The Monty Hall Problem Illustrates the Issues of playing AK

[Dwarf]

For those unfamiliar: https://en.wikipedia.org/wiki/Monty_Hall_problem

The Monty Hall problem parallels making post flop decisions.

In the game show example, contestants who switch have a

2/3​

chance of winning the car

This makes sense because the act of switching does not change your earlier decisions probability. You had a 1/3 chance of being right the first time and given an opportunity switching gives your 2/3 chance of picking incorrectly winning odds.

This is a lot like playing AK (In the negative.)

Odds are AK will win 45%+ of the time.
Odds are AK will not flop an A or K 66% of the time.

In general, this means changing your decision of how you are playing your AK is the opposite of the Monty Hall problem. You lose (in general) not playing it out to the river.

Why do I mention this?

Because AK is played in 2 very different ways. Some folks like to 3bet/4bet/Shove (capitalizing on all their potential equity). Other folks like to 3bet/flat call, and play out the hand.

My point:

Playing an aggressive style while holding AK preflop is good for balancing your AA KK QQ hands. HOWEVER Giving up on the flop if you don't hit Ace or King (even though you bet aggressive preflop) is a -EV play. If you are going to give up on the flop without hitting an Ace/King -> you should play Ace King to trap... Don't 3bet, don't call 4bets, don't lead out when OOP. Then when you do hit your A/K plan to check call/check raise.

 

[kozong]

but check raising AK gonna seems too strong no?

n if every1else check behind, arent we losing value?

 

[ph_il]

Odds are AK will win 45%+ of the time.

AK has 45% equity vs pairs 22-QQ when in all-in situations. Against different hands all-in, it has different equity.

vs KK = ~35%
vs AA = ~10%
vs A2-AQ = ~65-70% depending if hands are suited
vs K2-KQ = ~70-75% depending on if hands are suited
vs 56s or J8o (non-paired hands w/o A or K) = ~65%

Again, this is all preflop and the odds that AK will win by the river.

I do agree that check/folding if you don't flop an A or K is -EV because of how much fold equity AK has on dry boards. There definitely should be a balance between c-betting and check/calling or check/folding when you miss the flop with AK, but i think i most situations, c-betting is the better option when you miss.

 

[Drhat63]

The last 3 tournaments I have busted out with AK, I wish I had played differently... playing a "trap" strategy seems to be great because no one ever puts you on AK, however I feel like pot control is still best when playing OOP, or against a very aggressive opponent.

 

[BentleyBoy]

Interesting proposition; however, the true answer to this problem has nothing to do with the way you play your hand and the impression this gives to other players, as that does not impact on the probability of the next card or cards being a A or K.

I would distinguish the Monty Hall problem from poker because in the monty hall problem, there are only two choices to make. In poker, there are far more! The monty hall problem is also influenced by the purposeful behaviour of the host, this is not the case in poker. ( but there is a similarity). Let me explain.

In the monty hall problem, you have to choose one option from three. So you have a 1/3 chance of winning.

In poker, you are provided with two cards and you choose whether to play them. How you play them is also important. This is totally different from picking one of three doors.

Secondly, once you have made your choice in poker, there are various other components involved in your next play, i.e. The acts of the other players, and how they act, and of course how you play if they raise you. This is not the case in the monty hall problem, as you play alone.

So, once round one is over in poker, you are dealt three cards (assuming we relate this to holdem). In the monty hall problem, the host opens one of the unchosen doors. This is a purposeful act as it will always be a door that is a NONE winning door. (In poker you may get dealt a winning hand) Having done this, the host gives you a chance to choose again. You now have a better chance at 1/2. However, you still don't know which is the winning door. The only additional information you have is that the other door now has a better chance of being a Winning door as the host did not open it! But you are still at 1/2.

The impact in poker is totally different. The act of the dealer is not purposeful. It is random depending on which cards are next in the pack. (It would be different if the dealer could choose which cards to deal) (If you liken this random act to the monty hall problem, a random act of the host could result in the winning door being opened and you lose - similar to a random act of dealing AAA and therefore you win!). The fact at an A or K is not dealt reduces your chance of winning, albeit crazily increases the chances of an A or K being dealt on the turn or river, (which is where I think you are trying to make the connection between poker probability and the monty hall problem.).

I believe that the only link between the two is the issue of probability. I do not believe the monty hall problem specifically relates to poker.

Nice topic and great thread though!

BB

 

[Dwarf]

Interesting proposition; however, the true answer to this problem has nothing to do with the way you play your hand and the impression this gives to other players, as that does not impact on the probability of the next card or cards being a A or K.

I'm suggesting rethinking the general plan to play AK. Many people treat it like a monster hand, however it only truly realizes its Monster preflop equity by the river. This makes a notable difference when considering the following tournament situations.

A) Being a short stack and shoving.
B) Being a large stack and 4betting with AK.

Interesting proposition; however, the true answer to this problem has nothing to do with the way you play your hand and the impression this gives to other players, as that does not impact on the probability of the next card or cards being a A or K.

True, how you play your hands doesn't change your probabilities or impact the next card being A or K.

However it does impact what your realizable equity is.

AK has
33% pre-flop equity vs pocket pairs if you only see the flop
40% if you go to the turn
44% if you go to the the river

This is why what your plan is should greatly change how you play AK. It cant just be simply treated like a monster preflop.

In the monty hall problem, you have to choose one option from three. So you have a 1/3 chance of winning.

In the monty hall problem, the host opens one of the unchosen doors. This is a purposeful act as it will always be a door that is a NONE winning door. Having done this, the host gives you a chance to choose again. You now have a better chance at 1/2. However, you still don't know which is the winning door. The only additional information you have is that the other door now has a better chance of being a Winning door as the host did not open it! But you are still at 1/2.

Switching to the winning door gives you a 2/3 chance of being right, not a 1/2.
That's because the host offering you a switch doesn't change the probability of your initial choice. 2/3 of the time you pick wrong, you are gaining information with his reveal. This is different from just picking randomly from 2 doors.

Imagine it with 100 doors 99 goats and 1 prize.
If the host opens 98 doors and offers you a switch. 99/100 times you would pick the wrong door initially. He is then revealing to you a door that 99/100 times has a prize behind, your initial choice still has a 1/100 chance of being correct.


This parallels to poker decision making with the opposite effect. Playing fit or fold with better hands presents you very different preflop equities when you aren't going to see the river.

I think AK vs 22 is a great example of this in another light.
General Preflop equities is AK 45% 22 55%
Playing only to the flop 22 is a 62% favorite.
However most people play 22 fit or fold. Which means you are essentially playing the hand with 15% equity.

What I am trying to get at probably applies to tournaments more than cash games. Playing AK like a monster preflop can be a major leak. There are lots of reasons to 3bet/cold call a 4bet with it. Depending on your opponents, your position and your stack size. You need to be wary of getting into preflop raising wars with it.

4 betting than folding to a big flop bet essentially reduces your preflop equity at least 12%. Calling a 3 bet and a flop bet risks less chips, and allows you to realize your equity more often.

Your thoughts?

 

[BentleyBoy]

Poker and the monty hall problem are two different things!

 

[Dwarf]

Poker and the monty hall problem are two different things!

Omaha, Holdem, Stud, and Hi/Lo are 4 different things!
Gravitational Force and Mass are Two different things!
They all have related concepts though!!!

Poker is a game where you gain information that affects your statistical advantage. The Monty Hall problem demonstrates a game where you gain information that affects your statistical advantage.

Hence the analogy.