Pre Flop - Higher equity with higher pair against over cards

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ptomalley35

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I am pretty new as far as learning about equity and I have been putting some pre flop hands into equilab and observing the equities.

I am confused why a higher pair gives you more equity against the same over cards. Take this example:

In the first situation with a pair of 9s against AKo I am getting 55.27% equity

In the second situation with a pair of 8s against AKo I am getting 55.16% equity

In the third situation with a pair of 7s against AKo I am getting 54.98% equity

I don't see anyway for it to make a difference and if anything the 9s should have lower equity because your chance of hitting the 9,10,J,Q,K straight is reduced because a King is out of play.

What am I missing here?
 
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caracaski220

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caracaski220

I wwould think it is because cards that help th eAK hand make a straight help the higher pair hand make a straight more often than the lower pairs.
 
gabrielcsgo93

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I prefer connected over cards than a pair in hand!
 
vinnie

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I haven't taken out equilab to go through these specific numbers, but I am pretty certain it is due to the chance you get counterfeited.

A board of :9s4: :9c4: :8h4: :8c4: :2d4: or :qd4: :jh4: :qh4: :3s4: :js4: are losing boards when you have 77 against AKo. There are fewer of these boards possible, as your pair increases. It doesn't happen very often, which explains the very small difference in the equities, but it is more likely to happen the smaller your pair is.
 
vinnie

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Alright, I have done a little bit of the math.

Chance you get counterfeited.

  • 77: 0.67%
  • 88: 0.40%
  • 99: 0.20%
I am not 100% sure that I did the math correctly. I am pretty sure about the math but it seems like equilab didn't give you as much of an equity difference between the three. Still, this seems like the most likely explanation for the difference. I don't think it's the straights or flushes that cause the drop-off in value.
 
Poker_Mike

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Odds Calculator

I am pretty new as far as learning about equity and I have been putting some pre flop hands into equilab and observing the equities.

I am confused why a higher pair gives you more equity against the same over cards. Take this example:

In the first situation with a pair of 9s against AKo I am getting 55.27% equity

In the second situation with a pair of 8s against AKo I am getting 55.16% equity

In the third situation with a pair of 7s against AKo I am getting 54.98% equity

I don't see anyway for it to make a difference and if anything the 9s should have lower equity because your chance of hitting the 9,10,J,Q,K straight is reduced because a King is out of play.

What am I missing here?


It is your odds calculator that is giving you slightly different numbers.

If you run each hand three (or more) times - and average all three numbers - then the averaged number will be closer for all three hands.

Why does the odds calculator give a slightly different number every time? I don't know.

In general I advise not getting hung up on 0.2% of anything.

I don't pay attention until there is more than 5% difference. And for me this is an arbitrary number.

Over a lifetime of play - the edge of a pocket pair vs. over cards can make a difference.

Good luck !
 
Collin Moshman

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I haven't taken out equilab to go through these specific numbers, but I am pretty certain it is due to the chance you get counterfeited.

A board of :9s4: :9c4: :8h4: :8c4: :2d4: or :qd4: :jh4: :qh4: :3s4: :js4: are losing boards when you have 77 against AKo. There are fewer of these boards possible, as your pair increases. It doesn't happen very often, which explains the very small difference in the equities, but it is more likely to happen the smaller your pair is.


This is exactly it. The probability of getting counterfeited has the biggest impact on 99 having higher equity against AK compared to 77, for example.
 
deeznutzz

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Equilab runs the cards through a hand simulator hundreds of thousands of times and then gives you that data. Imagine if you were to play pocket 7's a hundred times against AA and then you played pocket 6's a hundred times against AA. Say the 7's won 21 out of the 100 times would you expect the 6's to win exactly 21 times? Of course not. The reason that there is such a small deviation in the statistics is because of how many times they've run the hands
 
Collin Moshman

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Equilab runs the cards through a hand simulator hundreds of thousands of times and then gives you that data. Imagine if you were to play pocket 7's a hundred times against AA and then you played pocket 6's a hundred times against AA. Say the 7's won 21 out of the 100 times would you expect the 6's to win exactly 21 times? Of course not. The reason that there is such a small deviation in the statistics is because of how many times they've run the hands


That's a good point, but to clarify, whether it's an analytical result or a simulation, there would always be a difference in 77/66 equity due to the counterfeiting effect.
 
deeznutzz

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That's a good point, but to clarify, whether it's an analytical result or a simulation, there would always be a difference in 77/66 equity due to the counterfeiting effect.
I think I follow. 66 is counterfeit on a 2-6 board where 77 on the same board is not and that's the reason for the difference in equity?
 
Nr98

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This is exactly it. The probability of getting counterfeited has the biggest impact on 99 having higher equity against AK compared to 77, for example.


Exactly, it's the simple fact that 77 has more overcards than 99, and thus is more likely to be counterfeited :top:

As for OP, good to hear you're playing around with equilab a bit (or any similar software for that matter I'm not trying to advertise haha). Getting a feel for how hands perform against certain hands is important! If you expand that to how hands perform vs ranges you're gonna have a good intuition for some all in spots. Keep it up!
 
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fundiver199

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I think I follow. 66 is counterfeit on a 2-6 board where 77 on the same board is not and that's the reason for the difference in equity?

Not quite I think. The reason for the counterfeit is, there is no such thing as 3 pair in NLH. So if the board already contain two pair, which are both higher than your pocket pair, then you can only improve on the board by having a better kicker. For instance on 88772 a hand like 66 is still better than 54 or 43. But that is not much to beat, and if the board is 88779, then 66 is playing the board and can only hope to chop the pot. Of course the lower your pair, the more often it will be worse than the two pair on the board. AA or KK can never be counterfeited by a dubble paired board, while 22 and 33 are counterfeited by any dubble paired board.
 
deeznutzz

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Not quite I think. The reason for the counterfeit is, there is no such thing as 3 pair in NLH. So if the board already contain two pair, which are both higher than your pocket pair, then you can only improve on the board by having a better kicker. For instance on 88772 a hand like 66 is still better than 54 or 43. But that is not much to beat, and if the board is 88779, then 66 is playing the board and can only hope to chop the pot. Of course the lower your pair, the more often it will be worse than the two pair on the board. AA or KK can never be counterfeited by a dubble paired board, while 22 and 33 are counterfeited by any dubble paired board.
Right, and that's kinda how I understand counterfeiting to mean but the op is talking about the equity difference between 99 88 and 77 vs AKo. Against a hand like 78 or 89 the change in equity makes sense but against any non paired hands were both cards are lower than 7 or any non paired hand that has at least one card higher than 9 the equity wouldn't change
 
venycyos

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I didn't take the balance to go through these specific numbers, but I'm pretty sure it's due to the chance that you will be faked.

A board :9s4: :9c4: :8h4: :8c4: :2d4:or :qd4: :jh4: :qh4: :3s4: :js4:is losing board when you have 77 against AKo. There are fewer cards possible, as your pair increases. This does not happen very often, which explains the very small difference between stocks, but it is more likely to happen the smaller your pair.


This is exactly the reason, it also has some flush that the villain will have an advantage.
 
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