Equity calculation power of 4 and 2

[arun9179]

Hi,
i get the power of 4 and 2, multiply by 4 by your out if you have 2 cards to come or multiply by 2 if you have 1 card to come. Is there any shortcut to calculate if we need runner runner for straight or flush draw? i mean if i have AdKd on a 7d6s3c board what is my odd to hit a nut diamond flush?
Thanks
Arun

 

[okeedokalee]

Don't know the odds, but I get plenty of suck outs against me by those runner runner hands so they are not that uncommon.

 

[honorwar]

4 and 2 I specialy don't play.The equity is not good for me.

 

[xRanieri]

Think mathematically. To hit a backdoor flush draw, you need the turn to be a diamond, and the river to be another diamond. On the flop, 5 cards are visible, 3 of them diamonds. That means there's 10 diamonds left, 47 cards left (You don't take into account the other players folded cards, as the probabilities would be the exact same as how we're doing it, but much more complicated).

The probability of event A (diamond of turn) and event B (diamond on river) aren't mutually exclusive. If event A happens, it affects the probability of event B.

p(A) and p(B) = (10/47) * (9/46)
= 0.0416, so about 4%.

When it comes to multiplying your outs by 8 to get your equity on the flop and multiplying your outs by 4 to get your equity on the river, that's just a close approximation. Yes, backdoor straight and backdoor flush draws increase your equity by a couple percentages, but it's not as simple as adding up the probabilities. It's quite advanced.

 

[arun9179]

Thanks!

Think mathematically. To hit a backdoor flush draw, you need the turn to be a diamond, and the river to be another diamond. On the flop, 5 cards are visible, 3 of them diamonds. That means there's 10 diamonds left, 47 cards left (You don't take into account the other players folded cards, as the probabilities would be the exact same as how we're doing it, but much more complicated).

The probability of event A (diamond of turn) and event B (diamond on river) aren't mutually exclusive. If event A happens, it affects the probability of event B.

p(A) and p(B) = (10/47) * (9/46)
= 0.0416, so about 4%.

When it comes to multiplying your outs by 8 to get your equity on the flop and multiplying your outs by 4 to get your equity on the river, that's just a close approximation. Yes, backdoor straight and backdoor flush draws increase your equity by a couple percentages, but it's not as simple as adding up the probabilities. It's quite advanced.

 

[NWPatriot]

When it comes to multiplying your outs by 8 to get your equity on the flop and multiplying your outs by 4 to get your equity on the river, that's just a close approximation. .

Simplistically, if you need EITHER the turn OR river, then you can ADD these two percentages together. If you need BOTH the turn AND river, then you can MULTIPLY these two percentages together.

A word of caution regarding terminology used in this thread. These calculations are giving you the percentage of time you will catch the card you are seeking. This is not the same as your equity in the hand. Your actual equity in the hand is the percent chance you will WIN the hand. You may lose even if you catch your cards. You may pair up and win the hand as well. Equity is a much more complex discussion than just calculating outs.

 

[Nymets5]

Think mathematically. To hit a backdoor flush draw, you need the turn to be a diamond, and the river to be another diamond. On the flop, 5 cards are visible, 3 of them diamonds. That means there's 10 diamonds left, 47 cards left (You don't take into account the other players folded cards, as the probabilities would be the exact same as how we're doing it, but much more complicated).

The probability of event A (diamond of turn) and event B (diamond on river) aren't mutually exclusive. If event A happens, it affects the probability of event B.

p(A) and p(B) = (10/47) * (9/46)
= 0.0416, so about 4%.

When it comes to multiplying your outs by 8 to get your equity on the flop and multiplying your outs by 4 to get your equity on the river, that's just a close approximation. Yes, backdoor straight and backdoor flush draws increase your equity by a couple percentages, but it's not as simple as adding up the probabilities. It's quite advanced.

That's a good explanation, thank you. Need to take time and think more, the clock online always freeks me out and I end up playing bad hands.

 

[ekgbeat]

Equity is a much more complex discussion than just calculating outs.

This is a very good point. Would you mind elaborating on some of those factors that we should be considering?

 

[NWPatriot]

T....Need to take time and think more, the clock online always freeks me out and I end up playing bad hands.

yeah, that is a serious drawback playing online. You do not have a lot of time to be working out all the numbers and all the possibilities. Over time, most of these situations will repeat themselves and you will have a better "feeling" about what to do. The best thing you can do to help your situation is to try and do as much of your thinking before you are on the clock, so that you already have an idea of your action before you get there. Obviously, this isn't always possible, but if you are multi-tabling or distracted by other things, then you really do have a limited time to make your decisions.

 

[Nymets5]

yeah, that is a serious drawback playing online. You do not have a lot of time to be working out all the numbers and all the possibilities. Over time, most of these situations will repeat themselves and you will have a better "feeling" about what to do. The best thing you can do to help your situation is to try and do as much of your thinking before you are on the clock, so that you already have an idea of your action before you get there. Obviously, this isn't always possible, but if you are multi-tabling or distracted by other things, then you really do have a limited time to make your decisions.

Thanks for the advice. I just need some more experience

 

[NWPatriot]

...Would you mind elaborating on some of those factors that we should be considering?

I can try...lol - I will stick with the simplified 2x and 4x method from this thread

Let's say you have ThJh, and the flop is 8c9s5h.

• you need 2 hearts to get your flush - 10x2 x 9x2 = 3.6% chance of hitting your flush
• you need a Q or a 7 to get your straight - 8x4 = 32% if you pay for both cards (8x2 = 16% if you play one card at a time)
  • note if you intend to pay to see both cards then you have to consider the implied odds of future bets that you do not yet know
• Of course, T's or J's can improve your hand, and would actually be top pair given this flop - 6x4 = 24%.

Looking only at your own situation, you might then assume you have a 59.6% chance (3.6 + 32 + 24) of improving your hand. None of these 3 improvements guarantee you that you will actually win the hand. The possibility of a better straight is possible if the Q comes, a better flush is possible, and your top pair might be good but a single pair is easily defeated.

Using Equilab, against a single opponent who generally plays top 25% of starting combos, your equity in this situation is 45%. This means you are not favored to win this hand, even with all these outs. Of course this is why we calculate pot odds to help with our decisions.

If the question was how can we estimate actual equity in real time, well... how much space do we have?? there are probably much better sources than me for this, but here is an uber simplistic stab at it. (I would generally make 2 assessments and then attempt to merge the results - one assessment assuming I am ahead, and another assuming I am behind).

• For this assessment, I will only assume we are behind, as we do not believe that J high will win the hand. (This is confirmed by our 45% equity - we must improve to have an advantage).
• Now let's take our three improvement possibilities and see what we think.
  • the flush: the likelihood that our opponent also has 2 hearts is only about 4%, but if he does have 2 hearts, one is very likely better than ours since we know he only plays the top 25% of hands, so we have to reduce our flush results by 4% (meaning we can only take credit for 96% (100% - 4%) of our initial value - 3.6 x .96 = 3.5% or so - not a significant impact.
  • the straight - an opponent with a K affects our analysis if we are looking for a Q. our opponent has 2 chances at a K, which is 4x2 + 4x2 = 16% chance of having a K, and a K is definitely in his range, so we must consider this. So, we can only take credit for 84% (100%-16%) of our straight assumptions - 32% x 84% = 27% remaining for our straight.
  • Top pair - there are so many ways for us to lose with top pair, that we really need to be careful including this in our equity. Your opponent can already have 2 pair or a set, he could have 1 pair, and need one more card for 2 pair, an A, K or Q is waiting to beat your top pair. Even if you get top pair, he may also get the same pair and will likely out kick you. Per the equity data, you are behind in all one pair, 2 pair, and set scenarios. Though top pair sounds good, it may just be a disaster here - i would be comfortable ignoring this 24% all together, but at the most, taking forward one quarter of this 24% may be OK assuming that if you catch your pair on the turn, you are best half of the time, and then you still have to survive the river with a meaningless card and you only have half the deck to work with - so 24% x 50% x 50% = 6% (very rough and quick analysis wrought with missing pieces...)

So... Where initially we thought we had about 60% chance of improving, when we try and convert this to equity, we are now left with only about a 37% (3.5 + 27 + 6 = 37) chance of these 3 scenarios winning the hand - equity is % likelihood of winning the hand. This is close to the 45% calculated in equilab (Note that we didn't add in runner-runner sets (<1%), runner-runner 2-pairs (3%), and even some of the other runner-runner straight possibilities (<1%) which would inch the 37% up a little closer to 42% - so this is fairly close.

Back to my original point being made here that % chance of improving your hand is different than hand equity. It takes a lot of words to explain the thought process, but with some practice it can be done. You are only trying to approximate all of this, not to do these calculations to the 2nd decimal point. +- 5% is enough to help with your decision.

Did I answer the question?? or did I completely miss the whole thing?? Sorry for being so verbose here, but this is really only scratching the surface of the subject. I hope I did it justice.

 

[ekgbeat]

I can try...lol - I will stick with the simplified 2x and 4x method from this thread

Let's say you have ThJh, and the flop is 8c9s5h.

• you need 2 hearts to get your flush - 10x2 x 9x2 = 3.6% chance of hitting your flush
• you need a Q or a 7 to get your straight - 8x4 = 32% if you pay for both cards (8x2 = 16% if you play one card at a time)
  • note if you intend to pay to see both cards then you have to consider the implied odds of future bets that you do not yet know
• Of course, T's or J's can improve your hand, and would actually be top pair given this flop - 6x4 = 24%.

Looking only at your own situation, you might then assume you have a 59.6% chance (3.6 + 32 + 24) of improving your hand. None of these 3 improvements guarantee you that you will actually win the hand. The possibility of a better straight is possible if the Q comes, a better flush is possible, and your top pair might be good but a single pair is easily defeated.

Using Equilab, against a single opponent who generally plays top 25% of starting combos, your equity in this situation is 45%. This means you are not favored to win this hand, even with all these outs. Of course this is why we calculate pot odds to help with our decisions.

If the question was how can we estimate actual equity in real time, well... how much space do we have?? there are probably much better sources than me for this, but here is an uber simplistic stab at it. (I would generally make 2 assessments and then attempt to merge the results - one assessment assuming I am ahead, and another assuming I am behind).

• For this assessment, I will only assume we are behind, as we do not believe that J high will win the hand. (This is confirmed by our 45% equity - we must improve to have an advantage).
• Now let's take our three improvement possibilities and see what we think.
  • the flush: the likelihood that our opponent also has 2 hearts is only about 4%, but if he does have 2 hearts, one is very likely better than ours since we know he only plays the top 25% of hands, so we have to reduce our flush results by 4% (meaning we can only take credit for 96% (100% - 4%) of our initial value - 3.6 x .96 = 3.5% or so - not a significant impact.
  • the straight - an opponent with a K affects our analysis if we are looking for a Q. our opponent has 2 chances at a K, which is 4x2 + 4x2 = 16% chance of having a K, and a K is definitely in his range, so we must consider this. So, we can only take credit for 84% (100%-16%) of our straight assumptions - 32% x 84% = 27% remaining for our straight.
  • Top pair - there are so many ways for us to lose with top pair, that we really need to be careful including this in our equity. Your opponent can already have 2 pair or a set, he could have 1 pair, and need one more card for 2 pair, an A, K or Q is waiting to beat your top pair. Even if you get top pair, he may also get the same pair and will likely out kick you. Per the equity data, you are behind in all one pair, 2 pair, and set scenarios. Though top pair sounds good, it may just be a disaster here - i would be comfortable ignoring this 24% all together, but at the most, taking forward one quarter of this 24% may be OK assuming that if you catch your pair on the turn, you are best half of the time, and then you still have to survive the river with a meaningless card and you only have half the deck to work with - so 24% x 50% x 50% = 6% (very rough and quick analysis wrought with missing pieces...)

So... Where initially we thought we had about 60% chance of improving, when we try and convert this to equity, we are now left with only about a 37% (3.5 + 27 + 6 = 37) chance of these 3 scenarios winning the hand - equity is % likelihood of winning the hand. This is close to the 45% calculated in equilab (Note that we didn't add in runner-runner sets (<1%), runner-runner 2-pairs (3%), and even some of the other runner-runner straight possibilities (<1%) which would inch the 37% up a little closer to 42% - so this is fairly close.

Back to my original point being made here that % chance of improving your hand is different than hand equity. It takes a lot of words to explain the thought process, but with some practice it can be done. You are only trying to approximate all of this, not to do these calculations to the 2nd decimal point. +- 5% is enough to help with your decision.

Did I answer the question?? or did I completely miss the whole thing?? Sorry for being so verbose here, but this is really only scratching the surface of the subject. I hope I did it justice.

Wow, this deserves it's own thread, and I have so many more questions. What is the best source to get a fundamental understanding of the frame work that you described above? I get what you are saying in general, but some parts lost me, didn't get how the math worked on some of it.

I would like to be able to apply the principles described to different board textures, and I don't think I'm getting all of the concepts. This post really has me thinking now.

 

[NWPatriot]

Sorry about that. I started to keep it simple and it got away from me - I actually screwed up on the straight analysis above (I was trying to describe a bad situation where we hit the idiot end of a straight and get beat by a bigger straight, but my specific example does not allow this - T9 with a JQX board may not want to make his straight with the K is the example i should have used).

The real message is still - "% chances of hitting the cards you want to see, is not the same as your equity in the hand". The best way to visualize this point is by using one of the many poker odds calculators out there. Start simply with an AK that misses the flop, you can figure out what your odds are of catching an A or K on turn/river and compare that to your equity of winning the hand - they are very different numbers.

• Cardschat has an odds calculator - available here and simply gives odds
• Card Player website has a good calculator - this is a good web based calculator - it has two advantages that many others don't have; it provides nice graphs that i haven't seen anywhere else and it is possible to analyze based on a single flop card like an A, without confusing the issue with non consequential other random flop cards.
• (PokerStrategy.com) Equilab is a good downloadable calculator - you can save ranges, it has a lot of pre-stored ranges, and it has a good post flop "hand strength distribution" table, among other bells and whistles.
• Pokerstove is an oldy but goody but doesn't have some of the advanced tools as more recent tools.
• There are other calculators that have to be purchased, that provide even more functionality.

 

[ekgbeat]

Thanks for all of the info. I use Equilab and I'm pretty happy with that one.