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# Applying Sklansky's Theorem

• 22-06-2007 9:12am
Closed Accounts Posts: 240 ✭✭

I was thinking how the following situation is is related to Sklansky’s Fundemental Theorem of Poker. i.e. You are making a mistake whenever you act differently than you would if you could see you’re opponent’s hole cards. Is option (a) or (b) the mistake??

Situation:

You’re heads up against one player and you flop the nuts. You’re hole cards are 89o. Flop is 567 with two hearts.

Lets say you have a history with this player and have a fantastic read on him (you’ve noticed that his nostrils flare whenever he is on a flush draw….) and you figure him for AK hearts ( the nut flush draw ).

The pot is € 100 , you have € 90 left and your opponent has you covered.

You’re opponent checks to you.

If you go All-in now, he has the correct pot odds call.

However if you check behind, you have the choice of folding if a heart falls on the Turn, or going All-in on the Turn if a blank hits. It is definitely incorrect for him to call you’re All-in on the Turn.

Question: Which of the following actions is the “theoretically correct” action in a cash game and which is the mose +VE? (i.e. this is not a tournament, survival is not a factor, and you have a large bankroll if you need to reload )

a) Go All-in on the flop. Assume you’re opponent will always correctly call in this spot.
b) Check the flop. Then fold the turn if a heart hits (saving €90) , and go All-in on the turn if a Blank hits (this will force a fold and you probably losing an extra € 90 bet if the river is also a blank). Assume that you’re opponent will always correctly check/fold to your All-in when a blank hits the turn.

p.s. I’m not asking what people “would” or “usually” do, but rather, which action is the best if you want to maximise expectation

• Closed Accounts Posts: 1,639 ✭✭✭

a is the mistake..

• Registered Users, Registered Users 2 Posts: 717 ✭✭✭

Pushing the turn is the only way that you can offer your opponent a chance to make a mistake, so thats the correct action. He way well fold thinking you have a made straight but will probably call.

• Closed Accounts Posts: 657 ✭✭✭

just because he has the right odds to call doesn't mean that you should not try to get max value out of your hand by going all in on the flop. if you know that he will fold if given the wrong odds on the turn then you don't get any value from flopping the nuts. going allin on the flop is the correct play as you know he will call and regardless of whether it's a winning or losing play for him it's a winning play for you.

• Registered Users, Registered Users 2 Posts: 2,481 ✭✭✭

I have a feeling that B is the mistake. Picking B is only to your advantage when the turn is a heart. Essentially, you're betting that the turn IS a heart as a kind of hedge. However, the turn will be a heart less than half the time, and your opponent will match anything you put in the pot, so it must be a +ev move.

• Closed Accounts Posts: 900 ✭✭✭

This is the type of question that wrecks my head when I try to think about the Fundamental Theorem of Poker.

On the one hand I can see the logic behind waiting to see the turn and then making a bet which it would be a mistake to call.

On the other hand, aren't you making a mistake by giving your opponent a free draw to his flush when you have the nuts?

I hope someone breaks out the mathematics on this one as I'd be interested to know what the theoretically +EV thing to do would be.

• Closed Accounts Posts: 900 ✭✭✭

Ok so I haven't done this before but I was curious so decided to have a crack at it.

Chances of a heart coming in the last 2 cards = 1/3
Chances of a heart coming on the turn = 1/6

a) Push the flop

2/3 of the time we end up with 280
1/3 of the time we win 0

EV = 280 * 2/3 = 184.8

b) Push the turn if no heart, fold if a heart comes

5/6 of the time we end up with 190
1/6 of the time we end up with 90

EV = (190 * 5/6) + (90 * 1/6) = 173.33

So this seems to show that there's a higher overall expectation for pushing on the flop, unless I'm making a mistake.

Which is a relief because if I could see my opponent's cards that's what I'd do in this situation every time.

EDIT: I had the maths wrong the 1st time and I've corrected it, so it's closer than I originally thought.

I guess what this means is that if you were on the bubble in a tournament then the correct thing to do would be to check and see the turn, since that leaves you with 0% chance of going broke in this hand. But in a cash game pushing the flop would always be right.

In a real-life situation you would never know exactly what your opponent has so I can't see this problem having any practical applications.

• Closed Accounts Posts: 900 ✭✭✭

Pushing the turn is the only way that you can offer your opponent a chance to make a mistake, so thats the correct action. He way well fold thinking you have a made straight but will probably call.

The only way you can offer your opponent the chance to make a mistake here is by making a mistake yourself.

• Registered Users, Registered Users 2 Posts: 36,399 ✭✭✭✭

This post has been deleted.

• Registered Users, Registered Users 2 Posts: 1,151 ✭✭✭

Surely the mistake is getting 35% of your stack in preflop with 89?

• Registered Users Posts: 200 ✭✭

It doesn't matter that its correct for him to call. Its sort of the FTOP in reverse, you are the one making the mistake by not betting. Suppose the pot was \$1000 and you both have \$1 left, you have the best hand and the most probable to win so you want to put your money in, simple.

• Closed Accounts Posts: 375 ✭✭

Captain Nemo I like the stats. Any idea what the stats on the flop would be on betting 30
and on 50% of the time the oppo flat calling and 50% of him rerasing you all-in ?
assuming he can get away from it on the turn or should he ?
(I know he shouldnt flat call the bet, but we dont always do what we should)

• Closed Accounts Posts: 900 ✭✭✭

kebabfest wrote:
Captain Nemo I like the stats. Any idea what the stats on the flop would be on betting 30
and on 50% of the time the oppo flat calling and 50% of him rerasing you all-in ?
assuming he can get away from it on the turn or should he ?
(I know he shouldnt flat call the bet, but we dont always do what we should)

I don't want to work out the stats for that as it would probably give me a headache but I'd say in effect it's the same as going all-in on the flop because if he flat calls and a heart doesn't come on the turn then he will be getting the odds to call to see the river.

• Closed Accounts Posts: 240 ✭✭

In a real-life situation you would never know exactly what your opponent has so I can't see this problem having any practical applications.

Well the problem has practical application if the EV of one play is greater than the other.

Realistically you can only guess that you’re either opponent has a draw, or a made 2nd best hand. In the situations where he has a 2nd best hand, you’re course of action has less impact, the money will probably be going into the centre anyway and to a showdown. In the situation where he has a draw, you’re course of action does effect the EV.

This suggests you should chose the course of action that maximises profit when you’re opponent is drawing to a flush. (drawing to a full house with a set can be ignored, since in this you’re opponent will never fold (except when a freak draft of wind blows his cards into the muck, or his flaring of the nostrils causes him to sneeze and blow his cards into the muck).

p.s. Your method of calculations looks correct, good job, but there is an error: the odds of hitting a flush with 1 card to come are approx 1/5 (18%) , not 1/6
LuckyLloyd wrote:
The correct play here is to go arrrr iiiin on the flop

LILY!??! I heart lily.

• Closed Accounts Posts: 2,793 ✭✭✭

the correct plays are:

check behind the flop - if you push and he calls/folds - both are not mistakes by him

fold to bet if H on turn - call all other bets - if he hits his A or K he will prob think he's good

you have position - your biggest chance of him making a mistake is for him to push bluff a blank river or think a K/A is good - if a H comes fold again - if blank and checked into you - value bet small and hope for a call or a bluff reraise

pushing the flop means whatever decision he makes is not the wrong one (assuming that it's 2/1 for the call - i know your figures are slightly out)

• Registered Users Posts: 1,158 ✭✭✭

Not betting gives him infite odds to hit his draw. So betting although it will give him correct odds to call is still the correct play. What would you do if playing limit holdem or 7 card stud? Check?

• Registered Users, Registered Users 2 Posts: 6,696 ✭✭✭

Its much easier to work it out if the pot is 100 and the bet is 100

if you push the flop you get 67% equity of a \$200 pot. Thats \$134.

if you push the turn after no heart and he folds you have an equity of \$100. But you will have lost the hand about 1/5 of the time, so your real equity is \$80

if you push the turn after no heart and he calls 1/5 of the time you lose the pot on the turn. Of the other 4/5 of the time you get \$200 4/5 and 1/5 of the time you lose on the river. 4/5 of 200 is 160. 4/5 of this is \$128

So you can see you are always better off betting the flop.

• Registered Users, Registered Users 2 Posts: 6,696 ✭✭✭

the point is that you should still bet even if your opponent isnt making a mistake in calling. The opponent can call the all in on the flop because the pot is big enough. But you still win 2/3 of all the money he puts in on the flop. So you make a profit on the money entering the pot, and your opponent has a break even play based on the pot. If you dont bet he gets a free 1/5 chance of winning the pot, so his equity actually goes up, and yours goes down.

• Registered Users, Registered Users 2 Posts: 2,327 ✭✭✭

Why is the only bet option on the flop an all in?

• Registered Users, Registered Users 2 Posts: 2,481 ✭✭✭

Your method of calculations looks correct, good job, but there is an error: the odds of hitting a flush with 1 card to come are approx 1/5 (18%) , not 1/6

I'm picking nits here, I know, but 18% is closer to 1/6 (16.6% repeating) than it is to 1/5 (20%)

• Registered Users, Registered Users 2 Posts: 3,450 ✭✭✭

This is a very good question and unlike what some have said here is not irrelevant at all.
Its basic questions like this that really test the fundamental knowledge of players and how good they understand poker.

If you have a true grasp of the fundamentals then you can correctly decide the correct course of action in any complex situation for your self and basically adapt to any given situation, which is what poker really is.
Any complex situation can basically be broken down and when you do you always get to a point where you can’t break down any further and those are the fundamentals.
As simple as this question may look like I really doubt there are that many people who can answer it correctly and among those who would answer correctly, most just know the answer through memorizing it and not really understanding why.
A lot of people think the hardest thing about NL holdem (or generally games with hidden information) is the hidden information part. in this case not knowing your opponents cards.
People think they should work on their “reading abilities” as that’s what poker is all about and sure if you knew your opponents cards then you couldn’t possibly lose right?
Wrong!
You can easily play open NL holdem with a lot of people and beat them quite easily.
Even though an open (by open I mean both opponents cards are revealed) NL poker would be considered a solved game, you still have to know the solution in order to win (or not lose) .
The solution is basically understanding the math behind it and most people don’t and throes that do have varying degree of knowing it.
A simple example of what im saying is this post.
A very simple question is posted here but as you can see people are disagreeing in the answer with some people not even knowing the answer.
Others are trying to complicate the issue by bringing in factors that have nothing to do what so ever with the question, but it’s the way they are used to answering questions (with a lot of factors involved) and when those factors are missing they are lost and don’t know what to do.

The theory says that every time your opponent acts any different than he would have ,had he seen your cards then he loses.
Every time you act any different had you seen your opponents cards then you lose.
To simplify lets say you know he has AhKh and he knows you have the str.

Now there is \$100 in the pot with you having \$90 behind and villain covers.

Just because your opponent can play correctly does not mean you cannot.
In this case just because he has the odds to call your push it does not mean you should not push which is the correct play.
The correct play is not always the absolute optimal play but if you have two plays and one of them is wrong and the other one is also wrong but less wrong you should take the second one as correct play.
If I wanted to go by EV terms, if you have two plays both with –EV’s then the correct play is the play that has lesser –EV.
In this example if you shove the flop you are offering your opponent a +EV bet and the correct play for him is to take it.
If you don’t bet it you are offering him an even bigger +EV bet which in turn makes your mistake bigger.
You have to make the play that has the highest EV for you but that does not mean that it will necessarily be –EV for you opponent.
End rant.

• Closed Accounts Posts: 1,266 ✭✭✭

Your giving him infinite odds to hit his flush if you check the flop. That mistake is a far greater mistake than giving him correct odds call the push. A very similar scenario to this is dicussed in Sklansky's TOP if i remember correctly

• Business & Finance Moderators, Entertainment Moderators Posts: 32,387 Mod ✭✭✭✭

Hectors explanation (and others) is correct. You might be wondering how it answers your question though. The english answer to the question is that while betting 100 on the flop allows him the correct odds to call, it doesnt offer him EVEN BETTER ODDS which is what you would be doing if you bet say, 50... or 20... or nothing.

Its not so much that you want HIM to make a mistake, its that YOU dont want to make one yourself.

Checking behind and pushing on a non-heart may make him make a mistake by calling, but you only get to this point by having made a bigger mistake yourself when you gave him a free card. The sum total of mistakes being in his favour. Also you risk him folding and escaping with a free card and never making a mistake himself, the worst outcome for you bar losing the pot.

DeV.

• Closed Accounts Posts: 5,124 ✭✭✭

2 players somehow see a flop with one player getting over 1/3 of his stack in with 89 preflop. He flops the nuts and his opponent checks while flaring his nostrils so immediately he puts him on the nut flush draw with 2 overcards and pushes all in.

Yeah that hand happens all the time.

• Registered Users, Registered Users 2 Posts: 5,404 ✭✭✭

nickyoD wrote:
2 players somehow see a flop with one player getting over 1/3 of his stack in with 89 preflop. He flops the nuts and his opponent checks while flaring his nostrils so immediately he puts him on the nut flush draw with 2 overcards and pushes all in.

Yeah that hand happens all the time.

LuckyLloid wrote:
The correct play here is to go arrrr iiiin on the flop because we can never realistically reduce our opponent to an exact holding after pre - flop and flop action.

Much like the old "the whole table goes all - in during the first hand of the WSOP and you look down on AA in the BB..." scenario - I really question the value gleaned from such discussions

Both of these posts are irrelevant, its a theoretical question, with theoretical answers. it doenst have to apply to real life sitaution, you will quite liekly never be in the exact same poker situations twice liek have 91 effective BB against a LAG with AQ who range changes constantly, but it still helps to decide whats best in certain situations. noone is saying that this exact situation has or will happen, but its useful to know the theory behind it so it can be applied to other situations.

• Registered Users, Registered Users 2 Posts: 36,399 ✭✭✭✭

This post has been deleted.

• Closed Accounts Posts: 1,639 ✭✭✭

i'm shocked that nobody has provided the maths to back up the correct answer yet.. it's really not that difficult, although i truely can't be arsed..

• Registered Users, Registered Users 2 Posts: 5,083 ✭✭✭

this thread is a good example of why people don't understand poker, even when they think they do.

The best post in the thread is by The_Daddy_H. If you understand his post you will understand.

• Registered Users Posts: 200 ✭✭

Booya! Thanks

• Registered Users Posts: 200 ✭✭

[nicK] wrote:
i'm shocked that nobody has provided the maths to back up the correct answer yet.. it's really not that difficult, although i truely can't be arsed..

The point is that EV calculations are not needed here. Whats in the pot is irrelevant. It only becomes relevant if we can assign a probability of the opponent calling a push on a non heart turn.

Since your opponent wont call a non heart turn you are effectively playing an equivalent poker variant game without a river card.