profit. Of course with the little information you give in your opening question we can't really give much of an answer since a lot of the factors we should consider aren't available to us such as implied odds or what our options are on the river (I'm assuming you care about the river, since you deliberately said we're on the turn )

Since you call it pot odds edition, I'll just say equity needed is:
(total bets we're calling)/(total bets we're calling + pot before we call the last bet)

Depends on stack sizes, and the nature of our hand and our opponent's likely holdings.

If the $10 puts you all in, it's pot odds. If you have $5 behind, you need 20% equity. If you have $10, you need 28.5% equity.

As stack sizes increase, the river action becomes more important - i.e. implied odds and the odds of someone getting bluffed off their hand.

If, on the river, you know whose hand is best and how your opponent will react, then you make much more money than otherwise. You can bluff him off his weak hands that beat you, you can extract the maximum when you have a strong hand, and you can fold when you're beat. Therefore the more we know this, the more +EV the river is, and the less equity we need on the turn. Conversely the more the opponent knows, the more -EV the river is, and the more equity we need on the turn.

If we have no made hand but are drawing to the nuts or near-nuts (e.g. nut flush draw on unpaired board), then we will almost always know if our hand is good or not, because on the river its value usually polarises to nuts or air. This means we don't get bluffed, don't get value towned, and don't miss value bets.

If we have a more marginal hand like TPGK, we have difficult decisions on the river. We'll sometimes have to fold the best hand when draws complete, we'll probably pay off TPTK+ hands, and we don't get value from much (missed draws will bluff or fold).

If we know our opponent's likely holdings and tendencies, this also helps. If we somehow know that our opponent has the nut flush vs our bottom set, and stacks are deep, you can play the river perfectly and so calling is +EV with only ~23% equity.

If your opponent's range is more balanced and you don't have reads, when he bets pot on the river you're sometimes going to get bluffed or pay off big hands, and when he checks you'll sometimes miss value or get checkraised.

So you need ~29% equity, but:

• Less if you're very short stacked

• Less if you're drawing to the nuts, more if you have a marginal hand

• Less if you can put your opponent on a narrow range, more if his range is balanced

• Less if your hand is face-up, more if it's disguised

• Less if your opponent is bad/exploitable, more if you're the one being outplayed

Some bounds, assuming $100 behind before the $10 bet:

0% suffices in some cases: You hold 27 and can put him squarely on 28 on a 8KQA board, and you know he'll fold to a river shove unless river is 2 or 8. You effectively have 44 outs with 0 implied odds, so a call is clearly +EV.

80% equity always suffices: Assuming you never win anything on the river and he takes your stack whenever he beats you (i.e. you call 100% on the river), you need (1-e)*(-100) + e*25 > 0.

Originally Posted by tunah

Some bounds, assuming $100 behind before the $10 bet:

0% suffices in some cases: You hold 27 and can put him squarely on 28 on a 8KQA board, and you know he'll fold to a river shove unless river is 2 or 8. You effectively have 44 outs with 0 implied odds, so a call is clearly +EV.

80% equity always suffices: Assuming you never win anything on the river and he takes your stack whenever he beats you (i.e. you call 100% on the river), you need (1-e)*(-100) + e*25 > 0.

what if we're $1000000 deep? nobody said our stack size

Originally Posted by bigspenda73

I wonder when Spoon thinks of these things, must be tough to find the time in between taking pictures of racist church signs and banging 14yr. old redheads.

I asked in IRC, "What would you like the next quiz to be about?" Someone replied, "Pot odds."

Originally Posted by killerkebab

Since you call it pot odds edition, I'll just say equity needed is:
(total bets we're calling)/(total bets we're calling + pot before we call the last bet)

I know what you're trying to say here, but you're a little off. The part in the bold is the reason you're a little off.

Originally Posted by tunah

If the $10 puts you all in, it's pot odds. If you have $5 behind, you need 20% equity. If you have $10, you need 28.5% equity.

Correct for the case that the $10 puts us all-in. That leaves some other cases, though.

Originally Posted by tunah

So you need ~29% equity, but:

Another case is when implied odds are going to be the deciding factor, and everything after this line describes the types of things that affect implied odds (one or more of which you described incorrectly). But there's a third case which you and killerkebab have barely touched on but haven't described in detail.

Originally Posted by tunah

0% suffices in some cases

This is an example of the fourth case I thought of. For what it's worth, I only came up with 4 cases.

Originally Posted by tunah

80% equity always suffices: Assuming you never win anything on the river and he takes your stack whenever he beats you (i.e. you call 100% on the river), you need (1-e)*(-100) + e*25 > 0.

You could argue this is an example of a 5th case that isn't always available.

Originally Posted by iopq

what if we're $1000000 deep? nobody said our stack size

This is key to a complete answer.

NOT ENOUGH INFORMATION PROVIDED. NO ANSWER CAN BE GIVEN AT THIS TIME.

That's what my poker bot said.

I'm sure I'm missing something/many things, but I see 5 cases?

1) Turn bet puts us all in (pot odds)
2) Turn bet puts opponent all in (pot odds)
3) Implied odds cases (2 mistakes listed above are: 1) we need less equity if we are short stacked (only if we don't have enough to cover the $10 bet, which puts us in case 1), and 2) we need less equity if our hand is face up, more if it is disguised (this is reversed, the better disguised our hand, the less equity we need since we can anticipate extracting more on the river when we hit).
4) 0% suffices case (already discussed)
5) We're potentially drawing to a split pot. For instance, we're drawing to a nut flush w/ a gutshot broadway draw and our opponent may already have broadway or tptk plus a broadway draw. This will increase the amount of equity we need (assuming we've got less than 50% equity) since the split pot takes away quite a bit of the value from our equity in the split pot case.

Originally Posted by okiman

since the split pot takes away quite a bit of the value from our equity in the split pot case.

No it doesn't. Equity includes split pots.

Originally Posted by iopq

Originally Posted by tunah

Some bounds, assuming $100 behind before the $10 bet:

what if we're $1000000 deep? nobody said our stack size

Yep, the bounds are going to vary with the effective depth, that was just an example. Sufficiently deep, and that strategy won't give you an upper bound. (If you know something about opponent's tendencies, you can get a better bound).

Hmm, I'm trying to think of a case where river play would be so optimal/pessimal that the bounds are relevant. Could be true if your opponent (or yourself) is a complete station, or possibly if effective stacks on the river are tiny. If this causes you to play badly you can shove over on the turn, but if (for example) you have the NFD, and there is so little behind that he can't fold his made hand on the river, then you can flat call with a little less equity because you'll win a slightly bigger pot than you'll lose. I guess this is just a case where the implied odds are precisely calculable.

Originally Posted by spoonitnow

everything after this line describes the types of things that affect implied odds (one or more of which you described incorrectly)

You'll tell me at the end, right?

Originally Posted by spoonitnow

Originally Posted by iopq

what if we're $1000000 deep? nobody said our stack size

This is key to a complete answer.

So the case that's missing is something that happens very deep? I'm trying to think of something that isn't just another way of saying 'implied odds'.

Maybe with a narrow enough hand range for opponent, scare cards are as good as outs?

Originally Posted by okiman

we need less equity if our hand is face up, more if it is disguised (this is reversed, the better disguised our hand, the less equity we need since we can anticipate extracting more on the river when we hit).

^^

Originally Posted by spoonitnow

Originally Posted by okiman

since the split pot takes away quite a bit of the value from our equity in the split pot case.

No it doesn't. Equity includes split pots.

I was thinking of equity as in how pokerstove gives it, which includes tie percentages despite the fact the win is less in split pots.

Originally Posted by okiman

Originally Posted by spoonitnow

Originally Posted by okiman

since the split pot takes away quite a bit of the value from our equity in the split pot case.

No it doesn't. Equity includes split pots.

I was thinking of equity as in how pokerstove gives it, which includes tie percentages despite the fact the win is less in split pots.

no, pokerstove adds splits as partial equity

Originally Posted by iopq

Originally Posted by okiman

Originally Posted by spoonitnow

Originally Posted by okiman

since the split pot takes away quite a bit of the value from our equity in the split pot case.

No it doesn't. Equity includes split pots.

I was thinking of equity as in how pokerstove gives it, which includes tie percentages despite the fact the win is less in split pots.

no, pokerstove adds splits as partial equity

Let me rephrase and be clear. I'm a moron.

Originally Posted by okiman

Originally Posted by iopq

Originally Posted by okiman

Originally Posted by spoonitnow

Originally Posted by okiman

since the split pot takes away quite a bit of the value from our equity in the split pot case.

No it doesn't. Equity includes split pots.

I was thinking of equity as in how pokerstove gives it, which includes tie percentages despite the fact the win is less in split pots.

no, pokerstove adds splits as partial equity

Let me rephrase and be clear. I'm a moron.

lol n1

this question can not be answered because to much info is missing.

Four areas I can think of.

1) Showdown equity locked in: Calling gets us all-in and we need pot odds to justify the the call based on our equity against our opponents range.
2) Implied odds situation: We think are currently behind, but we have outs to a hand we deem better than the opponents range. Against some part of the opponents range we won't be able to extract value, against other parts we will be able to extract a great deal of value, against some part of the range we will build a big pot and split, and against yet another part of the range we'll build a big pot and lose to a better hand. Stack sizes are crucially important as well as analysis of opponent tendencies - especially with each of the types of hand in his range that we hope to extract value from.
3) Reverse implied odds situation: We think we are currently best, and that if we call the bet we are also most likely best - but continued aggression on the river would narrow the opponent range towards hands that beat us. With large enough stack sizes the question can become that with 3,4 or 5 betting on turn or river we might suddenly find the range we play against to be beating our hand, but since flatting is an option for us at any point the worst case we need to consider is probably putting in $10 on the turn and $35 on the river to win $50 against a range of hands strong enough to bet both turn and river.
4) Steal equity: Calling the turn to steal on the river. A certain stack size is required for this to be effective. An alternative here is to raise the turn if opponent tendencies are such that this is more likely to be respected as strong. Steal can come in the shape of a bet, raise, check-raise, bet-3bet etc as stack sizes allow - or as the oversized shove. The important things here are consideration of your opponents capabilities, your image, your opponents likely range for you, the opponents likely hand (any weakness in his line to this point?), your opponents ability to lay down a second-nut hand or other hand good enough for him to bet strongly on turn and river etc.

Interesting about this hand is also that we don't know what limit this is. $15 pot and a $10 bet - is this 10nl in a hand that was 3bet aggressively pre and c-bet big on the flop? Or just raised pre and check-raised on the flop? Or did it see a sequence of puny near-min raises? Is it 25nl with a raised pot multiway to the flop where just one person called the cbet? Who took the initiative pre and post? Who has been making bets and who has been calling them? Is this 50nl? While it is important to know the stack of money behind, it is also important to know the size of the big blind, to give us some idea what kind of action has seen us to this point and what that tells us about the likely hand ranges.

equity =

Originally Posted by spoonitnow

In NLHE we're heads up on the turn, the pot is $15 and our opponent bets another $10. How much equity do we need against his range to call?

Thanks again Spoon for doing these... I do like them even though I'm normally wrong. They do help.

based upon the thread title I'm disregarding all but Pot Odds. It is my understanding that would be the pot compared to our amount to call... which is $25 against $10. Or 2.5 to 1. Pot Equity says our equit must be greater than our pot odds, thus our chance of winning needs to be better than 1/2.5 = .4 = 40% thus we need to be better than a 40% favorite to win against his range to call profitably...

Close?

Now I'll go back and read the other answers...

Originally Posted by Monty3038

Originally Posted by spoonitnow

In NLHE we're heads up on the turn, the pot is $15 and our opponent bets another $10. How much equity do we need against his range to call?

Thanks again Spoon for doing these... I do like them even though I'm normally wrong. They do help.

based upon the thread title I'm disregarding all but Pot Odds. It is my understanding that would be the pot compared to our amount to call... which is $25 against $10. Or 2.5 to 1. Pot Equity says our equit must be greater than our pot odds, thus our chance of winning needs to be better than 1/2.5 = .4 = 40% thus we need to be better than a 40% favorite to win against his range to call profitably...

Close?

Now I'll go back and read the other answers...

Seeing the other answers, I see the fact that I'm miscalculating pot odds though, it appears I need to add in my bet as part of what I am calculating... but I'm unclear as towards why. I understand that ONCE I bet the total pot will be $35 but the fact remains I'm betting 10 to win 25. Not to win 35, as I haven't put it in yet, so the decision needs to be worth putting it in, I guess... but maybe that is what the decision should be based on, the assumption it is in.

That is the confusion on my part I think, guess it's back to basics for me... since it would seem you wouldn't put it in if the odds were bad...

Doing it the other way leads to 1/3.5 = 28.6% so I would need to be ahead of his range more than 28.6% of the time to make this profitable... if I understand it right.

Originally Posted by Monty3038

That is the confusion on my part I think, guess it's back to basics for me... since it would seem you wouldn't put it in if the odds were bad...

Doing it the other way leads to 1/3.5 = 28.6% so I would need to be ahead of his range more than 28.6% of the time to make this profitable... if I understand it right.

it's an issue of converting ratios into percentages that makes most people lost on this. your risk:reward ratio is 10:25 because you are putting $10 at risk for a chance at the $25 that are already in there (the original pot of 15+his bet of 10). so in order to make this a break even endeavor your odds need to be 10:25, so for every 25 times you lose, you win 10 times. so there are 35 total scenarios (25 losses and 10 wins), so you win 10/35 or 28.6% times.

so you just "add the money you're putting in" just as a sort of shortcut to achieving the math, it's not actually what's logically taking place. what's really going on is that ratios compare how many wins happen for every loss, whereas percentages compare how many wins total over the course of 100 hypothetical scenarios. ratios apply more directly to the problem at hand but percentages are easier to calculate with/convert equity with

Originally Posted by surviva316

Originally Posted by Monty3038

That is the confusion on my part I think, guess it's back to basics for me... since it would seem you wouldn't put it in if the odds were bad...

Doing it the other way leads to 1/3.5 = 28.6% so I would need to be ahead of his range more than 28.6% of the time to make this profitable... if I understand it right.

it's an issue of converting ratios into percentages that makes most people lost on this. your risk:reward ratio is 10:25 because you are putting $10 at risk for a chance at the $25 that are already in there (the original pot of 15+his bet of 10). so in order to make this a break even endeavor your odds need to be 10:25, so for every 25 times you lose, you win 10 times. so there are 35 total scenarios (25 losses and 10 wins), so you win 10/35 or 28.6% times.

so you just "add the money you're putting in" just as a sort of shortcut to achieving the math, it's not actually what's logically taking place. what's really going on is that ratios compare how many wins happen for every loss, whereas percentages compare how many wins total over the course of 100 hypothetical scenarios. ratios apply more directly to the problem at hand but percentages are easier to calculate with/convert equity with

Thanks for the explanation, that does make some sense with the ratios thing now... In the past I've pretty much went with the pot compared to amount to call, then once resolved to a x to 1 ratio, just added one to the bigger number.

Originally Posted by littleogre

this question can not be answered because to much info is missing.

It can be answered in cases, much like what Erpel has broken up for us here:

Originally Posted by Erpel

Four areas I can think of.

1) allin blah blah go go gadget math problem
2) we have a hand that improves some % of the time and we're trying to make more money when it does
3) we have a hand that rarely improves and we're going to be in a shitty spot on the next street because we won't know if we're ahead or behind
4) we have a shit hand and can rely on fold equity on the next street

Interesting about this hand is also that we don't know what limit this is.

Everything is right except for the bold. The stakes aren't what changes the types of things you've listed.

So anyway, the whole point is that (besides an idea of your opponent's range) sometimes pot odds are all you need to know for a hand, while other times there is a lot more to it.

A more intuitive approach is just doing the equation.

Y is the % you win
(1-Y) is the % you loose
And to see what Y needs to be for you to win $0:

Yx25 - (1-Y)x10 = 0

Then you just solve that and there you go.

But if you're not all-in then this is not what you're looking for. blah blah implied odds blah blah reverse implied blah blah

And in case any one else's brain works like mine, for pot odds:

You're putting $10 in to get a share of the pot. The total pot will be $35, and obviously you want your share to be worth at least $10, so as a percentage it's $10/$35 = 29%.

edit this is just how I remember the pot odds/equity formula, and should only be applied to pot-odds situations. not suitable as a complete milk food for infants.

Originally Posted by tunah

And in case any one else's brain works like mine, for pot odds:

You're putting $10 in to get a share of the pot. The total pot will be $35, and obviously you want your share to be worth at least $10, so as a percentage it's $10/$35 = 29%.

If there is no more betting.