Simulation Results AA3sQs vs AQQs3s

[DPCondit]

I did some simulations on Poker Calculator to determine the improvement of low wins with AA3Q vs A3QQ. You can see that AA3Q wins low about 50% more often than A3QQ, and ties slightly less often. I included simulations of Omaha High with the same hands to show how often the ties were on the high side, because the simulator doesn't specify tie low or tie high.

Random flop vs 8 random opponents, 100,000 hands each.


Omaha Hold'em hi/lo 8/b, 100000 combinations tested.

Hand 1:
AsAcQd3d


Hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
------+------+------+------+------+------+------+------+------+------+
High | 8414 | 5023 | 5164 | 4998 | 4988 | 4931 | 5094 | 4924 | 5050 |
Draw | 8428 | 4649 | 4636 | 4766 | 4766 | 4655 | 4724 | 4784 | 4882 |
Lose | 61758| 82896| 83075| 83054| 82876| 83007| 82743| 83097| 82798|
Scoop | 6733 | 4467 | 4425 | 4422 | 4517 | 4595 | 4603 | 4537 | 4513 |
Low | 15273| 3347 | 3078 | 3178 | 3219 | 3169 | 3189 | 3083 | 3146 |
------+------+------+------+------+------+------+------+------+------+
Win% |20.77%| 9.93%| 9.82%| 9.81%| 9.92%| 9.92%|10.04%| 9.84%| 9.95%|
------+------+------+------+------+------+------+------+------+------+

Omaha Hold'em hi/lo 8/b, 100000 combinations tested.

Hand 1:
AcQdQs3s


Hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
------+------+------+------+------+------+------+------+------+------+
High | 4892 | 5795 | 5719 | 5737 | 5704 | 5700 | 5827 | 5613 | 5695 |
Draw | 9996 | 5582 | 5611 | 5574 | 5683 | 5573 | 5700 | 5590 | 5621 |
Lose | 66377| 81612| 81507| 81642| 81597| 81874| 81522| 81681| 81552|
Scoop | 8954 | 3972 | 4025 | 3946 | 3938 | 3855 | 3956 | 4046 | 4083 |
Low | 10719| 3574 | 3671 | 3597 | 3613 | 3546 | 3540 | 3588 | 3568 |
------+------+------+------+------+------+------+------+------+------+
Win% |19.26%|10.12%|10.17%|10.06%|10.07%| 9.93%|10.12%| 10.1%|10.18%|
------+------+------+------+------+------+------+------+------+------+


Omaha Hold'em, 100000 combinations tested.

Hand 1:
AsAcQd3d

Hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
------+------+------+------+------+------+------+------+------+------+
Win | 15164| 9566 | 9529 | 9432 | 9379 | 9652 | 9492 | 9476 | 9758 |
Draw | 872 | 2217 | 2120 | 2158 | 2188 | 2177 | 2106 | 2215 | 2076 |
Lose | 83964| 88217| 88351| 88410| 88433| 88171| 88402| 88309| 88166|
------+------+------+------+------+------+------+------+------+------+
Win% |15.58%|10.61%|10.53%|10.45%|10.41%|10.68%|10.49%| 10.52%|10.74%|
------+------+------+------+------+------+------+------+------+------+

Omaha Hold'em, 100000 combinations tested.

Hand 1:
AcQdQs3s


Hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
------+------+------+------+------+------+------+------+------+------+
Win | 13948| 9748 | 9675 | 9560 | 9826 | 9801 | 9618 | 9554 | 9739 |
Draw | 975 | 2146 | 2214 | 2136 | 2101 | 2147 | 2134 | 2173 | 2099 |
Lose | 85077| 88106| 88111| 88304| 88073| 88052| 88248| 88273| 88162|
------+------+------+------+------+------+------+------+------+------+
Win% |14.41%|10.76%|10.72%|10.56%|10.81%|10.81%|10.62%| 10.58%|10.73%|
------+------+------+------+------+------+------+------+------+------+

Don

[Buzz]

Hi Don - I love simulation data! Thanks!

Looking at the simulation data you have kindly provided, even though you show simulations of Omaha High with the same hands to show how about often the ties were on the high side, I still can’t tell how many of those scoops are wins when no low is possible and how many of those scoops are wins when low is possible. In other words, should I add the scoops to the lows to get the total low wins or not?

In addition, although the bulk of the decrease in losses for low when a queen in your hand is replaced by a second ace would seem to be accounted for by the decreased possibility of facing an opponent with an ace plus a deuce, the loss of an available ace would also make a loss for low to A4XX, A5XX, A6XX, and A7XX less likely. Might seem a little far fetched for AA3Q to lose for low to A7JJ, for example, but if the board was 258K3, although AA3Q would qualify for low (8532A), A-7-J-J would make a better low (7532A). Indeed, even 67KK would make a better low (76532) with the same board. Thus you simply can’t ascribe all of the low losses of AA3Q to A2XX. Those losses where the hand makes the nuts on the flop or the turn and then gets counterfeited on the river - and, as you well know, there are a lot of them - are not due to A2XX. You might not often encounter an opponent in a real game playing a bare A7XX, but you do encounter them in Monte Carlo simulations (and in a real game you might butt heads with someone playing A27X or A37X as a starting hand who gets counterfeited and ends up using A7, or worse, as an “emergency” low).

Yes, there are clearly fewer aces available to make ace-deuce when you hold AA3Q as opposed to A3QQ, and yes, with only two aces instead of three in the pack with which to make a hand containing ace-deuce there should be roughly a one third decrease in the number of opponents you face who would be holding ace-deuce.

Thus, off the top of one’s head, one might expect approximately a 2 to 3 ratio of opponents with ace-deuce when you hold AA3Q and A3QQ, respectively. Roughly, but not exactly. What I actually calculated was a ratio of 2.165 to 3.

In other words, I got 29.3% as the probability in a nine handed game of encountering at least one opponent holding at least one ace and at least one deuce when you have AA3Q and 40.6% as the probability of encountering at least one opponent holding at least one ace and at least one deuce when you have A3QQ. Never a guarantee my math is correct, but I spent a lot of time trying to get this one right.

I can see from your simulation data (thanks) that AA3Q wins for low more often than A3QQ. And they are clearly both good hands. If we disregard scoops there is roughly a 3 to 2 low win ratio. (However, don’t some of those scoops involve making a winning low hand along with a winning high hand?)

AsAcQd3d-O8.......AcQdQs3s-O8
High 8414........High 4892
Draw 8428........Draw 9996
Lose 61758.......Lose 66377
Scoop 6733.......Scoop 8954
Low 15273 ......Low 10719
Win% 20.77%......Win% 19.26% -

AsAcQd3d-high AcQdQs3s-high
Win 15164.......Win 13948
Draw 872........Draw 975
Lose 83964......Lose 85077
Win% 15.58%......Win% 14.41%

Thanks again for the simulation data.

Buzz

[iblucky4u2]

One of the most interesting things about the sims you kindly provided is that the AQQ3 scoops 8954 to 6733 for the AAQ3. This shows how AA has a big downside when an A is flopped for a set. With KK, QQ and JJ when you flop the set you are more likely to scoop and that more than makes up for the difference in shared lows.

[DPCondit]

[ QUOTE ]
In addition, although the bulk of the decrease in losses for low when a queen in your hand is replaced by a second ace would seem to be accounted for by the decreased possibility of facing an opponent with an ace plus a deuce, the loss of an available ace would also make a loss for low to A4XX, A5XX, A6XX, and A7XX less likely. Might seem a little far fetched for AA3Q to lose for low to A7JJ, for example, but if the board was 258K3, although AA3Q would qualify for low (8532A), A-7-J-J would make a better low (7532A). Indeed, even 67KK would make a better low (76532) with the same board. Thus you simply can’t ascribe all of the low losses of AA3Q to A2XX. Those losses where the hand makes the nuts on the flop or the turn and then gets counterfeited on the river - and, as you well know, there are a lot of them - are not due to A2XX. You might not often encounter an opponent in a real game playing a bare A7XX, but you do encounter them in Monte Carlo simulations (and in a real game you might butt heads with someone playing A27X or A37X as a starting hand who gets counterfeited and ends up using A7, or worse, as an “emergency” low).


[/ QUOTE ]

Yes, there is no guarantee what low hand it is losing to. I am going to run some simulations with a low board and two high cards to see roughly what the low win percentages should be. With a stacked board of 678-Hi-Hi, A3 can only lose low to A2, so that should answer that particular question.

[ QUOTE ]
Looking at the simulation data you have kindly provided, even though you show simulations of Omaha High with the same hands to show how about often the ties were on the high side, I still can’t tell how many of those scoops are wins when no low is possible and how many of those scoops are wins when low is possible. In other words, should I add the scoops to the lows to get the total low wins or not?


[/ QUOTE ]

Hmmmph, as I add the data together, it becomes obvious that one must add the high wins to the scoops to get the total number of (no draw) high wins, therefore they may have likely added some of the lows in there which did not show up under low wins. Every different simulator has its own way of showing Omaha/8 data, it is impossible to draw accurate conclusions without an intimate knowledge of how these numbers are generated (this is especially true with Turbo O/8, I had to email Bob Wilson with many questions to nail down exactly how his data was being calculated [which is actually somewhat different than it appears] this information is absolutely mandatory).

Ok, from the manual for Poker Calculator:

Scoop: Times this hand won the whole pot in a high low game. Note that if no low hand qualifies, the high hand winner is marked in here instead of "High".

Low: How many times this hand won the low half of the pot. Note that if this hand also wins the high half, it is marked under scoop instead.

Ok, I know how to do it. I will stack the board so that our hand ALWAYS WINS HIGH by giving it the unbreakable nut high. Since the board will be stacked that there is ALWAYS A LOW, all non-split lows will appear as "scoops", and all draws will represent low split pots. I will suit the ace and give us a nut flush with no straight flush possible on an unpaired board. This is the only way I can think of to produce an unadulterated number for the low wins.

Good catch, I would have seen it when I sat down to really analyze the data, which I hadn't done yet. There's almost always a roundabout way of obtaining the data you want, you have to be clever sometimes to get accurate Omaha/8 data, as often there is no straightforward way to do it in many programs.

Don

[Buzz]

"One of the most interesting things about the sims you kindly provided is that the AQQ3 scoops 8954 to 6733 for the AAQ3. This shows how AA has a big downside when an A is flopped for a set. With KK, QQ and JJ when you flop the set you are more likely to scoop and that more than makes up for the difference in shared lows."

ibluck4u2 - You counterfeit your low when you flop an ace with either hand (or when you catch an ace on the turn or river, as well). This has to be roughly twice as likely when you only have one ace in your hand as when you have two. But catching an ace on the board is more of a downside when you only have one ace than when you have two.

Comparing the data for the two hands, it's true that AcQdQs3s scoops more than AsAcQd3d. That might seem to make AcQdQs3s more playable.

However, in my humble opinion, it isn't.

What the simulator doesn't show is how often either hand ends up second best. Although both hands are very nice hands, it's brutal when you get beaten on the high side with either of them. One important reason why a pair of queens in a starting hand is simply not as good as a pair of aces is because you end up second best with full houses involving queens more than you do with full houses involving aces.

In addition, although Don's data shows AcQdQs3s scoops 33% more than AsAcQd3d, it also shows that AsAcQd3d wins for high 72% more often and wins for low 42% more often.

I like scoops too. You have to scoop at this game to do well. But both of these hands do well in the scoop department. And scoops are only part of the picture here (albeit, I'll agree, an important part).

Just my opinion.

Buzz

AsAcQd3d-O8.......AcQdQs3s-O8
High 8414...............High 4892
Draw 8428..............Draw 9996
Lose 61758............Lose 66377
Scoop 6733...........Scoop 8954
Low 15273 ............Low 10719
Win% 20.77%.......Win% 19.26%

[Buzz]

AsAcQd3d-O8.......AcQdQs3s-O8
High 8414...............High 4892
Draw 8428..............Draw 9996
Lose 61758............Lose 66377
Scoop 6733...........Scoop 8954
Low 15273 ............Low 10719
Win% 20.77%.......Win% 19.26%

Hi Don - You counterfeit your low when you flop an ace with either hand (or when you catch an ace on the turn or river, as well). This has to be roughly twice as likely when you only have one ace in your hand.

I thought of a way to maybe explain to you why it's not exactly twice as likely.

Here's the math for no ace on the board:

P no A for AA3Q:
1-(46*45*44*43*42)/(48*47*46*45*44) =
1-(43*42)/(48*47)
0.1995.

P no A for A3QQ:
1-(47*46*45*44*43)/(48*47*46*45*44) =
1-43/48 =
0.1041.

Maybe that makes it clear.

0.1995 is close to twice as much as 0.1041.

Thus catching an ace on the board when you have only one ace figures to be almost twice as likely, but not quite twice as likely, as when when you have two aces.

"Ok, I know how to do it. I will stack the board so that our hand ALWAYS WINS HIGH by giving it the unbreakable nut high. Since the board will be stacked that there is ALWAYS A LOW, all non-split lows will appear as "scoops", and all draws will represent low split pots. I will suit the ace and give us a nut flush with no straight flush possible on an unpaired board. This is the only way I can think of to produce an unadulterated number for the low wins."

Great idea! Thanks. I had a series of questions regarding my own confusion about this. You already have answered some of them. Hopefully your game plan will answer the rest.

Thanks, as always, for your assistance.

Buzz

[iblucky4u2]

Your points are valid, but when you look at the bottom line, wins, there is only a 1.55% difference - and the scoops more than make up for that - IMHO.

[DPCondit]

[ QUOTE ]
Hi Don - You counterfeit your low when you flop an ace with either hand (or when you catch an ace on the turn or river, as well). This has to be roughly twice as likely when you only have one ace in your hand.

I thought of a way to maybe explain to you why it's not exactly twice as likely.

Here's the math for no ace on the board:

P no A for AA3Q:
1-(46*45*44*43*42)/(48*47*46*45*44) =
1-(43*42)/(48*47)
0.1995.

P no A for A3QQ:
1-(47*46*45*44*43)/(48*47*46*45*44) =
1-43/48 =
0.1041.

Maybe that makes it clear.

0.1995 is close to twice as much as 0.1041.

Thus catching an ace on the board when you have only one ace figures to be almost twice as likely, but not quite twice as likely, as when when you have two aces.



[/ QUOTE ]

Thanks, that's good data. Because of the way the data is presented in this program, it is impossible to figure this out in simulation without the program commingling the high and low information. Unfortunately, in order to completely separate out the low data from the high, I have to stack the board, which eliminates any counterfeit possibilities. But that is a different question, which needs a different approach.

[ QUOTE ]
Great idea! Thanks. I had a series of questions regarding my own confusion about this. You already have answered some of them. Hopefully your game plan will answer the rest.



[/ QUOTE ]

There will be some further explanation with the simulations. Hopefully I can answer your questions.

Don

[Buzz]

"....but when you look at the bottom line, wins, there is only a 1.55% difference - and the scoops more than make up for that...."

iblucky4u2 - True, the bottom line in this particular simulation is not much different between AA3Q and A3QQ. But it is the bottom line. Scoops have already been given their due in computing this bottom line. You can’t logically go back and say that the bottom line, which already weights scoops as worth twice as much as high wins or low wins and as worth four times as much as draws, is less important than scoops.

Yeah, scoops matter big time - but they’re not all that matters.

Other simulations, Boston’s for example, show that AA3Q hands are clearly better than A3QQ hands. It’s perhaps easier for an experienced Texas hold ‘em player who is just starting to play Omaha-8 to over play a pair of aces than a pair of queens. But assuming you play both the aces and the queens correctly (whatever that means), a pair of queens in a starting hand is simply not as good as a pair of aces, regardless of the fact that when you catch an ace on the board it counterfeits your own low and makes it easier for an opponent to make low. You are correct about that being a drawback - but even with that drawback, a pair of aces is still much better than a pair of queens in a starting hand. Period.

Take care. I always appreciate your posts and thinking, even when we disagree.

Buzz

[Fraubump]

One thing to consider here is that a not insignificant # of scoops happen in situations where you would never have gotten that far in the hand, like when the flop is 344. With A3QQ you are not calling any bets unless maybe you are heads up, so turn and river full houses and the odd queens up winner are lost instead of won. The way you are looking at the data is through an "all-in" perspective, which bears only a moderate correlation with in-hand playability. This is another factor that makes AA3Q more playable because, even though unimproved aces rarely hold up, you are more likely to hang around to the river with them than you are with QQ.