did I bo***cks this up?AA

[bravos1]

[ QUOTE ]

By your rationale then I'd like to see 9 callers at full ring every time I raise with AA. Maybe that's really the way the numbers work, but if it is then it's something I don't understand completely.

[/ QUOTE ]

Absolutely.. I want all 9.. [img]/images/graemlins/grin.gif[/img]
Let's take a quick look and run the numbers shall we?

Hero has AA vs 9 other random hands:
30,175,474 games 166.013 secs 181,765 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 29.746% 29.42% 00.33% 8878138 99092.67 { AA }
Hand 1: 07.813% 07.02% 00.80% 2117883 240196.58 { random }
Hand 2: 07.800% 07.01% 00.80% 2114022 240123.83 { random }
Hand 3: 07.801% 07.00% 00.80% 2113786 240509.50 { random }
Hand 4: 07.817% 07.02% 00.80% 2118244 240770.92 { random }
Hand 5: 07.801% 07.01% 00.79% 2114754 239517.67 { random }
Hand 6: 07.809% 07.01% 00.80% 2116252 240370.08 { random }
Hand 7: 07.803% 07.01% 00.80% 2114833 240044.00 { random }
Hand 8: 07.802% 07.01% 00.80% 2114150 240621.17 { random }
Hand 9: 07.808% 07.01% 00.80% 2116127 240426.58 { random }

So what does this mean? We will win about 30% of the time vs a normal distribution of 10%. Let's pretend that every person just puts $10 into the pot preflop and there is no betting afterwards. Each hand the pot is $100 (no rake) and you win 3 times out of 10 so you win $300. The other 7 hands you lose a total of $70. Do you see why this is favorable for you?

Add in additional factors and it is even more profitable. A good player will be able to lay down AA when it is obvious they are beat in those 7/10 times, but a good player will also make MORE money off of bad players in the other 3 hands because they call down w/ garbage like K5o on a KQ629 board and there will be 9 people available to pad your pot.

Is it frustrating when someone cracks your AA with 93s? Sure, but it is even better when 3 of them are chasing/calling down to the river w/ garbage..

and that makes me [img]/images/graemlins/grin.gif[/img].

[DrModern]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
...But, I'd also rather play AA against as few people as possible.

[/ QUOTE ]

Hmmm well that doesn't make sense.

Situation 1:

You raise with AA, three villains call with J8o, KQo and 44 respectively.

Situation 2:

You raise with AA, one villain calls with KTo.

In which of these do you make more money?

[/ QUOTE ]

Well, the obvious answer is before the flop you make more money with more callers. After the flop it's a different story. Your chances of winning the hand after the flop obviously decline with more callers.

By your rationale then I'd like to see 9 callers at full ring every time I raise with AA. Maybe that's really the way the numbers work, but if it is then it's something I don't understand completely. Does having more callers always fully make up for the lower liklihood of winning the hand? It's just a theoretical question, since I can't really control the number of callers, but I'm not clear on the answer.

[/ QUOTE ]

The answer, as always, is "it depends."

[mmctrab]

[ QUOTE ]
[ QUOTE ]

By your rationale then I'd like to see 9 callers at full ring every time I raise with AA. Maybe that's really the way the numbers work, but if it is then it's something I don't understand completely.

[/ QUOTE ]

Absolutely.. I want all 9.. [img]/images/graemlins/grin.gif[/img]
Let's take a quick look and run the numbers shall we?

Hero has AA vs 9 other random hands:
30,175,474 games 166.013 secs 181,765 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 29.746% 29.42% 00.33% 8878138 99092.67 { AA }
Hand 1: 07.813% 07.02% 00.80% 2117883 240196.58 { random }
Hand 2: 07.800% 07.01% 00.80% 2114022 240123.83 { random }
Hand 3: 07.801% 07.00% 00.80% 2113786 240509.50 { random }
Hand 4: 07.817% 07.02% 00.80% 2118244 240770.92 { random }
Hand 5: 07.801% 07.01% 00.79% 2114754 239517.67 { random }
Hand 6: 07.809% 07.01% 00.80% 2116252 240370.08 { random }
Hand 7: 07.803% 07.01% 00.80% 2114833 240044.00 { random }
Hand 8: 07.802% 07.01% 00.80% 2114150 240621.17 { random }
Hand 9: 07.808% 07.01% 00.80% 2116127 240426.58 { random }

So what does this mean? We will win about 30% of the time vs a normal distribution of 10%. Let's pretend that every person just puts $10 into the pot preflop and there is no betting afterwards. Each hand the pot is $100 (no rake) and you win 3 times out of 10 so you win $300. The other 7 hands you lose a total of $70. Do you see why this is favorable for you?

Add in additional factors and it is even more profitable. A good player will be able to lay down AA when it is obvious they are beat in those 7/10 times, but a good player will also make MORE money off of bad players in the other 3 hands because they call down w/ garbage like K5o on a KQ629 board and there will be 9 people available to pad your pot.

Is it frustrating when someone cracks your AA with 93s? Sure, but it is even better when 3 of them are chasing/calling down to the river w/ garbage..

and that makes me [img]/images/graemlins/grin.gif[/img].

[/ QUOTE ]

Okay, good. Thanks for doing that. I mean, I always raise AA, reraise and cap if it gets to that. But then, I've also wondered whether there was a point where having more callers reduced your post flop expectation more than the preflop raise increased your expectation. Thanks again.

[argybargy2002]

A good way to think about aces preflop is that if you are on the button with them you don't really care how many limpers or raises there are to you because any number is good.

If there's only one limper, raise and think "great I've got about an 80% chance of winning the pot". If there's lots, raise and think I've got a good chance of winning a huge pot. Either way its all good. Just make sure you raise it preflop

[TheCardGeek]

[ QUOTE ]

Hero has AA vs 9 other random hands:
30,175,474 games 166.013 secs 181,765 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 29.746% 29.42% 00.33% 8878138 99092.67 { AA }
Hand 1: 07.813% 07.02% 00.80% 2117883 240196.58 { random }
Hand 2: 07.800% 07.01% 00.80% 2114022 240123.83 { random }
Hand 3: 07.801% 07.00% 00.80% 2113786 240509.50 { random }
Hand 4: 07.817% 07.02% 00.80% 2118244 240770.92 { random }
Hand 5: 07.801% 07.01% 00.79% 2114754 239517.67 { random }
Hand 6: 07.809% 07.01% 00.80% 2116252 240370.08 { random }
Hand 7: 07.803% 07.01% 00.80% 2114833 240044.00 { random }
Hand 8: 07.802% 07.01% 00.80% 2114150 240621.17 { random }
Hand 9: 07.808% 07.01% 00.80% 2116127 240426.58 { random }

So what does this mean? We will win about 30% of the time vs a normal distribution of 10%. Let's pretend that every person just puts $10 into the pot preflop and there is no betting afterwards. Each hand the pot is $100 (no rake) and you win 3 times out of 10 so you win $300. The other 7 hands you lose a total of $70. Do you see why this is favorable for you?


[/ QUOTE ]

These statistics are misleading. While they are accurate - they ignore that AA actually has a better equity advantage with less people in the pot.

Here are some numbers I created awhile back studying this exact phenominon:



The Y Axis represents the equity advantage a hand has over average hands.

As you can see, AA's advantage over other hands dimenishes with each player beyond 3. While the pots will be larger with more people in, and this CAN translate to more profit - it is more likely to translate into more variance, and tougher post flop decisions.

I've created the following tables to compare equities against various opponent ranges:

Random Opponent Hands:


Opponents with Top 22% Hands


The row on the bottom multiplies the number of opponents by the equity of AA, and it shows that you have more "equity value" with more players in - but it also shows that value scales less and less with each additional player.

When you compare these two tables together, you can see that AA has more of an equity edge, and equity value against opponents with higher hand ranges.

So, why is it important to raise AA preflop?
The most important reason, is to capitalize on your equity advantage PreFlop. A lesser, but still valuable reason is to limit the field to those opponents with better hands - as you have a bigger equity advantage over them.

Optimally, you want to limit your field to 3 to 5 players.

[bravos1]

I'm not going to post a huge reply to your comments but........

These numbers are not misleading at all. They are what they are. We all understand that AA loses relative equity when more people enter the pot. This is true for any hand that is a favorite preflop and is simple math. This was the issue that the OP was having.

My numbers show the worst case scenario, eg. your AA vs 9 other people. In the end, you will still come out ahead... please realize that the end is FAR FAR away when variance and probability even out.

It is plain and simply wrong to think what you wrote in your last sentence.. "Optimally, you want to limit your field to 3 to 5 players."!

Also this makes no sense to me.... "A lesser, but still valuable reason is to limit the field to those opponents with better hands - as you have a bigger equity advantage over them." I am guessing that you mean "better" as compared to the others in the pot? Even that makes no sense. 89s is a far better hand then 72o, and yet I have a less equity advantage over 89s.

So, why do we raise AA preflop? Is it to fold 72o? 89s?

NO!!!!!!ONE MILLION!!!!! it is because we have the largest possible equity preflop and we need to be getting that $$ in! Does it sometimes make it correct for draws to call on later streets? Yup.. but who cares? When you win, you win big, and when you lose, you will lose small compared to pot size. Even your chart shows this fact. Look at the row you call "AA Equity". You will notice that it still continues to increase even though your "equity edge" decreases. What does that mean?? I means we are making money, and personally I [img]/images/graemlins/heart.gif[/img] making money!

Take this scenario...

Your playing NL or uncapped Limit and nine people push it all in PF. Are you going to fold AA? Should you (mathematically speaking) ever just call when you can still raise? Why not?

OK.. guess my reply ended up being longer than I thought.. [img]/images/graemlins/tongue.gif[/img]


BTW, please do not relate this to the sanity which may be lost at times losing to donks cold calling w/ garbage.

[unterfish]

Geek,
nice post.
If I understand your numbers right, the interesting thing is that you gain in equity the more selective the opponents are preflop.
Edit: You mentioned that in your post. Have to read the whole post before I reply I guess [img]/images/graemlins/smile.gif[/img]

I did some of these calculations on my own some time ago, because I wanted to know why PF charts are how they are.
I think it'd be valuable for some people (like me) if the guys who create these charts would explain why. Maybe not in their books because maths/statistics is boring for most people, but somewhere else.

Edited for grammar

[DrModern]

[ QUOTE ]
Geek,
nice post.
If I understand your numbers right, the interesting thing is that you gain in equity the more selective the opponents are preflop.
Edit: You mentioned that in your post. Have to read the whole post before I reply I guess [img]/images/graemlins/smile.gif[/img]

I did some of these calculations on my own some time ago, because I wanted to know why PF charts are how they are.
I think it'd be valuable for some people (like me) if the guys who create these charts would explain why. Maybe not in their books because maths/statistics is boring for most people, but somewhere else.

Edited for grammar

[/ QUOTE ]

Um, please read Bravos' reply to this. There are some statements in CardGeek's post that are totally wrong.

[unterfish]

Ok, I did read bravos post [img]/images/graemlins/smile.gif[/img]
And he's right. And I would always raise AA's - in any situation.
But I just wanted to mention that I thought about preflop charts and why they are what they are .
Maybe it didn't belong here (but where else?).
I just thought geeks post was nice because he tried to answer this question.
In general I mean: we all speak about PF decisions all the time. IMO, PF is boring. But that's only my personal opinion.
But when we talk PF, how do we know that coldcalling AJs is better than raising or folding?
How do we know it's actually better multi-handed than short-handed?
And how much difference is there between AJs and AJo?

I just think those are fair questions which I don't know the correct answers to.
Do you?

[DrModern]

[ QUOTE ]
Ok, I did read bravos post [img]/images/graemlins/smile.gif[/img]
And he's right. And I would always raise AA's - in any situation.
But I just wanted to mention that I thought about preflop charts and why they are what they are .
Maybe it didn't belong here (but where else?).
I just thought geeks post was nice because he tried to answer this question.
In general I mean: we all speak about PF decisions all the time. IMO, PF is boring. But that's only my personal opinion.
But when we talk PF, how do we know that coldcalling AJs is better than raising or folding?
How do we know it's actually better multi-handed than short-handed?
And how much difference is there between AJs and AJo?

I just think those are fair questions which I don't know the correct answers to.
Do you?

[/ QUOTE ]

Right, they are fair questions. No problem with asking them. Just trying to say that Bravos has things straight here. They're all good questions to be asking, and while you can just memorize a decent play for all hands, it's worth inquiring as to why a good play is good. If you have a specific preflop question, start a thread about it. Make up a hand as an example if you need to.