Hand Odds

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Ingrid

Hey bassboy229,

Thanks for your question.

So you'll hit a pair roughly 1/3 times on the flop if you played every hand. Which also means any hand you do play, will pair up approx 33% of the time.

Assuming all your outs are clean, you'll have two cards to give you a set.

An effective scenario to analyze this, is when two players both have two-pair and one is dominated.

You have A6o, your opponent has A7o, you flop two-pair, while he turns a 7. At this point, you are drawing to 4 outs only, provided they are clean, you have just under 7% Equity on the turn. Your outs are any ace and any six.

If we discount both remaining aces as dead cards, and give yourself the two sixes as outs, we have something more like 4.5% Equity.

Keep in mind, we are looking at absolute hand strength in this scenario, relative hand-strength is more important, so: How does my hand or range perform against my opponents range in this specific context? (By context I mean the actions both of you have taken until this point)

All in all, if you both hit two-pair, it's a setup and if you hit two-pair against your opponent, you will almost always be happy to take it to showdown, unless there are so many hands that can beat you, that the relative hand strength of your two-pair is reduced too much, for example, when any one of a certain suit, makes a flush, two-pair does not seem at all attractive anymore to a pot-sized river bet from your Villain.

I'm not entirely sure what you mean with the 12%. If you hit your hand and have 12% Equity, then you must be so insanely dominated (such as with the two-pair hand), that you wouldn't see it coming, usually you will have more Equity than this pre and postflop if you choose your starting hands well and don't run terribly.

AA vs KK is an 82/18 split of Equity, so to have 12% means you're unlucky or just in a tough spot, again, if you make your decisions well it shouldn't happen too often, if your specific hand has 12% Equity against a random range on a certain board, it's a clear fold unless he's betting say 4 cents into a 50 cent pot.
If you find yourself in a spot, where you have 12% Equity against your opponents calculated hand-range, and his betting is not giving you the odds to call, of course you need to fold.

There are situations where we simply need to call to see another card because our opponents are betting so small, recently I have witnessed this most at iPoker, where I see many Villains betting 1 BB into a 25BB pot for three streets to take their Ace high to showdown after some pre-flop action. But usually, you'll not often get good odds to call someone down with 12% Equity, and those situations should be avoided as much as possible.

I hope this answers your question & helps somewhat!

Let me know if you want to discuss anything further!

All the best,

-E

I think what i meant was, if i, say, had AA.. there's only 2 outs that can improve that to AAA.. so that's 2 outs - should i just remember this as 8:1 = 11% of hitting a set on the flop? for all pocket pairs?.. but if you don't hit, then of course, you only have 2 outs to improve on the hand to hit a set.. surely then using the rule of 4 that's 2outs x 4 to = 8%? with a hand like AA, 8% chance on improvement post flop, pre turn, doesn't seem great.. especially if the pot hits up around 1200 pre flop as i would have raised, depending on position...

if then i'm being asked to call a 400 bet into a 1600 pot, that's 25% pot odds minimum, but the chance of improving is only 8%? would this depend entirely on context of the player in previous hands, and what is on the flop?

so: with an Js Qs 7c flop, they may well have hit a straight draw, a flush draw, a straight flush draw, or a high pair.. To my pocket Aces with 8% of improving to a set, i am unsure whether or not a bet of 400 into a 1600 would be classed as worth it?

As for simple pairs, if i had KcQs off, and the flop came out Ks Js 4c.. i then have top pair, and a backdoor flush draw.. in this case, what are the odds of hitting a set of Kings - a flush (using 2 drawing cards, would that be the number of outs x4.. as a decimal, ^2, as probabilities would need to be multiplied together, or is that me over complicating the maths of it?

Ps, fantastic help and i'm really grateful for the speeding reply.

Bassy.

hi guys,

some pretty maths discussion going on here, im already.

regarding the AA scenario (on JQ7cc flop), here are some things you might want to ask yourself:
- do you need to improve to a set to win?
- what hands are in his range? how are you doing against that range?
- is it a heads up pot? because consider that having a flush draw+ straightdraw would mean he has 9cTc which is just one combo if you had the Ace of clubs yourself. this is also the reason why AA decreases in equity versus many opponents who would have combined outs (meaning 1 guy has FD, one guy has SD, etc)

i would strongly advise you to download the Equilab or Equilator and play around with it a bit. (click on the "Strategy" tab --> go to "Poker Tools" (in the gray bar below it) --> download Equilator or Equilab.

i will leave Euan or more mathematically inclined members to answer your other questions

smiles,
wendy

Originally posted by bassyboy229
I think what i meant was, if i, say, had AA.. there's only 2 outs that can improve that to AAA.. so that's 2 outs - should i just remember this as 8:1 = 11% of hitting a set on the flop? for all pocket pairs?.. but if you don't hit, then of course, you only have 2 outs to improve on the hand to hit a set.. surely then using the rule of 4 that's 2outs x 4 to = 8%? with a hand like AA, 8% chance on improvement post flop, pre turn, doesn't seem great.. especially if the pot hits up around 1200 pre flop as i would have raised, depending on position...

You have two outs with AA, but only if your opponent has a hand on the flop, which beats your top-pair, which no draw does, and with AA you will very often have the best hand. Play around with the Equilab to gauge how AA performs against certain other hands & ranges on certain boards.

Originally posted by bassyboy229
if then i'm being asked to call a 400 bet into a 1600 pot, that's 25% pot odds minimum, but the chance of improving is only 8%? would this depend entirely on context of the player in previous hands, and what is on the flop?

Consider relative hand strength and absolute hand strength. With AA on the flop, you only have low equity if your opponent hits his set or straight; again use Equilab to calculate. Most time if you are referring to any form of Hold em, AA will win at showdown, only if you are dominated before then will it not, our objective then is to lose most money, so we use the board and our opponents actions to learn more about what would be the correct action for us in that situation. But all in all aces will be very strong on most board runouts.

Originally posted by bassyboy229
so: with an Js Qs 7c flop, they may well have hit a straight draw, a flush draw, a straight flush draw, or a high pair.. To my pocket Aces with 8% of improving to a set, i am unsure whether or not a bet of 400 into a 1600 would be classed as worth it?

What was the pre-flop action? What do we hold? What are our opponents statistics, stack sizes? 400 into 1600 means we need to call 400 to win 2000 so we have really good odds for most of our own draws and we can raise with fairly strong holdings, but again more information would be required here to make a more accurate assessment.

Originally posted by bassyboy229
As for simple pairs, if i had KcQs off, and the flop came out Ks Js 4c.. i then have top pair, and a backdoor flush draw.. in this case, what are the odds of hitting a set of Kings - a flush (using 2 drawing cards, would that be the number of outs x4.. as a decimal, ^2, as probabilities would need to be multiplied together, or is that me over complicating the maths of it?

We have K Q
Flop K J 4

Outs for set: K :diamond:, K
Outs for Flush draw (provided no-one else has a :spade:): A :spade:,2 :spade:,3 :spade:,4 :spade:,5 :spade:,6 :spade:,7 :spade:,8 :spade:,9 :spade:,T
Outs for two-pair: Q Q :diamond:, Q

2 for a set
10 for a flush draw
3 for two-pair (any queen)

so AA, KK, JJ, 44, KJ, K4 and J4 are ahead of us

aprrox Equity against with our KQ:
AA - 22%
KK - 6%
JJ - 8%
44 - 8%
KJ - 21%
K4 - 35%
J4 - 32%

if our opponent only has those hands on that flop when we have our hand on that flop, on average we have around 18% equity, but consider that this will be a rare occurrence as you will play many more hands and as such will have many more hands in your range ; this is on average (consider our discounted outs in relation to our opponents holdings) when our opponent holds something that beats our top pair on the flop, and we would need certain outs to beat certain hands, but consider that those hands that beat us here which are previously mentiond, are only a few combos of our opponents range, which can be defined in the actions he has taken pre-flop. Against aces on that flop, we have just under 22% Equity, which would be a call if say for example the pot was $100 and our opponent bets $15.

Hope this helps!

-E

Fantastic advice, really appreciate it!!

However, forgive me for sounding dumb, but how do you calculate against other hands and set your opponent on a range.. and should i use those odds as guidelines for the context of the game, you say?

I feel bad having such a short reply to your dissertation!

Thankyou!!

Originally posted by bassyboy229
Fantastic advice, really appreciate it!!

However, forgive me for sounding dumb, but how do you calculate against other hands and set your opponent on a range.. and should i use those odds as guidelines for the context of the game, you say?

I feel bad having such a short reply to your dissertation!

Thankyou!!

Hey bassy!

You set you opponent on a range from the information he gives you. The more information, the more you can define his range. Before I continue here, did you download Equilab?

If not, do this now.

So there are 1326 combos of cards your opponent can have in NL Hold 'em.
The range is the number of combos you estimate him to have gotten to that point with, taking into consideration the actions you both have taken until that point. This is all assuming your opponent plays a reasonable game.

Let's say for example, a Villain is notorious for posting his blinds out of position, every time he does this and then checks, he has any two cards, because he will raise strong holdings, therefore your opponent has a weak range when he posts OOP and checks, and this means it is profitable to raise most of your own holdings into his blind because he will fold a large percentage of his range.

Range is important because the type of poker we study and practice is only effective over a sample size so large that averages are all we can take into consideration when trying to make assumptions about our opponents.

You can calculate ranges using Equilab, where there are pre-sets for what your opponent could have, depending on his position and his action.

Lets say you are in the Big Blind on two separate occasions.
The first time, UTG Raises 4 BB. How does your range perform here when you 3-Bet?
The second time the Small Blind raises 3 BB. How does your range perform when you 3-Bet the SB?

If you think about these two scenarios, you'll see how ranges perform / compare to each other, Equilab will not differentiate between positions in terms of absolute Equity when it comes to hands, because position does not have any value in terms of equity, but only information to gague your equity, and within Equilab, this information is stored in the form of the pre-sets from the various positions.

KK vs AA is always the same, 19% vs 81% regardless of position. Positional equity advantages come from the ranges we expect our opponent to open raise, call, limp, 3-bet from the various positions. Information is key to defining our opponents range.

It's imperative you play around with Equilab and the various options to gain an understanding here. Use Equilab while at the table.

Your questions can be as long as you like! I'm very happy to see you asking more!

-E

Thanks Euan, great answer much better than the one i started to write

Ah sorry Ex,

I know how bad that is when you go to post something and someone got there first, apologies!

-E

no need for apologies your post smashed mine into the ground then stood on its nuts while it was down!

Some great discussion ITT keep the questions coming if you have anymore bassyboy229

Carl

Yea bassy, keep the questions coming, we can do the same with answers!