Xanadu's limit tip Charrip o' the whenever.

I thought I'd start posting some occassional limit tips here on the Beginner's forum. I figured a blatant rip off of Chardrian's tip topic subjects would be the best way to do it (Charrip). Forshizzle.

Most of these will probably be in response to questions posed in another post here on the beginner's forum. Today's tip is in response to MortimerJazz's question on pot odds, and is on a closely related subject: pot equity

Today's tip: Evaluating the pot equity of a drawing hand.

So you flop a draw of some kind and need to know if you can call a bet. The first step is to determine your pot odds. Say the pot is 6SB (small bets), and you are last to act and it is 1SB to you. Easy, you are getting 6:1 pot odds. But this is only half of the information you need to make the decision to call or not. The other half is your pot equity, also known as hand equity. Pot equity is your 'share' of the pot, the estimated chances you have of winning the hand. Pot equity is actually made up of 3 components: 1. The chances you are ahead right now and your hand will still be the best at showdown, 2. fold equity(the chances of picking up the pot with a bet or raise now or on later streets), and 3. the chances of hitting an out to improve your hand and your improved hand will be best at showdown.

For now, we will ignore 1. and 2. and focus on 3. the chances of winning by hitting our draw. Ignoring 1 and 2 is not a mistake for the many hands where we are relatively certain we must improve to win, and are also relatively certain that aggressive play will not win the pot without a showdown (or at least that trying to fold out the opponents is a losing play because the chances of our opponents all folding do not justify the bets risked in the attempt)

To determine our hand's pot equity, we need to look at the outs we have to improve, and then assign a value to each of these outs based on our estimate of the chances that improving will make the best hand. A full value of 1 out only applies to a card that gives us the nuts. In some cases, even a nut out should not be assigned full value because of a high chance of splitting the pot. For example, you check the big blind with J7o. Flop comes AKQ rainbow. Any T gives you the nuts, but you will split the pot with any J, so your 4 nut outs probably are only worth about 60% because you will usually split this pot if you make the nut straight.

Each out is multiplied by the chance it has of making the best hand, and then all the outs are added up. This gives us a value for the hand in outs. Then we can determine our winning chances (pot equity) for this number of outs. I will do the math for this later in the post, but you can just look at a chart that shows chances of improving with a certain # of outs (something every poker player should know). A lot of factors go into making this estimation, and I will try to cover most of it in some examples.

Example 1: You have A2s and the flop comes Q95, 2 of your suit. You have a flush draw to the nuts, and an overcard. You have 9 flush outs, and 3 outs to top pair. Your flush outs are to the nuts, and unless the board pairs, you will always win when you make the flush. In addition, you will never split the pot with a flush, so we will count the 9 flush cards at full value, 9 outs. Actually, 1 of these outs pairs the board, and the board could pair on the river, but the chances of losing to the full house are pretty small, and if the decision is close enough that 2 or 3 tenths of an out would change the correct action, other factors like reads on opponents will be much more important. We have 3 outs to improve to top pair. Depending on our opponents, and the number of them in the pot, hitting top pair may win the hand anywhere from 25-75% of the time. So we'll count the 3 Ace outs at half value, 0.5 outs each (this is a little generous in most situations with no kicker). We can also improve with the 3 2s left in the deck. But the chances of winning the pot with bottom pair are fairly remote, so these outs should not be counted. So, in total, we have 9 outs for the flush cards, and 1.5 outs for the 3 Aces, so our hand is worth 10.5 outs. 10.5 outs on the flop gives us a pot equity of 40% (again, math below).

Example 2: You have 75o in the big blind, and the flop comes Ah6s3s. Here you have a gutshot straight draw to the nuts. Here any 4 gives you a straight, but only 3 of them are to the nuts, as the 4s puts 3 to a flush on board. The 4s should probably only be counted as about .6 outs because of the combined chances of someone holding 2 spades, and that both the turn and river will both come spades, in which case any spade beats you. Even if you make your hand on the turn, you could lose to a flush on the river. This hand is worth about 3.5 outs. Your pot equity here is only a little over 14% on the flop. If you miss the turn, your pot equity will be 7% (or less if the turn was a spade)

Example 3: you have AhKh. The flop comes 9h8c7d. You have 6 outs to TPTK. You also have a backdoor flush draw. A backdoor flush draw is worth about 1.5 outs, and these outs are to the nuts. Your 6 outs to TPTK, however, are less valuable than usual (usually an out to top pair should be counted around 1/2-3/4 depending on how many people in the pot ... the more people, the less the chance top pair will be good). If there are a lot of people in the pot, It is very likely at least one of them has an OESD. Add this to the chances that someone has made 2pair, a set, or will improve to 2 pair, and your TPTK outs are probably only worth a little over a third an out each. If you are heads up, however, I would give the TPTK outs at least 80% value. In that case, though, your chances of being ahead with A high are also significant, and it is unlikely that you are going to be folding. Let's be generous and give our TPTK outs a value of 2.5. Added to the backdoor flush outs, this gives us a hand worth 4 outs. A 4 out hand has a pot equity of 16.5% on the flop.

Example 4: you have QJh and the flop comes Th9h5s. You have a monster draw. You have a straight flush draw with 2 overcards. You have 9 outs to a flush, 2 of which are a straight flush. The other 7 hearts, however, you could lose to a higher flush. These should not be discounted too much, however. I would knock about half an out off for losing to a higher flush, giving us 8.5 outs for the 9 hearts. The 3 non-heart Kings and 3 non-heart 8s give us the nut straight. These should be valued fully, for another 6 outs. In addition, we have 2 overcards. The 6 overcard outs are probably worth about 2.5 outs here, maybe a little less. In total, we have a hand worth about 17 outs. On the flop, our pot equity is nearly 60%, so with a draw this good, you want to get as much money in the pot as possible.

I hope these examples have given you an idea of how to look at hands to evaluate their drawing strength. Once you know your pot equity, you can now compare it to your pot odds. As long as the percentage of the pot you have to contribute with your bet is smaller than the percentage of the time you will win the hand, you are making a good call, and have the right pot odds to continue. You can usually consider the pot to be a few bets bigger when making this decision because of the implied odds that come from winning bets on later streets when you do make your draw.

And now, the math on how to get your pot equity from your # of outs:

The easiest way to do this is to first figure out the chances you will not make your draw. On the flop, there are 47 unknown cards (you see the 2 in your hand plus 3 on the board). If you have x outs, you will miss the draw on the turn 47-x times out of 47 possibilities. Then on the river, after missing the turn, you will miss 46-x times out of 46 possibilities. The chances of missing is the product of these 2 occurences:
P(missing your draw on both turn and river)=((47-x)/47)*((46-x)/46)
Subtract this from one, and you get the chances of making your draw.

If you have 5 outs, the chances of missing your draw on both the turn and river is: (42/47)*(41/46)= 0.796, just under 80%.
So the chances of making your draw is 1 - 0.796=0.204, just over 20%.

It is fine to use partial outs in this formula. To get the equity for just the river to come, it is just (# of outs)/46. So if you have 10.5 outs after the turn, your equity is 10.5/46= 0.228.

Feel free to PM me if you have a topic in limit hold-em you would like me to discuss, and if I think the topic is appropriate for the beginner's forum, and I know enough about it to make a useful post, I'll make a Charrip tip post.

-X

Wow - lot's of goot info in there.

Feel free to keep ripping me off.

Nice post Xanadu


I think I’ve got this, here goes.

Example.

I have a gut-shot draw to the nuts. 4 outs, on a rainbow flop.

The pot is 12 small bets to me; I have to call a single small bet. No possibilities to call a raise too.

I have to contribute 12% to the pot
My pot equity is around 19%
Pot odds around 10.5-1

(Contribute) 12% < (equity) 19% , pot odds 10.5 to win 12, EASY CALL.

Have I got this right?

Would it be better to create a table of pot equity and memorize, rather than doing the math every time?

You've got it right dvda. And you don't need to do the math everytime. You just need to use a table that gives the odds to complete a draw with a certain # of outs. The adjustment to be made is how you count your outs ... for example, AKo with only the overcard draw is 6 outs, but in a 6-way pot is worth maybe 3, so you look at the 3 outs line on your table to get the pot equity. 6 outs tells you how often you will improve, but 3 tells you how often you will win when you improve. I don't have a link to a table on me, but they are all over the place. Any of the quick gimmicks like multiply outs by 2 and add 2 with one card to come and so on will get you close enough. You usually don't have to know the numbers exactly, you just have to know them close enough to make a good decision at the table and not do things like call with a gutshot heads up when there are 5 bets in the pot when your hand is T high.

Something to add here ...

If you are a limit player, and you want to make the right decisions on your draws (and a limit player has to make correct decisions with small equity differences over and over to be a winning player), you absolutely must know the numbers on the chances to improve with a certain # of outs. This doesn't take any math skills other than being able to count and add and compare 2 numbers to each other. If you can count the # of bets in the pot, and count your effective outs, and look up a # on a table, you have all you need to make the percentage play on a draw. If you aren't doing this now, start now! Either use one of the estimation rules, or memorize an outs chart, or tape the chart to your computer. But one way or another, you need to know when you are paying too much for a draw and should fold. NL players may be losing players because they make a big mistake they shouldn't once in a while, but a limit player tends to lose money by making small mistakes over and over that may each only lose as little as a tenth of a small bet.

If I have pot odds, do I not always have pot equity, and vice versa?

If not can you give an example?

Originally Posted by dvda

If I have pot odds, do I not always have pot equity, and vice versa?

If not can you give an example?

It depends on how you use the terms really. Usually when people say 'I have pot odds (to continue)' what they mean is 'my pot equity is greater than my pot odds and therefore I have the necessary odds to continue the hand'. Similarly one could use the term pot equity in the same manner, although most people don't say 'I had the pot equity to continue'. Whenever you must make the decision to call a bet, you are given odds by the pot on your bet, and this is your pot odds. Your hand also always has pot equity, although it is 0 if you are drawing dead ... you almost never know you are drawing dead though, so you always have at least some small expectation of winning the hand ... your pot equity. Usually it is the comparison between pot odds and pot equity that someone is talking about when they say 'I had pot odds'.

Putting it simply,
pot odds = the ratio between the pot size and the bet you have to call. If you have to call 1 bet into a 7 bet pot, you have 7:1 pot odds, or 12.5% as a percentage.
pot equity = your estimated winning chances for the hand as a whole

In many cases, the direct pot odds (I'm using this term to mean the pot odds only at the time of your decision taking nothing into account what may happen after you act in the betting round) is not what you really want to use, but the 'expected pot odds', which is your best guess on your pot odds at the end of the betting round. A couple examples:

1. Your call will close the betting. Your expected pot odds and direct pot odds are the same.

2. The pot is 6-way, with 7 bets in it after SB leads out the flop. You are in the BB. You are getting 7:1 direct pot odds. If this is a table where everyone always calls on the flop and almost no one ever raises no matter how good their hand is, you can make your decision based on this information, and assume that 4 more bets are going in with almost no chance of a raise. Your effective pot odds are 11:1. At this passive table, calling with a gutshot here is correct, but if it was an aggressive table with a good chance for a raise and 3-bet on the flop, you would probably fold (think about the different scenarios here, and what your effective pot odds would be).

3. The pot is 3-way on the flop, with 8 bets in it after SB leads out. You are in CO position. You know from past experience that the Button, who raised preflop, will almost always raise here. You also know that SB never leads out the flop without a very good hand and will usually 3-bet here if raised. Button will always cap a flop he raised. Here, you are getting 8:1 pot odds on your call initially, but this isn't the whole story. If Button raises and SB calls and you call, you are putting 2 bets in while each of the opponents put 2 bets in with 7 in the pot before the round. This makes your pot odds 11:2 (5.5:1), much worse than 8:1. If SB 3-bets and Button caps, your pot odds will be 15:4 (notice that the initial pot and all your opponent's bets go on one side, and only your bets on the other ... you don't 'win' your own bets). In this case, your effective pot odds are worse than 4:1, making draws like overcards, gutshots, backdoors, and low pairs losing propositions. Now, you might estimate that half the time you will have to call 2 bets, and half the time 4 bets in this hand, so what you do is either add the two sides of the seperate odds (since they happen with the same frequency) giving 26:6, or work it halfway for calling 3bets, giving you 13:3 which is the same thing. This situation is not uncommon in hold'em, and can make you go wrong if you don't take reads into account ... you had a pretty easy call with a gutshot getting 8:1 direct odds, but it turned out such a call would be horrible because your effective pot odds end up being only a little better than 4:1.

Some of you might think this is too much work, but you don't have to do the math in this detailed fashion. You just need to have a rough idea here in most cases. In the last, more complicated example, you know you are going to have to put in 2 or more bets almost all the time, and if your opponents each put in 2, those 2 bets are risked to win 11, and that is probably your best case scenario. There is a fairly clear cut break in most of the drawing hands out there ... weak draws of 1.5-3 outs like one or 2 backdoor draws or a set draw or overcard, marginal draws of 4-5 outs such as gutshots and low pairs (drawing to 2pair or trips), strong draws of 8-9 outs like OESD and flush draws, and monster combination draws of 11+ outs like flush+gutshot, OESFD, flush plus overcards. Put your hand in one of these categories, and know what kind of pot odds you are looking for to continue. Usually the decision is pretty clear cut.

Here an outs to odds chart I found through google: http://casinogambling.about.com/libr...y/aa050103.htm

Thanks, Harry, that's exactly what you need to know to find pot equity. Once you have your hand value in outs, you just look it up on the chart and that's your pot equity for your draw.