One-pocket + game theory

Andrew Manning

Aspiring know-it-all
Silver Member
So I often hear it said that one-pocket is like chess.

I personally think that's a pretty inaccurate comparison, because in chess when you moved king's knight to f3, you're absolutely guaranteed that when you're done, that knight will sit on that space. In one-pocket, every move includes a probability of successful execution, and a range of likely unsuccessful outcomes, all of which may need to be taken into account.

But in terms of selecting a shot, particularly early in the rack, I do admit that one might utilize a chess-like application of game theory, and particularly the minimax theorem seems of value. Paraphrased based on my rudimentary understanding, to implement minimax, you'd consider each of your possible shot options, and assess your opponent's best possible reply to each. Whichever of your shots results in your opponent having the worst reply, is the shot you should take. Your goal is to minimize the maximum utility available to your opponent.

Anybody aware of a scholarly application of game theory to one-pocket? Anybody have an opinion on whether minimax is a good approach to bring to one-pocket shot selection? Anybody have an alternate algorithm for one-pocket shot selection?

-Andrew

Beware_of_Dawg

..................
Silver Member
Very interesting information available on the decison making concepts you raise...

Seems there is no infalible solution concept for decision making in 1P, (Minimax theorem & Negamax, Maximin, Nash equilibria, subgame perfect equilibrium, etc) 1P is played in the absence of perfect information. Refinements and extensions of the Nash equilibrium concept share the main insight on which Nash's concept rests: all equilibrium concepts analyze what choices will be made when each player takes into account the decision-making of others.

I would think that depending on the player and opponent any number of these algorythms could be applied, mosy likely the ability to utilize many of them in a fluid manner would be the most effective & nessasary approach...?

Very interesting to think about. Wish I had more time to chew on this brain candy... File it away with the other "when I get a chance" stuff Id like to spend more time thinking about. In the mean time, I would be interesting in reading further opinions on the subject or my initial thoughts.

Black-Balled

AzB Silver Member
Silver Member
While the incoming positions are not as defined as chess, at points in the game 1p is close enough to be equated to chess...consider sequence:

P1 top L) pocket, comes to this shot:

1.

CueTable Help

Leaving ball off bottom rail will mean P2 must remove 1b:
2.

CueTable Help

Meaning P1 will likely get to play a bank on the 8 or clear 15 (though the 2railer is also good from here.
3.

CueTable Help

That's how I see it!

The Nitcracker
Silver Member
I see it like this... In chess, your opponent can argue with you. "You moved your piece!" "No I didn't, I was adjusting it!" "You lying sack of sh*t!"

In one pocket, the same can happen. "You stole my ball!" "No I didn't, I made the 13!" "You lying sack of sh*t!"

You can see the similarities, no?

CreeDo

Fargo Rating 597
Silver Member
People compare things to chess because it's a handy lazy analogy. Mentally, they have four shelves full of "things that sound like they require being smart". Chess is sitting right there on the bottom shelf, waiting to be plucked. They never reach to the upper shelves.

I'm sure someone somewhere has compared jai alai, Counterstrike, and autocross to chess as well.

On the theory of minimax - sure, that makes sense when you phrase it like that. The ideal action is to make a ball in your hole (zero response for your opponent to make except to stay seated).

However it doesn't apply always. Conventional wisdom is that when you're behind in score, you must gamble a little. So you take the marginal shots hoping to turn things around. A safety would minimize their potential responses much more than a shot attempt, but the shot attempt could win the game. I guess you could argue you're not minimizing their response in the short term, but minimizing their ability to win the game in the long haul.

tucson9ball

AzB Silver Member
Silver Member
Very interesting information available on the decison making concepts you raise...

Seems there is no infalible solution concept for decision making in 1P, (Minimax theorem & Negamax, Maximin, Nash equilibria, subgame perfect equilibrium, etc) 1P is played in the absence of perfect information. Refinements and extensions of the Nash equilibrium concept share the main insight on which Nash's concept rests: all equilibrium concepts analyze what choices will be made when each player takes into account the decision-making of others.

I would think that depending on the player and opponent any number of these algorythms could be applied, mosy likely the ability to utilize many of them in a fluid manner would be the most effective & nessasary approach...?

Very interesting to think about. Wish I had more time to chew on this brain candy... File it away with the other "when I get a chance" stuff Id like to spend more time thinking about. In the mean time, I would be interesting in reading further opinions on the subject or my initial thoughts.

WTH!!! Minimax? Algorythms? Are we talking about 1 pocket or the space shuttle. jk
Some of us have not expanded our vocabularies since high school, please come down a notch.

DRW

AzB Silver Member
Silver Member
chess/1-pocket

When whoever said first that 1-pocket was like playing chess, I would think you could just put it off as a figure of speech.

blah blah

Shoebat
I see what you're trying to do here, but I don't think it's feasible- whether for a book or a computer- because the possibilities (permutations) are nearly limitless. Your decision tree is going to be humongous.

And you have to mark out every possible decision and then assign values before you can ever start dancing up and down the branches.

Take any 1p layout- and I think you make it worse by stipulating that it's at the beginning of the rack because now you've got 15 potential ob's. But pretend it's a dense stack and you can really only see maybe 7 of the possible ob's.

So you have 7 possible balls to make contact with first. Without even getting into reading the stack's possibilities, you have 7 balls to hit- and each ball you can hit with, (we'll have to make another limit here) you can make 1/4, 1/2, 3/4, and full ball contact with the cueball. AND that's in each left- right direction, so that means you can hit the ob with 7 different contact points (quarter ball increments plus center)- and we can agree that's really only just a small part of the truth there.

So now that you have 7 choices, and 7 different contact points, we can pretend that there are only 9 different englishes (clock and center).

Then we can talk about the type of stroke you can hit each of those 7 balls with each of those 7 contact fullnesses and each of those 9 englishes. I know the formula for figuring this out includes the " ! " symbol, but that's all I remember.

Before we try to list and describe the strokes and speeds, you've already got... *&^. Yes, I said *&^. See, I majored in Political Science, not math. We Poli Sci people wander around in game theory but when it comes to the math part it's time to just swear and call in math experts. : )

My point is that this whole line of thinking is not feasible in a game (toooo much time), terribly difficult for programming into a computer, and then you have every single shot situation to consider. We didn't even get into value assignments. Or assumptions of your own (and the opponent's) skill and knowledge levels.

I really think this exercise makes a strong case for relying on practice, experience, and studying both patterns and shots. And cussing.

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jay helfert

Shoot Pool, not people
Gold Member
Silver Member
I've often said that One Pocket is the "chess game" of pool, but it's actually much harder than that. In chess there are a finite number of moves and possibilities. In One Pocket there are limitless possibilities, which are a factor of each players creativity. After about a zillion hours of watching and playing One Pocket, I still learn new shots. Just one player alone (a certain Mr. Reyes), has constantly amazed me with his imagination.

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Gold Member
Silver Member
duplicate post

Tramp Steamer

One Pocket enthusiast.
Silver Member
I would agree that comparing Chess to One Pocket is only metaphorical, but I also feel that since the strategy involved is so thought provoking, especially when compared to the other cue games we play, the comparison shows considerable merit.
One Pocket also requires such refined abilities as imagination, resourcefulness, and ingenuity, just to name a few, along with a willingness to devote an uncommon percentage of one's time in developing the skills necessary to becoming a sucessfull player. As Grady says: "One Pocket is no meager undertaking."
It is because of all this I have decided to quit the game and help my ex-brother-in-law open up a scooter rental stand in downtown Peoria.
We hope to be open in time for Octoberfest.

Andrew Manning

Aspiring know-it-all
Silver Member
I see what you're trying to do here, but I don't think it's feasible- whether for a book or a computer- because the possibilities (permutations) are nearly limitless. Your decision tree is going to be humongous.

And you have to mark out every possible decision and then assign values before you can ever start dancing up and down the branches.

Take any 1p layout- and I think you make it worse by stipulating that it's at the beginning of the rack because now you've got 15 potential ob's. But pretend it's a dense stack and you can really only see maybe 7 of the possible ob's.

So you have 7 possible balls to make contact with first. Without even getting into reading the stack's possibilities, you have 7 balls to hit- and each ball you can hit with, (we'll have to make another limit here) you can make 1/4, 1/2, 3/4, and full ball contact with the cueball. AND that's in each left- right direction, so that means you can hit the ob with 7 different contact points (quarter ball increments plus center)- and we can agree that's really only just a small part of the truth there.

So now that you have 7 choices, and 7 different contact points, we can pretend that there are only 9 different englishes (clock and center).

Then we can talk about the type of stroke you can hit each of those 7 balls with each of those 7 contact fullnesses and each of those 9 englishes. I know the formula for figuring this out includes the " ! " symbol, but that's all I remember.

Before we try to list and describe the strokes and speeds, you've already got... *&^. Yes, I said *&^. See, I majored in Political Science, not math. We Poli Sci people wander around in game theory but when it comes to the math part it's time to just swear and call in math experts. : )

My point is that this whole line of thinking is not feasible in a game (toooo much time), terribly difficult for programming into a computer, and then you have every single shot situation to consider. We didn't even get into value assignments. Or assumptions of your own (and the opponent's) skill and knowledge levels.

I really think this exercise makes a strong case for relying on practice, experience, and studying both patterns and shots. And cussing.

What you're pointing out is an assumption I was using as a starting point, but that I didn't explicitly state; the idea that through intuition and totally unscientific creative effort, you'd come up with a small handful (2 to 6 or so, depending on the situation) of potential shots to choose between. Obviously ANY consideration of every combination of object ball, thickness of hit, speed, and english would be absolutely impossible. For all intents and purposes, you'd be talking about an infinite number of options.

But I find myself, while considering what move to make, unable to decide between 3 or 4 shots, and I often either just choose the easiest one to execute regardless of how much value it will actually gain me, or the one with the biggest upside regardless of potential disaster. I often settle for one of these two extremes because I lack a reliable way to actually evaluate which of the potential shots really gives me the best chance to achieve victory in the end.

-Andrew

ironman

AzB Silver Member
Silver Member
When whoever said first that 1-pocket was like playing chess, I would think you could just put it off as a figure of speech.

DIng ding ding!!!!Wehave a winner and the most intelligent response yet! LOL

K Knight

AzB Silver Member
Silver Member
But I find myself, while considering what move to make, unable to decide between 3 or 4 shots, and I often either just choose the easiest one to execute regardless of how much value it will actually gain me, or the one with the biggest upside regardless of potential disaster. I often settle for one of these two extremes because I lack a reliable way to actually evaluate which of the potential shots really gives me the best chance to achieve victory in the end.

-Andrew

Thus, you need more experience to make your decision between harder shot/natural leave vs. easy shot/ tough leave. Game theory's economics roots is dependent on finite requirements. The application to pool in general is more of a freakenomics thing. While completely relevant, it is not finite, and therefore will not result in a finite/definitive answer. All players have different strengths and weaknesses, and need to play their game to compliment their strengths and not expose their weaknesses. The approach you are taking implies there is a "correct" run-out path regardless of who is shooting. Experience can't be learned, it must be earned.

Andrew Manning

Aspiring know-it-all
Silver Member
The approach you are taking implies there is a "correct" run-out path regardless of who is shooting.

I was certainly not talking about how to run out. If I have an opportunity to run out, it's because I've already done the process I'm talking about in this thread correctly. I have taken the right shots to manipulate the game such that I have a good opportunity to run balls before my opponent does.

What you're saying does apply to the point I was making, though, in that one's own skillset and one's opponents skillset must also be taken into account, along with which shot yields the best strategic positional advantage.

-Andrew

freddy the beard

Freddy Bentivegna
Silver Member
My theories -- released

I wasn't going to do this, but I relented in order to start off my new upgraded website. Advanced Onepocket theory -- long:

http://bankingwiththebeard.com/?p=354

the Beard

PS I might answer questions, but I aint lookin' to debate it. If it helps, fine. If not, stick to nine ball.

TxSkin

AzB Silver Member
Silver Member
So I often hear it said that one-pocket is like chess.

If someone who knows the game of one-pocket says it is like chess, it is because he is trying to give the flavor of it to someone who is unfamaliar with it. Very much like when describing a meat (say, rattlesnake) that is unfamaliar to another person, the person who has eaten it may say that it "tastes like chicken". LOL

At any rate, I think 1p is more like Chinese checkers than chess.

TxSkin

CocoboloCowboy

Cowboys are my hero's
Silver Member
I wasn't going to do this, but I relented in order to start off my new upgraded website. Advanced Onepocket theory -- long:

http://bankingwiththebeard.com/?p=354

the Beard

PS I might answer questions, but I aint lookin' to debate it. If it helps, fine. If not, stick to nine ball.

Andrew Manning

Aspiring know-it-all
Silver Member
I wasn't going to do this, but I relented in order to start off my new upgraded website. Advanced Onepocket theory -- long:

http://bankingwiththebeard.com/?p=354

the Beard

PS I might answer questions, but I aint lookin' to debate it. If it helps, fine. If not, stick to nine ball.

I love the clear advice, Freddy. Excellent. The mathematics of selling out is an interesting revelation, and the point you focused a lot on regarding dealing with the fear of selling out is something I could really use in my one-pocket game. I get so out of stroke playing 1-hole, and concentrate so hard on "holding" the CB, that I lose my physical technique, and end up with way worse CB control (to say nothing of much worse odds of doing what I wanted with any of the other balls on the table).

The way this directly applies to the point of my thread, as I see it, is that the algorithmic style of shot selection would at best only apply when the player is winning or the game is even. When behind, you have to move away from that mindset.

I do wish you would expand on this statement:
Everybody with any common sense knows pretty much what to do in ordinary situations in One pocket. That can all be easily taught. You don’t need me for that.

In such a complex game, what qualifies as an "ordinary situation"? As a relatively experienced 8-ball and 9-ball player who is pretty much a rank beginner at one-pocket, I think I struggle with making the right decision in "ordinary" situations as I do in extraordinary ones.