Table Change!

Online players probably won't find this every interesting, because they can sit at as many tables as they want simultaneously, and even many live players don't have much use for it. At Hawaiian Gardens, for example, as soon as you step foot into the top section to play limit hold 'em the act of table changing ceases to exist as an option. All the 20/40 and 40/80 games are structured in a must move chain; you're in the game you're in, and that's that. Commerce is also employs a must move system, but they don't daisy chain the games all the way up; if there are, say, four games, one of them will serve as a must move to the other three, which are all of equal status main games. In a situation like this (or the blissful community of Bay 101 20/40, where generally three main games are running from before lunch until well after dinner) a savvy live player will have the opportunity to request table changes to better his position for any reason he sees fit. I'm not going to go into the reasons for table changing (your friend is at the other table, there are weaker players at the other table, your image is shot, the guy on your left smells) or the method by which they are requested and offered (this is the single best reason to tip the floor I have yet found). I want to focus simply on the math of the table change, which I spent some effort thinking about yesterday for the first time in a while (at Bay 101 table changing was a key maneuver in my arsenal, but these days I find little use for it).

First the logistics. When you change tables, as a rule of thumb you are supposed to leave your current table "immediately" and must post to enter the game to which you're changing. Now a lot of players take great pains to play as many of their "free" hand as possible after being granted a table change, and others don't even understand that they are supposed to leave right away. "I'm going to play until my blind" they say, and scratch their heads pensively when Archie tells them "Just one more hand I have a player waiting." But for my little exercise I'm going to assume you leave instantly, or at least know exactly how many hands you're going to miss, and have an idea of the button position in the other game (which is sorta of silly since people may even change seats before you get their, rendering your knowledge useless). So here are the principles at play.

Limit Hold 'Em is a struggle for the blinds in which position is vital. Even very bad players wouldn't lose if they got the button every hand, and good players win from every position except the blinds. In theory any player could be taught to win from every position but the blinds by simply playing only aces. Would he win enough to offset his loses in the blinds? Of course not. But he would still win. For a talented live player who wins 1 big bet per hour at an averagely good table (this will come into play later), I'm going to postulate where that win comes from each hour by position:

UTG = .1
UTG+1 = .2
UTG+2 = .3
LJ = .3
HJ = .4
CO = .5
OTB = .6
SB = -.4
BB = -1.0

In truth this is way over simplified, but the numbers probably aren't off by much, and happen to add up to 1 which is really my only constraint. If anybody has access to a bunch of their HEM data and would like to back me up, I'd appreciate it, although you'd have to have a really big win rate per 100 hands to match up with this. Anyway, let's also assume that in each hour you play 4 orbits (36 hands, again an estimate but an extremely reasonable one) and so that each hand is worth 1/4th of the money I showed above. That is for 20/40:

UTG = $1
UTG+1 = $2
UTG+2 = $3
LJ = $3
HJ = $4
CO = $5
OTB = $6
SB = -$4
BB = $10

And therefore each lap you win $10, or .25 big bets. But that's really not the whole story, as I alluded to a little while back. Your win rate is not constant. Otherwise you'd never bother with changing tables in the first place, right? So let us assume that you're considering moving to a "juicy" table from your "just average" one, where you win rate rates to be substantially higher, say 1.25 big bets, or $50 per hour. In truth I believe that the disparities you see are often greater than this, but without knowing which seat you're going to get at the new table it would be hard to make such a claim. Anyway, by now you should probably be able to see where I'm going with this. Suppose you are offered such a table change that is going to cost you 4 "free hands" (UTG - LJ) worth $9. Suppose also that you "know" which seat is going to be yours at the new table and you're going to be able to post your big blind at about the same time you would have at your current table This simplifies things, as in a sense you literally just sit out 4 free hands. You could get to post your big blind sooner, which would make up for some of your losses, or have to wait interminably while your new table mates play musical chairs in excruciating linear fashion. I once waited almost 2 entire orbits to get into a game because of seat changes and the ensuing wait to post in reasonable position. Anyway, as you can see from just this exercise, which it looks like I'm going to abort a little short of where I'd hoped, it will be almost an hour before you make any money on your table change, since you gave up $9 at the old table and are only expecting to win about $10 more per hour at the new game.

And here's the kicker. You can never be sure how long your seat or your game is going to remain good or bad. So many times in my life I have table changed only to see that either by bad luck or opponents tendencies (Indian Jay at Bay 101 refuses to play with me; I once table changed to his game simply to piss off French Fry and JS because I knew he'd change away and they'd have to follow him) my old game looking great (often because I got replaced by a terrible player) and my new game looking not so hot. So here are my cliff's notes:

Giving up free hands is like giving up free money. Missing especially any late position hands is extremely bad. Never accept a table change that costs you more than 2-3 hands without extenuating circumstance. For example, if Neal is at Bay 101 and you get offered a chance to sit at his game, you should probably be willing to give up an entire orbit so long as you have at least 3-4 hours to play. He's not going anywhere anytime soon, and his table could be way better than yours for quite some time. My general strategy at Commerce is to ask for a table change a few hands before my blind when I'm planning to take a break for an entire lap. That way if I get the change any time in the next 15 minutes or so I'm good to go without giving up any free hands.