Can one overcome the rake at low limit poker games?

In a game with no rake and no toking, there is no question that in the long run (with the cards breaking even) the better players will win money at the expense of the weaker players. The question is: Can strong players win enough from the weak players to more than cover the expenses in a game with a rake and/or toking?

How much do the rake and tokes cost us? It varies, but we can calculate some ranges. Let's assume a 10 seat $2/$4 game dealing 40 hands per hour. Assume a rake of 10% to $4. As a good player, you are somewhat tighter than your opponents, so let's assume you win an average of 3.5 pots per hour (4 would be your "fair share"). Your average rake expense ranges from a probable low of around $1.46 per pot (from TTH sims) to a probable high of around twice that amount (in line with the observations of experienced players in certain games). Add in a $1 toke per pot, and your average expense per hour likely falls somewhere between $8.50 and $14. In terms of big bets, this is 2.25 to 3.5 big bets per hour. Across other limits we can calculate expense ranges the same way:

10% rake to $4, $1 toke
      Est. Total Hourly
Limit Expense (Big Bets)
----- -----------------
10-20 0.76 to 0.88
5-10  1.23 to 1.66
3-6   1.91 to 2.62
2-4   2.25 to 3.50

Some games have lower expenses. For example, some on-line games feature a rake of 5% to a max of $3 with, obviously, no toking. The expenses here (From TTH sims) are:

5% rake to $3, $0 toke
Est.  Total Hourly
Limit Expense (BB)
----- ------------
10-20 0.45 and up
5-10  0.55 and up
3-6   0.58 and up
2-4   0.53 and up

Now we need to estimate the win rate for a good player in a sufficiently weak game. Unfortunately this resists a straightforward mathematical solution. Our best source of information comes from the observations of top theorists and experienced players. These sources have cited approximately 1 BB per hour (after expenses) as the approximate profit a strong player might expect at limits of 15-30 and up. This corresponds to a pre-expense win rate of about 1.5 BB / hr. (TTH sim showed a .54 BB expense factor for 15-30). Experienced players have reported higher win rates in exceptionally weak low limit games. Players in the softest of games report win rates as high as 3+ BB per hour after expenses So, a good player in a weak enough game can achieve a pre-expense win rate of 1.5 BB / hr and up, perhaps exceeding 4 BB / hour in extremely favorable circumstances.

This indicates that the rake can be overcome in even the lowest limit games if you are sufficiently strong and your opponents sufficiently weak. Remember, if you're not one of the better players in a given game, it wouldn't matter if there were no expenses, you'd still lose.

Any given poker game at a given time comprises many factors: fixed factors such as the rake, betting structure and rules; variable factors such as the talent, mood, and motivation (etc.) of you opponents; and personal factors such as your ability, discipline, and toking level (etc.). Therefore, the question we should really be asking is "Can I beat the players at *this* table at a rate sufficient to overcome the particular expenses of *this* game?" This all points back to the importance of skill #0, judicious table selection.