# Estimating equity

Following the advice received in answers to my last question, I’ve started practising estimating equity using Equilab - and I’ve been very disappointed to find that I’m nowhere near where I thought I was in terms of accuracy!

On to the question …

I was dealt QsQh, flop comes 2s9hAd. In this exercise the villain is playing any 2 cards.

It’s not unlikely that the villain has 2 pair or a small set so I need a queen on the turn or river to take the hand.

There’s 2 queens in the deck giving me 2 outs on the turn and 2 outs on the river = 4 outs. Multiply by 4 to give me 16% equity.

Equilab calculated 78% equity … a rather large difference, much worse than even I normally get, so I’m wondering what I missed in my estimation?

Regards
TA

If V is playing any 2 cards, he won’t usually have an ace.

The vast majority of his range will not have 2 pair or a set there, or even an ace.

You have 2 outs twice to make a set, but the queens will stand up most of the time, so you won’t need to make that set.

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By the way, you don’t multiply your outs by 4 on the turn AND on the river. 2 outs twice is about 8%, not 16%.

This rough estimation is based on the idea that, if there were 50 cards in a deck, each would have a 2% cnance of showing up. There are 52 cards in a deck, so this isn’t exact, but it’s often close enough (and easy to calculate) that it’s useful.

So you have 2 outs to a set on the turn and 2 on the river,. and 4+4 = 8.

Technically, we can’t just add the %s there either, but again, it’s close enough for an “on the fly” estimation. You have two 4% chances, not one 8% chance. We can illustrate this easily by considering coin flips.There is a 50% chance of making heads on any one flip, but that doesn’t mean that there’s a 100% chance of it being heads if you flip it twice or a 150% chance if flipped 3 times. Each flip is a new event.

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Just for kicks, let’s see how accurate that 4% for 2 outs is.

On the flop, we have seen the 3 flop cards and our 2 hole cards, for a total of 5 cards seen. There are 52 cards in the deck, so we have not seen 47 cards, Two of these are queens, so (2/47) X 100 = 4.25%

On the turn we have now seen 6 cards, leaving 46, and (2/46) X 100 = 4.35%

I would call that close enough.

To calculate the actual chance of hitting a queen over both streets, we can calculate how often we WON’T catch a queen. If we have a 4.25% chance of a queen on the turn, that means it won’t be a queen 95.75% of the time. Of these times, 95.65% of the time, we will miss the river too. So (0.9575 X 0.9565) X 100 = 91.58% of the time we miss, which means 100% - 91.58% = 8.42% we hit at least one queen by showdown.

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Yes, thank you … I can see my mistake.

So, to correct my maths in the subsequent post:
old: V has 4 outs twice to make a full house = approx 30% which puts my estimate at 70%
new: V has 4 outs twice to make a full house = approx 15% which puts my estimate at 85%

You really are very patient with me, it’s appreciated

Regards,
TA

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Thanks SPG … I agree with your statements but I still can’t discount the possibility of 2 pair either now or on the later streets. I can’t discount a royal flush on the river for that matter! However, of all the hands that might beat me, 2 pair seems most likely and so that is the hand I want to defend against.

It’s the mathematics behind equilabs estimate that I don’t understand. I feel that I should be able to get to a number much closer than I did. If I’d been able to calculate anything over 60% I’d feel confident that I’m getting my calculations close enough. In fact, my “guess” was 65% before I did any calculating.

Is this just a situation where I don’t have enough time and ability to count outs so I need to rely on “intuition”?

Can I do something like reverse outs? Assume that I’m going to get another Q and V has 2 pair. I’m at 100% (QQQ), V has 4 outs twice to make a full house = approx 30% which puts my estimate at 70% or am I just making numbers up to fit my desired result?

Regards,
TA

You are comparing apples and oranges here.

Equity is the share of the pot that is yours based on the odds that you will win the pot at that point in play.

This is not the same as calculating the chance that you will improve your hand. In the example you gave, you could make a set and still lose the hand. Conversely, you could miss and still win.

I’ve never played with Equilab, but if you have to input V’s range, it’s probably counting all of the possible hands V could have, calculating each hand’s odds of improving, including yours, then looking to see how many of V’s possible combos will produce the winning hand. In other words, it’s telling you how your hand will do against V’s entire range, not just one or 2 specific hands within that range.

“Outs” are cards that would complete a hand or improve it sufficiently to win the pot. For example, if you have QQ on the turn and V has KKK, you don’t have 2 outs because hitting another queen won’t win the pot. You will see this sort of thing a lot, especially with straight draws vs flush draws. If there are 8 cards that can fill your straight, but 2 of these will give your opponent a flush, those 2 cards aren’t outs!

Yes, you can do reverse odds like you mentioned in the last bit of your post. However, he can’t make a full house unless the board pairs, and if it does, you will have a full house too.

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Thanks again SPG!

One of the websites that I use states in an article:

The easiest way to get your equity is to remember these two simple rules:

• On the flop, multiply your outs by four
• On the turn, multiply your outs by two

This means with an open-ended straight draw (eight outs) you have a 32% chance of making your straight with two cards left to come.

There is a modification in the case of having more than 8 outs but it’s not important here. I’d also note that I have seen this estimation technique many times in different places.

Now that you’ve explained the most likely way Equilab is doing it’s calculations (yes, you’re right about inputting Vs range), it makes perfect sense and I should have thought of it myself!

I was doing really well with my estimates using the above guide until this particular hand came up. Given that it’s not complete nonsense to work in reverse outs I will see how that works next time something like this occurs.

You really are a great help

Regards,
TA

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Strictly speaking, this isn’t calculating equity, it’s estimating your chance of making a particular hand. You could miss and still win with high card, or make some goofy one pair hand that wins. These possibilities are also part of your actual equity.

I understand that it isn’t exact and of course there’s all sorts of weird stuff that happens every day.

All I’m looking for is something +/- 10% (or 5%!) … as I said, with the hand that puzzled me, there’s a non-zero probability of V drawing a royal flush. If that happens, I’ll just cop it as the universe moving in mysterious ways as the universe tends to do I am certainly not going to calculate and memorise the probabilities of that event.

As I get better at counting outs I can start to allow for more events. For example, a straight draw also has a 2 pair draw or maybe a flush draw and so on. Even if I had the ability (I doubt if anybody does!), I most certainly don’t have the time to calculate every possible outcome - all I can do is refine my estimate to the most common winning hands based on my estimate of Vs range.

The reason for the original question is that I estimated 16% vs a calculated 78% and I don’t know if I missed some really obvious draws that increased the number of outs that I should have seen. I now think it is as you said: the programme accounts for every possible draw for both players and determined that, over the long run, QQ is a really strong hand on this flop.

I really like the idea of using reverse outs under some circumstances now that you’ve said it’s not complete rubbish. I think it will be applicable mostly when I’ve got a high pair and there’s a low board as in this particular case. More practise time will soon determine that!

As always, your time and interest is very much appreciated!

Regards,
TA

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Effectively, yes. It looks at each combo in each range that you enter and calculates the winner on each possible runout.

Hey, when did you join the ranks of the accountants?

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2004, which was the same year I started applying game theory, information theory, decision theory, and psychology to poker.

But hahaha, I’m not an accountant, I’m a scientist!

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You don’t know there are two queens still in the deck. There might be none, one or two. Doesn’t that mean calculating anything is an impossibility? (I’m not a math whiz, as everyone probably has discerned by now, so I’d like to know what I’m missing if it’s that obvious.)

Any body ever think about pot odds I have not heard a thing on this topic and at some point this must come into play.

Pot odds are part of most discussions about bet sizing. Yeah, pot odds are part of every decision you make in poker.

Is there something specific you would like to know about concerning pot odds?

Yes you are right. All these calculators use either enumeration or simulation to predict the probabilities. Its impossible to calculate the probabilities.

Like to hear comments from others,

The probabilities are easy to calculate, it’s the certainties that are difficult.

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