Optimizing Poker Strategies: The Impact of Cooperation in Hold'em Poker

[motorhead]

When playing poker at a 10 person table, each player obviously has a 10% chance of winning. This means that, when a person is the first player to act at the table, he should only play hole cards that are in the top 10%, in terms of non-losing percentage (ties count as wins here).

[In any given head-to-head showdown, pocket aces have the best odds of not losing, at 85.5% and 3-2 offsuit have the worst odds at 35.3%.]

If the first player to act does not have a top 10% hand, he should fold them, and the next player's hand should be the best out of nine possible hands, or in the top 11.1%. If people continue to fold in this manner, we eventually arrive at the second to last person, whose hole cards should be in the top 50% of all possible poker hands (there are 169 possible hands).

Now, this is all supposing that every player is in fact playing against every other player. In other words, it is an ideal "game".

On the other hand, suppose that 2 of the players are husband and wife, and they only care whether their combined efforts are at least break even.

In this case, what is the correct percentage of hands that they should both play from first position? At first, I thought you should be able to double the percentage of hands to 20% to come up with the best result. But then I thought that they should be able to play even more hands than this because .2*.2=.04, or: two 20% probability events taken together equal one 4% event. In order to find the most optimal percentage in this spot, don't you do sqrt(.1)=.312, meaning that they should both play 31.2% of their hands?

Likewise, if either of them is in the second to last position (aka "small blind") in this table folding situation, shouldn't they both play sqrt(.5)=.707, or 70.7% of their hands?

I've been thinking about getting into some games for quite awhile now, but I've just been trying to understand the math before I get started. I've come to realize that it would be insane to try to make a living at it all on my own, given my low bankroll.

I think that I have a good handle on "ideal", non-cooperative game percentages, but now I'm just wondering how the dynamics change when 2+ people are on the same "team", as it were!

(If anyone is interested in getting in on this, let me know!)

 

[motorhead]

To show you guys that I'm serious about this, I have been writing computer programs regarding various aspects of poker for about a month now. I have written a really good odds calculator in C as well as the beginnings of a game simulator in Perl. I really enjoy the theoretical aspects of the game, but I also want to put this theory into action! Anybody want to make some money?

 

[CRGreathouse]

Suppose the first person is dealt the 16th-best hand out of 169 (9.4%). The chance that the first person has the best hand is ((169-16)/169)^9 = 40.8...%. The chance they tie for best is 2.46...%.

Actually, try as I might I can't come up with a simple model with more than two players that describes the essence of the situation. It becomes complicated, because bluffing can be a good move in this situation.

 

[motorhead]

I'm not quite sure what you are getting at. The ninth best hand in poker is 77, and there is a (8/169)*100=4.7% chance that someone else will draw a better hand. Also, 77 has a 66.7% chance of winning (or tying) any heads-up showdown.

Anyways, I wrote a pretty in-depth explanation of the heart of the situation on another forum:

Only if all the players are equal. This is only true if you deal the cards out, turn them face up, and don't gamble.

If your statement were true, there'd be no professional gamblers.

Yes, I am only talking about the objective probabilities here. I have not yet gotten into the subjective, strategic aspects of the game.

Also, I know it is a matter of semantics, but I don't consider professional poker players to be "gamblers". Craps and roulette are gambling, but most casino card games are not.

In particular, poker is all about knowing the percentages that your hand is a winner versus any given situation, and correlating this to the "price" of getting in on a pot (ie "pot odds").

In other words, all poker players know that there is about a 20% chance of hitting a flush when you have 4 cards of the same suit. Therefore, you should look to only call a bet of $1 with a flush draw if it is going to win you at least $5. The odds of hitting an open ended straight draw are slightly lower than this, and hitting a "gut shot" straight draw are even lower still (about 9%). Trying to make 3 of a kind, you are talking about 5%, and making 4 of a kind is just over 2%.

Every poker player knows these basic percentages, and will fold their cards if they are not given the right pot odds. Professional poker players are simply in the business of repeating these very rules over and over again, many thousands of times over their careers.

This is an interesting question. It is also tricky, because unless the two have perfect information of each other's hands, then there is no way to implement a strategy.

I'm glad you said this because it is a common misunderstanding of the dynamics of the game of poker. After all, we've all heard of stories where two people try to get an edge at a poker table by exchanging signals. This kind of activity can get you in a heap of trouble to say the least.

The point that I am trying to make is that when you have two or more people at a poker table who are using a common "bankroll", they can afford to make the action at the table more volatile. Without cooperation, the first person to act at a 10-person table should only play the best 10% of all hole cards. But with 2 people working together, they can both play about 31% of their cards from first position, because two 31% events in combination are as good as one 10% event.

Likewise, you can both call opening raises with lesser holdings than you normally would for the same basic reasons.

The effects of this type of "loosening" of the play at a poker table are subtle, yet profound. When more hands are at play and the pots become larger, players get out of their comfort zones. Professionals know that when a table becomes loose and wild, it is best to wait for the most premium hands before they decide to play. And if you back these professionals into enough of a corner, then they won't even be able to play enough hands in order to say ahead of the blinds, antes, and casino rake.

But the pros are not who I am targeting here. They will simply walk away and find another table in which they can play their style. Pros are pros and they will always find ways to make their "nut".

I'm talking about playing against the rank amateurs here. You know, the weekend casino types.

If you and one or two cooperatives can walk into a random casino, act like you don't know each other, bluff off a lot of chips for an hour or so, and then start to work together, then the profits could be enormous.

Once the "targets" feel comfortable that they are able to take you and your partners' money at will, then you can start to push the action. Slowly but surely, your actions become more systematic. You start playing the percentages exactly like any pro would, but because you are working as a team, you and your partners can start playing many more hands than normal, and get much more money flowing than normal.

At this point, the targets will slowly but surely get out of their comfort zones, and they will have the feeling that they are just getting "unlucky". In other words, they'll start to go on "tilt". Once they give up the money that they originally made and go into the red, they'll really start to gamble and make bad poker decisions.

So, you see that this is not really about "strategy", because poker strategy is always the same no matter what the situation is: do not call a bet on a drawing hand unless you are getting the right pot odds.

What is happening here is just that two or more people working from the same bankroll are able to work with wider ranges of hands than single players acting in opposition, and can therefore press the action, forcing inexperienced players to play a style to which they aren't accustomed.

The bottom line is that, to two people, 10% odds are really sqrt(.1)=31% odds and 20% odds are really sqrt(.2)=44.7%, and on down the line. For three people, the numbers get even larger: 10%=46.4% and 20%=58.5%.

 

[turbo]

motorhead, if you are thinking about doing this to friends in "friendly" hold 'em games, they may forgive you when they find out, but likely you will lose friends. If you do this to strangers who are a bit more serious about poker and can read a table better than your friends, you are likely to end up in a hospital. Tread carefully. Decent poker players know all about the advantages of collusion and they are alert to it.

 

[motorhead]

motorhead, if you are thinking about doing this to friends in "friendly" hold 'em games, they may forgive you when they find out, but likely you will lose friends. If you do this to strangers who are a bit more serious about poker and can read a table better than your friends, you are likely to end up in a hospital. Tread carefully. Decent poker players know all about the advantages of collusion and they are alert to it.

No, I'm talking about doing it with your friends, not to your friends... and in large, corporate casinos rather than back-alley card-rooms.

Also, this is not "collusion" in the classical sense of using signals to alert your friends of what you are holding. It is simply using the probabilistic advantages that working from the same bankroll offers. "Decent" poker players, as you say, do not care if a table loosens up in the manner that I am talking about because they will just wait for better hands to come around. And if a table becomes too loose, they'll just walk away to find a better opportunity. This is what they do for a living.

You just have to fool the weekend warriors who just play poker for kicks, and who go back to their day jobs after everything is said and done. You don't even have to worry about the casinos because this system will only increase their poker profits: their "rake" is based upon the sizes and numbers of contested pots.

Tell me how this is "collusion" in the sense of trying to attain an unfair mathematical advantage.

 

[motorhead]

From PokerCollusion.com: "Poker Collusion occurs when two or more partners decide to sit at one table and cheat the other unsuspecting players at that table. This is basically playing differently against one or more players than you do against others at the table."

This system has nothing to do with "playing differently" against anybody. It is just about two or more people playing a generally looser, more aggressive style of poker, forcing the other players into a style that they might not be used to.

The team players don't care if they lose pots to each other, so they aren't going to play any differently against each other!

 

[cristo]

The team players don't care if they lose pots to each other, so they aren't going to play any differently against each other!

But they do care if one player takes all their chips, and thus are never going to go all-in against one another, since then their advantage is gone.

Anyway, I say fair play to you; if you can pull this off then you deserve it. However, I would say that you should keep it two players, since putting more than this on one table may get tricky. I agree that it is probably no against any rules, but other players are not going to be too happy if they find out, and if several players are not happy with you, and kick up enough of a fuss, then you'll be the two that are thrown out of the casino, regardless of whether you broke rules or not.

 

[turbo]

Even worse if you're going to pull this stunt in a casino. The "eye in the sky" will catch you gaming the table, and a couple of solid-looking fellows will ask to speak to you, and you will never be allowed back in. You're not going to get the crap kicked out of you, like you would if you tried to pull this off in a high $$ private game, but you will be ejected.

I was once in a "friendly" poker game with some pretty nice pots and two guys who arrived separately and introduced themselves to one another started playing "bump and drop". When one would raise the other would re-raise to fatten the pot, and would fold when we approached the raise limit or if they had to see a couple of previous raises. After this happened a couple of times, I invited one of the guys to help me get some chips, etc, when another player wanted a bathroom break. In the kitchen, I invited him and his friend to leave and said that I wouldn't rat them out until they were long-gone so they wouldn't get pounded and thrown down the stairs. Some of the guys at the table were pretty big, so they left. I let the others in on the collusion after they had been gone a while. They were upset that I had not made a public announcement about the cheating, but relented when I pointed out that the police station was only a few buildings away, and that we might all have been in lock-up trying to make bail after they vented their frustration on the cheats. Word got out pretty quick, and the pair became persona non grata at card tables all over town.

 

[motorhead]

Okay, so here's the plan...

I train several young and hungry non-poker players for several months to play perfect, mathematical poker. Since I spend much of my time doing computer simulations, I can pretty much figure out all of the odds in any given situation. I create a solid game plan whose rules are meant to never be broken.

So all I'm trying to do is to develop the best players possible who wouldn't mind sharing a common source of funding. There's absolutely nothing wrong with this, is there?

Now, when it comes to playing poker, there are different styles:

-There are tight players who only select the most premium starting hands. In these cases, you only average a couple or so players per flop, and the hand often ends right there. Usually, the big bettor after the flop will win the pot. Occasionally, you'll see the turn card and it will only rarely come to a river showdown. This style of poker is highly predictable, and will keep a steady influx of cash for solid poker professionals. In this style, mathematical odds do not play a major part. But since the pot sizes tend to be fairly small, the earning potential is limited.


-There is loose play where 4, 5, or more players might see a flop. A few people might be in on the turn, and you will almost always go to a river showdown. In this style, big starting hands like AA and KK go down in value, and the "middling" drawing hands like 10-9 suited go up in value. The eventual winners will often have to navigate a series of fairly difficult "plot twists" that often involve doing some pretty involved mental calculations. The effort is worth it, however, because the end payoff is so much bigger.


So, to make the most money in a poker career, it pays to play a wider range of hands and to become accomplished at the subtle art of calculating win probabilities versus pot odds. However, the short term swings involved in playing looser poker are much greater than in paying tighter. This means that many individual bankrolls simply cannot afford to take on the risk that comes along with this style of play.

However, if individual players come together and agree to play from a common bankroll, then they can take the benefits of playing high-volatility poker while their average income will become much more dependable.

So, the part about the players being at the same table is not as important as the part about individual players using the same bankroll. The point is just that, if these players do find themselves at the same table, they can collectively "open up" the action to a much greater degree than they can individually. It is true that the other players at the table might not be "comfortable" playing like this, but it's a free country, isn't it? If the action has become too much for them to handle, or they simply find themselves outclassed, they should just walk away.

In the end, these team players are not going to make any more or less money over their careers because they decide to utilize the same bankroll. The long-term profit comes entirely from being skilled at playing a style of poker that most people are just not psychologically equipped to handle.

The major point is that young, skilled poker players with only limited funds stand a much better chance of "making it" in the short term if they work from a communal bankroll.




Another point is this: we live in the real world and not an ideal world. Since poker is a high-stakes endeavour, it is definitely more of a business and less of a "game".

Now, when it comes to the enormous varieties of poker situations that exist, don't you expect to find certain situations where two or more "grizzled veterans" who have played in the same games for several decades will -- without saying a word -- eventually be able to effectively "conspire" to defeat, say, an unwitting "hayseed" from some Midwest state who has a plan to waltz into the casino and bully everyone at the table?

When certain players see enough of the same situations, there tend to arise unwritten "codes" that kick into effect. This is just a natural consequence of the world that we live in. Two people who know each other will help each other out in the heat of battle. What ends up happening is this: the poker pros, who have been through hellfire together, don't mind losing pots to each other in the short term, because in the long term, their skill levels are so evenly matched that it ends up being a zero-sum game.

They eventually realize that the profits are in the random, unseasoned players who decide to walk in on their "turf" and dictate the action. They know that this idealized "game" that we call poker is actually a real world "battle" where every advantage must be taken in order to survive. So they do what only comes naturally to any biological entity: they work together. They swarm. They attack. They create traps. Whatever it is that can be done to defeat the enemy, they do it.

Now, all I'm doing is calling it like it is. People can sing about the virtues of "pure poker" all they want, but the second the money goes into the pot, the war is on. It just so happens that I am excited to fight this kind of war. But before I go into battle, I know that I need to be as prepared as I possibly can. I'm looking for comrades-in-arms. If you want to join me, that's great. If not, I'll look forward to trying to take you down when me meet in battle!



There is absolutely nothing that anyone can do about anything that I am advocating in a large casino setting. Two or more highly skilled players can sit down at any poker table that they want and play a variety of poker that many of the others at the table are not accomplished enough to handle. It's called being better at your craft than the next guy. This is truly not something that has to be "pulled off" or that must "avoid detection" in order to succeed.

 

[cristo]

This is truly not something that has to be "pulled off" or that must "avoid detection" in order to succeed.

Yes it is. If other people in the casino cotton on to what you are doing, and enough complain about it then you are most likely to be ejected, since casino bosses do not want large groups of angry people in their casino. It doesn't matter whether you have done something wrong or note: all such places reserve the right to refuse admission to anyone they please.

 

[motorhead]

Yes it is. If other people in the casino cotton on to what you are doing, and enough complain about it then you are most likely to be ejected, since casino bosses do not want large groups of angry people in their casino. It doesn't matter whether you have done something wrong or note: all such places reserve the right to refuse admission to anyone they please.

No, it really isn't. This is ultimately all about skill level. The people who get beat just aren't very good. These kinds of players are used to getting beat and don't go around complaining when it happens (unless they have direct proof of cheating such as using hand signals to communicate hole cards). The people who don't get beat are able to read the changing situation and they either adjust accordingly, or they move along.

I don't understand what you think it is that these team players are "doing" besides playing highly skilled, technical poker against inferior opponents.

So, yeah, I'd love to see the day that a bunch of bad players are able to band together and "banish" the very players who allow the casinos to rake in larger poker profits in the first place!

 

[D H]

From PokerCollusion.com: "Poker Collusion occurs when two or more partners decide to sit at one table and cheat the other unsuspecting players at that table. This is basically playing differently against one or more players than you do against others at the table."

This system has nothing to do with "playing differently" against anybody.

This system has everything to do with "playing differently". The whole point of this thread is about how two or more players should change strategy to take advantage of the collusion between the players.

I don't understand what you think it is that these team players are "doing" besides playing highly skilled, technical poker against inferior opponents.

These team players are cheating, pure and simple. Play this game on-line or in a public casino and you might well be asked to leave the table and leave your ill-gotten winnings behind. Play this game privately and you risk life and limb. Poker is an individual game of skill.

 

[CRGreathouse]

Has anyone actually demonstrated that the odds would noticeably improve through collusion? I've seen 31% vs. 10% mentioned, but I don't follow the derivation -- and don't believe it in any case, since if the first person drops out the second plays normally. In fact I'm not even sure that the basic assumptions of the 10% rule of thumb are sound. To have a 50% chance of having the best (hand, number, whatever) from identical independent uniform distributions with 10 people you'd need to be in the top 7.4%, not the top 10%, since (1-0.0741...)^9 = 50%.

 

[Hurkyl]

What you are seeking is cheating. You are not merely talking about a group of people sharing a bankroll to mitigate risk: you are actively seeking to alter your play style to exploit those situations a teammate is at your table. I will not tolerate this discussion.