Poker Question That Probably Only Interests Me...

...or maybe it's a math question.

I remember talking to my friend Tom (tdeem1) once about euchre strategy, and he said something like "there is euchre and there is ladder euchre." Part of what he meant was that in order to succeed, you had to know not only the game but the venue.

Which brings me to Zynga Poker. Zynga is a free poker game attached to Facebook. Players earn chips that give them access to various rooms, but really there is no money exchanged. So that's one difference right there. People tend to be more aggressive, play to a draw more often, etc., when there is nothing really at stake.

Zynga has what is called a "Shoot Out" progressive tournament. You buy in for $2000 imaginary Zynga dollars and everyone gets $1000 chips. The winner gets his/her stake back plus entry into round 2. (Second and third get partial amount of stake back.) In round 2 the top three places score and the winner gets entry into round 3, where the winner gets 500,000 imaginary dollars.

Because the cost of the buy in is so low for Round 1, because they have very little attention span, and because it is not real money, many players in Round 1 go "all-in" on the first hand regardless of what they have. Most tables the average number of players who go all in is around 5, though I've seen all 9. I've only on very few occasions seen less than 4.

So here is my question, for the average person for whom imaginary game site dollars are not low (I have like 600 K and the buy in is 2K), when should you move all-in on the first hand?

Various thoughts, followed by rationale, follow, but I'm interested in other people's, especially math guru's, thoughts. FWIW, bear in mind that the fewer people all in (like 4) the easier it is to win the hand but the less decided advantage the person has. If there are seven people all in, it is possible with the blinds still at 10 and 20 dollars, to buy in to most pre-flop hands, wait for a commanding advantage and win the game. Though I have beaten the first hand winner many times, even when he/she generally has a 4-1 or 5-1 chips advantage.

Thought #1: NEVER
The problem with ever entering these free for alls is that even pocket aces seldom win. It becomes more random. You are 4-1 to beat a lower pair, but if there are 2 lower pair, and someone has suited cards and someone else has connectors, well, you get the idea...the number of hands that can beat you increases the more hands that are in and you can rarely get people off the hand. I will usually ANNOUNCE quickly when I have pocket aces, and I usually get 2-4 calls anyway. My hope is that 1 or 2 people might wait a hand to go all in. The fewer hands, the higher my probability of winning the first hand. And even just doubling up the first hand puts me in a much better position to be patient to bust the winner of the eventual group all-in.

Thoguht #2: ALWAYS
If it's just random, you should win a certain percentage over the long run (times where you have aces losing to a flush evening out with times you have 7-2 and suck out someone with the better hand). Once you win, you are in a commanding position. And if you wait, you are playing catch up most of the game.

Thought #3: Sometimes
Okay, but when? Given the fact that most of the other players will go in with anything, my thought here is that if you only play higher probability hands, you will still lose a lot, but the goal is to win more than a strictly random amount. So if you fold the 7-2s and play the AA, well, you'll now and then miss out on the 2-2-2 flop and get sucked out by the flush or straight draw, but the latter will happen less frequently than the former, and so, over time, you'll win a higher percentage than accepting the coin flip.

I sort of go with #3...I'll join if I have two cards 10 or higher, suited connecters, or an Ace + 2, 8, or 9.

Part of my wondering here is that not EVERYONE goes all in, so it is not strictly random draw. If I assume most people similarly won't fold two high cards, I can reasonably assume that the more people who are all-in, the less likely I am to draw a hand since there will be more low cards in the deck to flop. So, part of me thinks if there are 4 or fewer, go all in with high cards, but 5 or more, go all in with low cards (or value suited-connectors more). Then again, a lot of the players are just randomly all-in, so it isn't as though I can seriously read anyone's hand.

Also, does table position matter in this situation at all? I see some people just call the big blind and wait to see how many go all in, but I've seen it go all the way around the table to the small blind only to have him go all in and players with AA or 2-9 follow around the table, so the notion that there is less likely to be more good hands if it calls almost all the way around isn't really valid.

Just wondering if any poker players or math people have some thoughts about the most logical way to play this first hand melee.