Theorem of poker

[sirtemple]

I think I've found the rift in logic. [ QUOTE ]

...but even when your hand is the best hand, you generally prefer your opponant to fold rather than call when the pot is large. The reason is that when you bet in a limit game and the pot is large, your opponants hand, though second best, is rarely so much of an underdog that he is not getting good enough odds to chase you. Hence, his calling you with good odds is a profitable play for him in the long run. Since he is correct to take the odds, you do not gain when he calls. You gain only when he folds and turns down those odds. When he calls, you lose even if you happen to win that particular pot; for over the long run his call has positive expectation. It will end up costing you money.
--


[/ QUOTE ]
An example:

$120 in the pot

Hero: A [img]/images/graemlins/diamond.gif[/img]A [img]/images/graemlins/heart.gif[/img]
LAP: 7 [img]/images/graemlins/club.gif[/img]8 [img]/images/graemlins/club.gif[/img]

Flop: J [img]/images/graemlins/diamond.gif[/img]6 [img]/images/graemlins/diamond.gif[/img]5 [img]/images/graemlins/spade.gif[/img]

You bet out $20

The LAP will make his hand 34% of the time. It is correct for him to call. If he folds you will win $120 100% of the time. If he calls you will win $140 66% of the time. Folding gives you an EV of $120 while calling only gives you an EV of $94. His calling cost you $26. This is why Slansky says you want him to fold.


So your EV on the Flop is:
120 if he folds
94 if he calls
0 if YOU fold

Clearly folding is an aweful choice.

But where did the $120 in the pot come from? You have positive EV either way because you got so much $ in the pot early. It is correct at this point for the LAP to chase. You are ignoring the fact that it was VERY wrong for him to get this far at all.

Asuming you each put in $60 of the $120 pre-flop your EV for the Hand based on flop decisions is:

He Folds: +60
He Calls: +14
You Fold: -60

It is even clearer now that we want him to fold, but there is no reason in the world WE would fold.

Calling any bets before the flop is the mistake these players make. That's why you dream of capping it preflop regardless of the number of players. After the flop their chansing hurts you, in so much as you will win less, but you've already won. Any capped pre-flop w/ aces is a positive EV for you. PERIOD. Regardless of who chases what, you've already made money.

Jason

[Monty Cantsin]

[ QUOTE ]
flopping any set against this many loose players is costly.

[/ QUOTE ]

Hm... is this entire thread one long shaggy bad beat story?

Forget the fundamental theorem of poker for a while and concentrate on avoiding the fundamental mistake of poker: results-oriented thinking. Yeah, your aces got cracked and your sets got cracked. Boo hoo.

You don't need to engage in any complicated theoretical strategic restructuring to beat loose games, if you play tight, aggressive, smart poker you will beat them. However, if you want to maximize your winnings in these games there are adjustments you should definitely make. Read "Small Stakes Holdem" by Ed Miller et al. Also the micro and small stakes forums are chock-a-block full with advice for optimal play under these game conditions.

But, mostly, the comment above makes me think you are falling in the trap of over-emphasising the results of a few unfortunate sessions. Suck it up.

/mc

[cnfuzzd]

<<<I am most certainly not an expert player. I am however a winning player. But that is because I am aware and humble of where my game has faults and I am careful to stay away from situations I know I will have a hard time with. Though as I said, its more frequent I run into situations I dont care for when playing online these days. I am on the quest to improve my game in these specific situations.>>>

For what its worth, i meant no denigration by my original comment, i hope it didnt come across that way. You are obviously a good enough player to examine your game and seek out leaks to plug. That having been said, you are essentially playing in a VERY weak tight manner, at least in these situations. If that makes you feel more comfortable, its your money, you can do whatever you want. But you must know that you are sacrificing huge amounts of EV in some of the most profitable games to be found. You are letting money go that should be your. Also, i think i realized your problem. You are focusin on winning pots, as opposed to money. You need to examine ALL your decision from the perspective of how to make the most money, and not care about who wins *this* pot. Thats why the example of aces vs a full field making over 1000bb's in profit is so accurate. More below.

<<<I currently have the best hand but I am not so sure I am the 'Favorite' to win there against 7 or more players with 2 cards to come, however. An open ended straight with a flush possability would be a 2 to 1 favorite over that hand wouldnt it?>>>

Its two to 1 AGAINST making the flush or straight, btw. However, even if your opponent holds 5s 7s, giving him the flush and OES draws, you are still going to win sixty percent of the time. Lets run the hundred hand example assuming putting a total of 4 bb's into the pot. In the above scenario, you will lose to the flush or straight 40 times out of 100, for a total loss of 160 big bets. You will win 60 times out of 100. Not counting the money you put into the pots you win, you will win 240 big bets. That is a profit 80 big bets with a hand you want to fold. That makes very little sense to me. Verbalize your thinking furhter.

<<<Holding up 35% of the time is losing 65% of the time.. isnt it?>>>

Yes, yes it is. But we dont play poker to win pots, we play it to win money. Reread the example i gave in my original post. You can lose 65% of the time and still be profitable, vastly so. Giving up these profitable situations has got to be killing your winrate.

<<<As for losing money over time in this situation, this is one of the theorem problems that made me scratch my head. I didnt make it up, it is actually discussed in The Theory of Poker. (I forget which chapter but I'll try to find the exact text later)If I understand it correctly... (this is not a quote from the book, just an example of how I understand, or don't understand it) If I were to consistantly play my big hands against a large field when the pot is laying sufficient odds to the drawing hands, It would be liken to the coin flip example of giving 2 to 1 on the flip. I would lose money over time.>>>

I did a cursory examination, and couldnt find anything, so you might want to post the text or at least a page number later. I would be curious to know if sklansky meant AA when he said big hands. Also, refer back to the examples to see how this is not losing money. You are the favorite, its simple. The vast magority of the deck are outs for you.

<<<I would tend to agree but my results in these situations are what kills my profits. One loss here will be for a lot of chips. Play on the flop will likely be raised without thinning the field. Gaining those chips back is usually a long slow grind. Remember that the situation I am describing is not 'average'. This is a family pot with player types that are not going away under any circumstances.>>>

well now you are getting into the discussion of variance. The more players who play, the higher your variance, but as long as you are a winning player, that also means higher profits. As you said these players are terrible, and like to put chips into the middle. Who could be a better opponent.

<<<I play all over the place. Ultimate bet, Party poker, Poker stars Full-Tilt and True Poker. Although I see this mostly at Party and UB lately. Party's 2/4 games will do this very often then settle back down. I'll raise UTG with a big hand and get called by the whole table. I usually throw it away in disgust right afterward and am almost always glad I did so when the guy with the small 2 or 3 gap hits the straight or the flush hits. Which 'seems' to be more often than not against this many players>>>

I too play in these games, and trust me, they are very profitable, for the exact things you DONT like about them.

<<< See, this is what confuses me. The contradiction. If Im going to lose most of the time against that many players isnt this a losing proposition in the long run? This is why Im asking if Its correct to just toss it and only play it against a smaller field.>>>

Look back at the example, which you seem to have not even read. [img]/images/graemlins/grin.gif[/img] Dont count the number of *pots* won, count the number of big bets accumulated by hero. thats whats important.


To sum up, i think if you want elevate your game, you should immediatly go out and buy small stakes holdem. like right now.


peace

john nickle

[jedi]

[ QUOTE ]

I currently have the best hand but I am not so sure I am the 'Favorite' to win there against 7 or more players with 2 cards to come, however. An open ended straight with a flush possability would be a 2 to 1 favorite over that hand wouldnt it?

Holding up 35% of the time is losing 65% of the time.. isnt it?


[/ QUOTE ]

Many others have chimed in, so I won't rehash everything, but think about this:

You discussed the 2 to 1 coin flip example as an example of why you wouldn't want to play AA. However, it's not like this at all.

In your quote above, you say that AA will win 35% of the time and lose 65% of the time 7 handed. Okay. So you will lose 4 bets (let's say) 65% of the time. The other 35% of the time you will win 24 bets.

Think of it another way. Roll a die. If you hit 5 or 6, you win 24 bets. If you roll a 1,2,3 or 4, you lose 4 bets. Is that more like the 2-1 coin flip example?

[purnell]

[ QUOTE ]
I currently have the best hand but I am not so sure I am the 'Favorite' to win there against 7 or more players with 2 cards to come, however. An open ended straight with a flush possability would be a 2 to 1 favorite over that hand wouldnt it?

Holding up 35% of the time is losing 65% of the time.. isnt it?

[/ QUOTE ]

Lets say I am holding a lottery with nine other entrants. Each entrant has a 7.2% chance of winning the prize, which is ten times the cost of a ticket. I am offering you a special ticket: if no one else hits the number, you win, giving you a 35% chance of winning. Will you buy this special ticket for the same price as everyone else?

[CurryLover]

[ QUOTE ]

If I am way off base in my understanding here please let me know.


[/ QUOTE ]

You are way off base in your understanding.

I thought your first post was a joke actually, but it seems from your second post that you are serious.

I'm not going to offer any long explanation to you because one of the other posters has already done that in detail. Either you haven't read and thought about it properly, or you just don't understand it.

[knightunner]

[ QUOTE ]

In limit holdem with 10 players-
You are on the button with Ac Ah.
UTG limpes in and is raised by UTG+1. 5 players cold call 2 bets to you.
Would it not be correct, according the the theorem, to fold your aces? If you call or raise, everyone will stay in the hand to see the flop. This would effectivly mean you are laying odds to any 2 suited cards or any connectors, which are likely in the field. By playing this way consistantly over time, you would loose money. Essentially you would be the imbecile giving 2 to 1 on the coin flip would you not?

Lets say you call or raise in this situation and everyone stays in. The flop is As 6h 4s. Early position bets and is then raised. The rest of the field calls to you. would it again not be correct to fold your set according the the theorem? Raising will not thin the field in any signifigant way and likely only lay better odds against your set for the rest of the hand. Over time, I see more flushes and straights panning out in this situation than Aces full.

Lets say your at the same table but UTG. You hold the same 2 aces. Would it not be correct to fold them UTG? If you make it 2 bets, you can be 99% sure of getting called by about 7 of the ten players. This would be putting yourself in the same situation of laying odds to the other hands over time wouldnt it? You'd see bad beat after bad beat time and time again wouldn't you?

[/ QUOTE ]

This is playing weak tight. The Fundamental Theorum of Poker, from my understanding, works both ways. If you fold a hand that you should have played against your opponents, you are contributing to their winnings. AA, preflop, is the nuts. Even if 2 suited cards hit on the flop along with your set ace, the odds of them hitting there flush are roughly 3:1. With the post flop nuts, and 5 people in the pot, you are getting more than enough pot odds to call. Really, at this point you want the pot to be as big as possible. If you know they are going to call, you need to raise and reraise.

Folding this hand goes against the Theorum.
~knight

[LinusKS]

Foo,

A couple of things. First, don't let snotty comments from players who may not know as much as they think they know (or as much as they'd like you to think they know) get under your skin.

There's nothing wrong with playing where you're comfortable, or avoiding high variance situations.

As to your questions about AA, here's a site that will help you: http://twodimes.net/poker.

If you look at the pokenum hand analyzer, you can get a good idea of how aces perform under different situations.

Under this situation, for example -

ah ad (hero)
ts 9s (suited connector)
2c 2h (small pair)
as 7s (Axs)
jh 6h (suited)
ks th (high cards)
qc 6c (suited)

The odds pre-flop are as follows:

HAND WIN%
Ad Ah 33.19
Ts 9s 9.19
2c 2h 16.66
As 7s 7.41
Jh 6h 8.97
Ks Th 7.27
Qc 6c 13.63

Since there's seven people in, the only other hand getting odds to call here preflop is the pair of twos (leaving aside the blinds for the moment).

The tricky thing about AA, though, is that you're not going to know when you're behind.

If a 2 comes, you're not going to know you're up against a set. If the flop happens to have a J and an 8 of spades, you're not going to know you're up against a straight-flush draw. And if a Q and 6 come, you're not going to know two pair is out there. Etc. etc. etc.

What this means is that they're getting implied odds.

If the 22 hits, he can confidently bet out on the flop.

The situation isn't nearly as easy for you.

If you're playing against a field of complete morons, you can probably bet your AA all the way to the river every time, and win money in the long run. This is because when you do win, you'll win very large pots, making up for all the losses.

If there are even a few good players sitting with you, the situation is more difficult, because you could be - without knowing it - giving huge implied odds to speculative hands.

Something to remember - when you hold AA at these kinds of tables, you will lose most of the time and when you do lose, you'll lose many bets.

If you have a small bankroll, or you can't handle huge swings, it doesn't take much in the way of a bad run to ruin you.

Another thing - if you are playing aces at a loose table, you should always put as much into the pot preflop as you possibly can.

It's after the flop that things start to get tricky.

[LinusKS]

The way that good players win money on loose tables with speculative hands (suited connectors, small pairs, Ax suited) is by folding when the flop misses them, and calling and raising when it hits. They're taking advantage of implied odds to beat hands like AA. That's another reason to get as much money into the pot as possible preflop. You want to narrow the implied odds on those kinds of hands as much as possible, or even eliminate them, if you can.

If you're losing money with big pairs, it could be that you're not folding enough post-flop - a very tricky thing to learn, IMO.

Or it could be that you've just been unlucky, especially your sample is not especially large.

[PokerFoo]

I understand the math here but I'm not sure you can use that like a holy grail on how to play. It doesnt take into account so many other things.

Like when you DO win you will likely win LESS than you lost if you played equally as aggressive in THESE situations.

Because the flop didn't hit the suited gap in any way and they didn't stay in. Or because you WILL pair the board and it scares off the flush and straight draws. Remember Your hand is the one that looks best so your going to pay off the hidden hands who can easily identify what they have to beat. You are not so sure against a field this large and loose what anyone can have.

With that many players though, your probably going to have to turn over a straight or better to take the pot. If I am wrong about this please show me some data to show otherwise.

Not to mention more often than not you wont hit the set and you will be in a trickier position of holding top pair only.

Lets not use the example I described in the first post as anything but a general way to articulate how loose the table is playing. Im not looking for advice on what the absolute best thing to do with those exact cards is.

Most texts say you should tighten up conciderably in these situations. But my own stats indicate that aces are not profitable against this large field and are in fact a huge leak.

I guess a simple way to ask the question is this. If your on the button and 7 or more players have all called 3 bets up to this point and your about to cap it....

The table has been playing like this for the last 30 minutes consistantly and you KNOW the flop play will be raised just like the pre-flop play...

What would you rather have? Aces, kings or 5 8 suited?

(I dont include Ax suited because I already know thats a profitable hand to have there. Im am trying to determine what other hand types I can play here without creating another leak)

Or am I better off doing what I have been doing and just not get involved at all when the table is like this? I can wait until it settles down and get in with the best hand against one or 2 players later.