Who gains when the game breaks up?

[pzhon]

I was just playing on Cryptologic when the server shut down for maintainence. All tables broke up. I had just posted the blinds at one table, and was annoyed because I didn't get my free hands. However, suppose everyone started each session by posting the big blind. Everyone at the table might feel cheated except the players UTG, who break even. Poker is 0-sum if you ignore the rake, so who gained to make up for our loss?

[TStoneMBD]

you just blew my mind dude.

[reubenf]

I think everyone except the poster gains when someone joins, so when everyone leaves all that value is lost.

I'm thinking aloud here sort of, and simplifying to one blind. If B is the blind size, your EV per hand is B/n for n players. Say you post with m players. You EV for that hand is B/m - B. Now another player joins in the blind, so you get m hands at an EV B/(m+1) each. So your EV for the orbit is B/m - B + mB/(m+1). So you profit B*(1/m - 1/(m+1)).

[tylerdurden]

I don't think anyone gains directly when the game breaks up. There are obviously some who have gained more than they have paid back (as far as blinds go), namely UTG as you point out.

In a more general sense, the worst players at the table "gain", since their losses are stopped.

[RayGarlington]

It seems that each player lost something that is of no value to anyone but themselves. Excepting UTG, each player feels cheated out of some free hands, yet no player gains monitarily as a result of their loss.

Possibilities?
Perhaps everyones' loss is emotional, which feeling is felt by UTG as smugness.

Perhaps everyones' loss is irrational, which is reflected in the house's indifference.

Perhaps it is a spiritual loss and the devil gains.

Perhaps this aspect of poker is not zero sum.

[bobbyi]

Let's look at the converse question: Who loses when a new game starts? When a new game is started, you draw for the button and someone is forced to pay blinds first. Everyone else gets to play several free hands before their blinds come up. From that point forward, they pay blinds and then play a full round, pay blind and then pay a full round, and so forth until they stop. If they are sensible, they will stop playing immdediately before the blinds get to them (after an indeterminate number of rounds). So, they break even on the blinds except for the fact that they got free hands before their first blinds, which people joining the game later don't get. So they got some free EV. From whence did that EV come? A gut instict is that it came from the players who got screwed by being forced to be the blinds first. But that's not true. They paid blinds and then got to play a full round. So the situation is break even for them and +EV (due to the free hands) for everyone else.

So we have EV magically appearing in the game when it first starts, with no apparent source. And, as you say, we have EV magically leaving the game when it breaks with no apparent sink. Put the two together...

Your EV went to the people who are going to get to play free hands whenever the games start back up because they don't draw a seat that forces them to start in the blind. Or, if you perfer, it went to the people who got to play free hands in your current game when it was first started.

Great question.

[reubenf]

I think this is the same as what I said. I don't know if either of us said it really clearly, though. Both of our explanations seem to imply that value appears from nowhere, then later disappears. This is a little odd, because while it's still zero-sum, it's sort of 'borrowing from the future.'

I think the question is misleading. The real question is, why is everyone (except UTG) behind at any given point in an orbit? Where did that value go? And the answer, as we've said, is that everyone at the table gained, in varying degrees depending on position, each time a new person joined.

If a table is two-handed, one person is ahead and one is behind at any point. Another person joins, and the original two are now ahead while the new person is behind. As the orbit goes around, whenever the new guy is UTG and his total value is zero, one of the other guys is ahead the same amount the other one is behind, even though they're both behind -for this orbit-. If the table breaks up now, nobody lost. If the table breaks up when the new guy is negative, one or both of the others gained. If one of the original guys leaves before posting a blind, he leaves ahead, taking value from the new guy.

I guess this all means that, ignoring rake, you can make money playing break-even poker by being the first to sit down at a table and the first to leave once it fills.

[bobbyi]

[ QUOTE ]
I think this is the same as what I said.

[/ QUOTE ]
It's not the same. Your anaylsis is about what happens as the number of players in the game increases and decreases and mine works without considering that. There are interesting theoretical issues there about blinds and EV, but we can answer the OP's question while keeping the number of players in the game constant. Imagine: A new game starts ten handed. The players draw for the button and someone starts as the blind (for simplicity, pretend it's a game with a single blind). From this point forward, whenever someone leaves, they do it after playing their UTG hand. Whenever someone leaves, a new player joins in the same seat and immediately takes the blind so the game always stays ten handed.

In this scenario, what is the EV for every player who joins after the game starts and leave before it breaks, considering only the blind? It is break even. They come in on the blind, and for each blind they post, they get a fulll round of play. What is the EV for the players who are there when the game starts? All of them but one get free EV because they get free hands before they have to pay the blind (the one remaining player is the one who starts with the blind and he breaks even). What is the EV for the players who are there when the game breaks? All of them but one lose EV because they pay their blind but don't subsequently play a full round (the one remaining player is the one who was UTG before the game ends and he breaks even).

The EV gain of the players there at the beginning will equal the EV loss of the players there at the end. Even if we don't vary the number of players at the table, we have a system where the people there when the game breaks (the OP in this case) give EV to the people there when the game starts. So that is the answer to his question. This EV shift is a separate phenomen from the EV shifts that occur as the number of players at the table increases and decreases at an existing game. Your analysis is mixing the latter and the former together, while I am keeping them separate and ignoring the latter entirely because the OP is aksing about the former.

[reubenf]

[ QUOTE ]
but we can answer the OP's question while keeping the number of players in the game constant. Imagine: A new game starts ten handed. The players draw for the button and someone starts as the blind

[/ QUOTE ]

The OP's question had everyone posting the blind when they came in. I think all your analysis requires people to gotten free hands at the beginning. Am I confused?

[pzhon]

[ QUOTE ]
I think this is the same as what I said.

[/ QUOTE ]
Actually, yours was more correct because games form by adding players. They don't start full.

[ QUOTE ]
everyone at the table gained, in varying degrees depending on position, each time a new person joined.

[/ QUOTE ]
That's the answer I was looking for. Also, whenever someone leaves rather than posting the big blind, that hurts the players at the table.

To make up for what I lost when the tables shut down, I sat down as the tables started up again.

[Shoe]

The site loses, and competitors gain. It might make players try another site where the "games last longer"

[RayGarlington]

Maybe this question has more to do with philosophy than math. Let’s assume there are two views of the game: “Pay it Forward” and “In the Moment”.

Pay it Forward
In this model, a person joins in, pays his BB and is thereby granted a free look at an unspecified number of future hands. As he pays his BB, he considers himself to be EV neutral and is eagerly anticipating his fair share of EV+ hands in the future. Most of the discussion above has assumed this model. It has been adequately demonstrated that this world-view results in some fairly elaborate theories.

In the Moment
Here, a person joins in, pays his BB and thinks, “dang, they really stuck me on this hand.” He considers himself to be EV- and everyone else to be EV neutral. This world view yields no discussion.