Determining Pot Equity (& losing my mind)

brianon

Ok. So I'm losing my mind trying to understand pot equity

Can anyone explain (try to anyway) it to me or show me where to go to get an explanation ?

Say with only river to come I've a four flush draw (20%|4:1 against to make it).
Pot is $200 of which I contributed $50.
Only one opponent left.
I'm UTG. How do I determine if I should bet ? and how much ?

This is wreckin my head !

DeVore

Um, I'm not sure I understand what you mean by Pot Equity. I also am wary that you are remembering how much you put into the pot. Its gone now so you should focus on the total and the amount you are being asked for primaraily. You're opponents stack and your remaining stack too.

If I have the nut flush draw I might well stick in a decent bet, say 100 dollars if the table is very tight. I might not do that on a different table and simply play meek to see if I hit. No point betting all in if he's only got 50 dollars left. He might not make you pay it to see the river and then you might save 50 notes if you dont hit.
There are a ton of ways to play it, Hector or Hyzepher would be the guys to ask as they play more online cash a day then I have entirely probably

DeV.

Eoin

Say with only river to come I've a four flush draw (20%|4:1 against to make it).
Pot is $200 of which I contributed $50.

Like Dev said, forget about how much you put in for the time being (being comitted to a pot is a totally different issue).

Lee Jone's book (winning low limit hold 'em - good beginners book) explains odds, implied odds etc quite well, and I think from a mathematical point of view it goes something like this:

You say that the odds are 20% (is this not 5:1 against, not 4:1?). Presuming it is 5:1, Then if the size of the pot is greater than 5 times the size of the bet you will have to call, then you should call as the odds of you hitting your hand are better than the odds you are getting.

For instance, if you played the same hand 5 times, you would expect to win once. Therefore if you were paid more than 5:1 each time you played the hand you would make a profit the one time out of 5 you did win.

This, of course, relies on your hand being the best one should the river hit you, and I'm nowhere near experienced enough to advise whether you should actually call or not in a real life scenario - I will leave that up to the people like Dev etc who actually know what they're talking about.

In fact, maybe someone more knowledgeable than me can let me know if I am way off base with what I did say?

Dr_Colossus

Eoin that's pretty much it. With the nut flush draw and only the river card to come you have a 1 in 5.11 chance of hitting your flush (you have seen 6 cards therefore 46 unknown, you have seen 4 are of your suit therefore 9 possible suited cards to fill your hand)
If you are under the gun and check into a pot of $200 and the one player behind you bets $45 then the pot is offering you pot odds of 5.44 (a call of $45 to win $245) From a statistical point of view alone a call is +EV. This +EV doesn't even factor in the implied odds that if your flush does hit and that the board doesn't pair thereby giving you the absolute nuts that your opponent might call an additional bet on the river.
Hope this helps.

Ian147100

If there are 2 clubs on board and you've got 2 in your hand then of the cards unseen to you there are 9 clubs left. If it's a 9 player ring game and 7 guys have folded then that's 14 unseen cards, your opponent has 2 unseen cards to make it 16, the 2 burnt cards are also unseen so that makes 18, there are 4 cards on the table, 2 in your hand and 28 left in the deck. Therefore there are 24 cards are in use and there are 28 are remaining.

People will tell you that one quarter (6) of the 24 used cards are clubs, so that's 4 clubs you can't rely on (because you've got 2 of the 6 in your hand). By this rationale you can determine that 5 of the 28 cards remaining are your suit and you're going to hit your river card 1 time in every 4.6 attempts and therefore your 25% chance of success has turned into around an 18% chance. I don't know if the math can be relied on that much but what I do know is that because I've got 2 clubs in my hand and there are 2 on board the likelihood is that there are less clubs left in the deal than any other suit.

At the end of the day though there isn't any way of accuratley calculating whether or not you're going to make your flush, there may be only 2 clubs left in the pack for all you know. I think that many other more important factors come into play e.g. am I drawing to the nut flush? What could his hole cards be? How has he played the hand until now? Will a big bet now put him off this pot? How many chips does he have in front of him? If I check will he bet and if so how much? If I bet will he re-raise and can my hand really stand a re-raise? Could he have picked up a back door flush draw on 4th street and does he normally bet his flush draws? Have I got an overcard(s) in my hand and if it hits will that top pair be good enough in a showdown? When I play hold 'em and I'm drawing to a flush on the river I try to get to look at that card as cheaply as possible, this doesn't mean however that I always check when first to speak. With 2 on board and 2 in my hand and only the river card remaining I always assume that I have 1 chance in 5 of making my flush. Whether or not I will call a bet when on the button will depend very much on the pot odds I'm getting, how many chips I have and how many chips my opponent has. If there's 1200 in the pot and his bet is 600 then I'd be risking 600 of my chips to win the 1800 in the pot and therefore be getting less than the true odds of my hand reflect, I might however make the call if I think I might draw the nuts and win a lot more chips from doing so.

It depends on so many things that you can't really be accuratley advised whether or not to bet/call/fold, I think a lot of it comes down to experience, confidence and just a plain gut feeling that you may or may not get about your hand and your opponent. Mathematically speaking it's a bad proposition but playing the hand may pay off in the long run. All this said if you're a beginner playing in a tournament which he plays in a once a week I'd check it and fold to any bet where the pot odds offered to me are at least 4/1.

P.S - Once your money goes into the pot it's not yours anymore and it's still used for the calculation of pot odds, you can't go around thinking that there's 200 in there and 90 of it is mine anyway therefore I can only win 110 more, that doesn't make sense.

BrendanB

OK, Ian, I think you're misunderstanding the whole concept of odds. Your reasoning about whether there are 2 or 9 clubs left in the deck is pointless. What the river card is has already been decided. It was the same from the end of the shuffle and the first card being dealt. You must go on the basis that the river is equally likely to be any of the unseen cards (there are one or two possible exceptions, where you are reasonably certain others are on the same flush draw, but this is unusual).

You have two cards in your hand, and there are 4 already shown on the table. There are 52 cards in the deck, thus there are 46 unseen cards. Presuming 4 of the six seen cards are of your suit, the chances of the river also being of your suit is 9 in 46, which is equivalent to 19.6% or 4.1 to 1 (9 wins, 37 losses). All this means is that 20% of the time you will hit, the rest you will miss.

The simplest situation is an all-in bet to you, when you are certain that if you miss you are behind.

Say there is 100 already in the pot and someone goes all in for 100. There is now 200 to be won, and you are being asked for 100 (pot odds are 2:1). It is a bad value call. If you call in the same situation 100 times, it will cost you 10000 and you will make 20*300=6000 back.

If they are all in for 33, there is 133 in the pot and you are being asked for 33 (pot odds are 4:1), even value call -> you will break even long term. 100 times cost is 3300, make 20*166 = 3300 back.

Obviously if the cost is less than 33 then it's good value.

Now if there is a possibility that you are ahead even if you miss (this often happens when you are on the nut flush draw and someone else is on a lesser flush draw) or if you are behind if you hit you need to consider this. Your pot odds should always be calculated with the likelihood you are to WIN, which is different to hitting. So while you might be 20% to improve, you might be 50% to win. At 50% to win, all calls are good value. (At exactly 50/50 long term you and you're opponent are chopping up the money already in the pot).

This is as far as I will ever go with direct odds calculation, and even then it's usually not a conscious decision making process.

On an intuitive level, as Ian says:
* how much do I stand to gain if I hit (a middler that your opponent will never put you on can be good value, or so I'm told)
* how much do I stand to lose if I get a second best hand
* will I make image money by making a loose call
* if I think I might be ahead is it a safer play to reraise someone out of it with a semi-bluff

In freezeout tournaments: FORGET POT ODDS. They get you in trouble except in the most trivial of cases. This is because the price of losing chips is far greater than the value of gaining chips. Yes, sometimes you can decide a gamble is good value in a freezeout, but very rarely. If you lose all your chips you cannot win any money, but the extra chips you do pick up will not necessarily gain you anything. Draws in freezeouts are bad.