Game Theory - We're surrounded!

Mr. Flibble

6 player NLH, unlimited BR. Everyone is very smart and of equal ability and playing their best. No body has an edge.

Now 5 of the 6 players soft-play each other and concentrate on beating one player. There's no hidden collusion - the 5 players may signal etc, but the 6th player has access to that info too; everyone knows what is going on.

Does anyone have an edge or at a disadvantage?

RedJoker

The 6th player has an advantage. When he is heads up there is no advantage. However in multiway pots his opponents must softplay against each other which means that they will also inadvertently be softplaying against him in spots, while he can play his usual game.

This assumes that they all have the same information, hidden collusion would swing the advantage the other way. i.e. the softplaying opponents can't just fold their weakest hand and leave the strongest hand to play heads-up as that would give away too much info about the strong hand.

If they don't softplay in multiway pots then there is no advantage to anyone.

Mr. Flibble

To clarify what I mean by softplaying: the 5 will each play optionally to beat player 6 and aren't concerned with beating each other.

Goodluck2me

Mr. Flibble wrote:

To clarify what I mean by softplaying: the 5 will each play optionally to beat player 6 and aren't concerned with beating each other.

thats not softplaying at all! thats a normal game in the jackpot against some random annoying person.

softplaying means they will never raise each other etc. the 6th player will have an advantage in this scenario as spots where he shouldnt get value he likely will be getting way over the odds. its def -ev for the group as when they calculate the odds of winning a hand they cant count the implied odds of each others stacks, they are effectively getting shorter odds. if they play for set value for ex they need to hit and 11-1 shot for the set and also maybe a 2-1 shot for the 6th player to hit aswell.

phantom_lord

the 6th guy is the only player playing optimally and using all the extra info for his own advantage so he should have an edge?

gerry87

Is that basically the same as the 5 players have position on him for 5/6 hands? And they get to choose between the 5 hands when he's on the sb, 4 hands when he's on the BB, 3 when he's utg...

Then they would obviously have the advantage, It's pretty much like a heads up match where you get 5 hands every time and 5 buttons in every 6.

Hitman Actual

When you say Game Theory, do you mean real Von Neumann/Nash GT? If so, the lone opponent can never win here, assuming that the 5 other players are playing optimally together. The 'value' of the game will always be negative for the lone opponent. He will be playing just to limit his losses.

Mellor

lenny_leonard wrote:

When you say Game Theory, do you mean real Von Neumann/Nash GT? If so, the lone opponent can never win here, assuming that the 5 other players are playing optimally together. The 'value' of the game will always be negative for the lone opponent. He will be playing just to limit his losses.

If the 5 players are softplaying together then they couldn't be considered as playing optimal. the optimal play is when the lone player is involved.

In hands were lone player isn't involved, the action is low as the other 5 slow play, this has no effect on the lone player as he isnt involved. And there is no advantage between the group as wins cancel losses for these games.

Where the lone player is involved, the group plays to bust the players. This should also have no affect, as the lone player only has to consider he is playing against a table of good lags.
There is no advantage for anyone.

The only way there is an advantage is where the group of players are going out of their way to bust the lone player, playing cards they shouldnt. callin draws they shouldn't etc, this is an advantage for the lone player, but not sure if it is rthe case in the OP.

There is also a situation where the lone player is at an advantage and that is a winner take all tourney, as the other players are unlikely to bust each other. but if the above (playing hands they shouldn't) applies, then these cancel out.

RedJoker

Mellor wrote:

If the 5 players are softplaying together then they couldn't be considered as playing optimal. the optimal play is when the lone player is involved.

In hands were lone player isn't involved, the action is low as the other 5 slow play, this has no effect on the lone player as he isnt involved. And there is no advantage between the group as wins cancel losses for these games.

Where the lone player is involved, the group plays to bust the players. This should also have no affect, as the lone player only has to consider he is playing against a table of good lags.
There is no advantage for anyone.

The only way there is an advantage is where the group of players are going out of their way to bust the lone player, playing cards they shouldnt. callin draws they shouldn't etc, this is an advantage for the lone player, but not sure if it is rthe case in the OP.

There is also a situation where the lone player is at an advantage and that is a winner take all tourney, as the other players are unlikely to bust each other. but if the above (playing hands they shouldn't) applies, then these cancel out.

Unlimited bankrolls, not possible to bust the player.

sikes

Are there any blinds in the game?

The players who have the button when the player who isnt colluding is in the blinds have the advantage.

Mellor

RedJoker wrote:

Unlimited bankrolls, not possible to bust the player.

if it is a tourney then of course its possible, my point related to tourney play.

I imagine the the OP included "unlimited BR" as he didnt want anyone to take how deepstacked it is into account. An unlimited BR is infact impossible.

Hitman Actual

I really don't see how the lone player can win here. Blind money on it's own will beat the player. You start at a 5/1 disadvantage in starting hands.

I believe in maths and logic; if anyone can come up with a solid theory that shows that the lone player can win here, they should get a Nobel prize.

Edit: Also, when I say the other players are playing optimally, I mean that they are playing in the best way to beat the lone player.

Mr. Flibble

goodluck2me wrote:

the 6th player will have an advantage in this scenario as spots where he shouldnt get value he likely will be getting way over the odds. its def -ev for the group as when they calculate the odds of winning a hand they cant count the implied odds of each others stacks, they are effectively getting shorter odds. if they play for set value for ex they need to hit and 11-1 shot for the set and also maybe a 2-1 shot for the 6th player to hit aswell.

Looking at the 5 as one group if one of them set over sets each other the grouo of 5 wins or looses nothing. Yes 6 has 5 people to set over set which is good for him, but 5 people can set over set him too so it balances out.

gerry87 wrote:

Is that basically the same as the 5 players have position on him for 5/6 hands? And they get to choose between the 5 hands when he's on the sb, 4 hands when he's on the BB, 3 when he's utg...

Then they would obviously have the advantage, It's pretty much like a heads up match where you get 5 hands every time and 5 buttons in every 6.

I don't think so. He will have position on somebody too for 5/6 hands.

lenny_leonard wrote:

When you say Game Theory, do you mean real Von Neumann/Nash GT? If so, the lone opponent can never win here, assuming that the 5 other players are playing optimally together. The 'value' of the game will always be negative for the lone opponent. He will be playing just to limit his losses.

I think so...are there specific criteria for what types of games fit into their gametheory? Perhaps you could look at the 5 players as one entity, with 5 sets of cards and stacks (but of course each stack only knows its own cards unless it is shared with player 6 along with the other stacks).

sikes wrote:

Are there any blinds in the game?
The players who have the button when the player who isnt colluding is in the blinds have the advantage.

Yeah, same as normal NLH. Go the group of 5 has an advantage when player 6 is in the blinds. This will cancel out when he is not in the blinds tho, right?

Mellor wrote:

The only way there is an advantage is where the group of players are going out of their way to bust the lone player, playing cards they shouldnt. callin draws they shouldn't etc, this is an advantage for the lone player, but not sure if it is rthe case in the OP.

As they are playing optimally they shouldn't do this.

Mellor wrote:

I imagine the the OP included "unlimited BR" as he didnt want anyone to take how deepstacked it is into account. An unlimited BR is infact impossible.

I included unlimited BR so that people can buy back as much as necessary, I don't think stack sizes are relevant. I don't think this criteria matters though - it would just mean that (in our heads) we would have to play lost of separate games instead of one long one if we couldn't rebuy.

lenny_leonard wrote:

I really don't see how the lone player can win here. Blind money on it's own will beat the player. You start at a 5/1 disadvantage in starting hands.
I believe in maths and logic; if anyone can come up with a solid theory that shows that the lone player can win here, they should get a Nobel prize.

If player 6 is in the blinds he is at a disadvantage alright, but how is the disadvantage any more than if every player was looking out for themselves (ie. a normal game)? A player in the group of 5 will be in the blinds for a much larger % of time than the 6th player so isn't this good for him?

gerry87

Mr. Flibble wrote:

I don't think so. He will have position on somebody too for 5/6 hands.

Ok, everything else even i'd say position is the main factor in this game. If two equally skilled players played heads up, but one was on the button every hand, the player with the button would win in the LR.

If the group of 5 have the arrangement to fold every hand OOP to the lone player, and all or one of the rest of the players who have position on him play the hand. Then 5/6 hands he would be OOP to at least one player, and on the hand he has position, the blinds would check fold all but the top hands. No?

If this was the case what would the lone players best response be? To fold every hand apart from raising the button regardless, making the blinds fold because they're OOP? Where would that leave him? Everyone breaking even again?

Hitman Actual

Mr. Flibble wrote:

I think so...are there specific criteria for what types of games fit into their gametheory? Perhaps you could look at the 5 players as one entity, with 5 sets of cards and stacks (but of course each stack only knows its own

I think the 5 other players have to play collectively in the best way to beat the lone player for it to be a valid game theory situation. So taking them as one entity sounds right.

Mr. Flibble wrote:

If player 6 is in the blinds he is at a disadvantage alright, but how is the disadvantage any more than if every player was looking out for themselves (ie. a normal game)? A player in the group of 5 will be in the blinds for a much larger % of time than the 6th player so isn't this good for him?

I'm not saying that the lone player is definitely at any more of a disadvantage in the blinds than if the game was being played normally (although I'm sure there's a strategy which means that he would be); what I mean is that he won't even make enough in the game to cover what he loses in paying blinds.

Mr. Flibble

lenny_leonard wrote:

I'm not saying that the lone player is definitely at any more of a disadvantage in the blinds than if the game was being played normally [...] what I mean is that he won't even make enough in the game to cover what he loses in paying blinds.

So 6 is at a disadvantage when he isn't in the blinds?

insafehands

How about if the lone player was on the button each time?

Hitman Actual

Mr. Flibble wrote:

So 6 is at a disadvantage when he isn't in the blinds?

He's at a disadvantage at all times. He can't beat this game, imo.

Hitman Actual

insafehands wrote:

How about if the lone player was on the button each time?

He'll lose at a slower rate, but he'll still lose.

sikes

Mr. Flibble wrote:

Yeah, same as normal NLH. Go the group of 5 has an advantage when player 6 is in the blinds. This will cancel out when he is not in the blinds tho, right?

I dont think so, becuase he has position once an orbit the 5 players have position the other 5 times.

BrendanB

Lone player is at a disadvantage.

1. Trivial case, all players play the same "optimum" way - all players make decisions independently, EV of each player is 0, ignoring rake.

2. Question: are there situations where a decision can be made by one of the colluding players that benefits them as a group and not the lone player. This is the only case you need to examine, if this is yes, then the colluding players have an advantage. They don't have to make any decisions which negatively affect their group EV. (This may or may not involve softplaying)

3. Situations can have a different EV for each player given more or less players in a pot.

E.g. colluding players believe lone player has small pocket. Against one other player, his EV is better than against multiple players with different overcards. Colluding players discuss which overcards they have, and make a decision about which ones will call and which won't. Group EV increases against lone EV.

Even if they are wrong, their situation is better than when they are playing for themselves, since of two players with AK, say, only one need call.

Mr. Flibble

BrendanB wrote:

E.g. colluding players believe lone player has small pocket. Against one other player, his EV is better than against multiple players with different overcards. Colluding players discuss which overcards they have, and make a decision about which ones will call and which won't. Group EV increases against lone EV.

Even if they are wrong, their situation is better than when they are playing for themselves, since of two players with AK, say, only one need call.

Any discussion like this would have to happen before the game starts or else it would have to be open for player 6 to hear.

If the 5 could discuss their cards without 6 knowing they would certainly have an advantage.

BrendanB

In fact, for a bonus reason:

The sharing of information may assist in making decisions. Only colluding players may share: river has been dealt - you have K high flush and are facing a call all-in. You may ask as a colluding player whether anyone else has folded the ace. This adds value to your call. Lone player cannot request this information, if he were in the same situation.

BrendanB

Mr Flibble - even if player 6 can hear, it's not necessarily beneficial to him (say this is the river and he has bet, the other players may compare their hands with each other, and only the best hand calls).

Mr. Flibble

They can't show each other their cards unless they show them to player 6 too. No information of any kind can be given shared unless 6 has access to it too.

BrendanB

Yeah, but they can decide when to show their cards/answer question. They show when it is beneficial to the group (e.g. when calling a river bet), and not otherwise.

Mr. Flibble

Give me an example.

BrendanB

Two colluding players and the lone player left, river has been dealt.

Lone player bets all in.

Colluding players compare hands. Only the better hand considers calling.

Mr. Flibble

Ah ha. Interesting. I had thought until now that the actual answer was that everybody is still 0ev and nothing is changed but it looks like the 5 do actually have an edge. Anyone have any counter arguments?

Mellor

If the five share info, they have an edge,
If they just softplay they don't.
I thought, from the OP, that they didnt share info.

Also, if the villains tell each others cards at the river, then the lone player could get them ruled dead. They are out to bust him, but they can't cheat.

As regarding position, and the group having position 5 out of six times. As a group, when one is in good position, there is a player in a bad position. And on every orbit, the positional advantage all cancels out.

RoundTower

Even if they don't share info, the 5 players have an advantage. I think it's pretty obvious.

There is no situation where the lone player can have an advantage, because the other 5 players can at worst play like they would normally. So if there is any situation where the other 5 players can vary their play to the advantage of the group, they improve their results. An easy example is if the first guy gets all in 3 ways, and the other 2 check it down.

Mr. Flibble

It looks like there are some examples where the 5 can gain an advantage only when the 6th player can no longer act, because he is all in for example.
Do they still have any advantage if all stacks are equal?

I agree that under no circumstances does player 6 have an advantage.