Open Bet Sizing

For the past few months I've been experimenting with open bet sizing as a function of position. As I've mentioned before on this blog, there are a number of competing theories amongst knowledgeable poker players on the amount one should bet in the early, middle, late and blind positions if you are first into a pot. Some pros advocate large bet sizes in EP and small bets in LP. Others suggest the opposite; i.e., small in EP and large in LP. Still others say you should bet the exact same amount regardless of your position. And still others say that in you should bet amounts that are a function of your card strength.

So, with that in mind, in between my normal $25NL and $50NL games, I've snuck in 20K hands of  $10NL full-ring Rush poker with four different bet sizing strategies. For the first 5K hands of this 20K block, I played a small bet in EP and big bet in LP approach. For the next 5K hands I reversed that. The third block of 5K hands were then played by betting the same 3xBB amount regardless of position. Finally, the last 5K hands I simple opened strong with strong hands, and weak with weak hands.

The sample sizes are fairly small, so I'm not sure if I can draw any super definitive conclusions from the experiment. That said, however, I did see a few interesting things develop: 

1. Small in EP, Big in LP Approach. This method returned the worst results. I made money over the 5K hands, but my win rate was only 2.4ptbb/100.
2. Big in EP, Small in LP Approach. This method returned the highest return, with a win rate of over 4.2 ptbb/100.
3. Constant Bet Size. This method earned me a steady 3.3 ptbb/100 over the 5K hands.
4. Bet Size Proportional To Hand Strength. Surprisingly, this method returned the same 4.2 ptbb/100 win rate as the BigEP/SmallLP approach. 

So what's going on? For starters, I think this experiment helps validate the old poker adage "Big Hand --> Big Pot; Small Hand --> Small Pot."  In other words, the hands I was opening in EP position were, by definition, premium hands such as 88+ and AQs+. These hands tend to have a lot of equity against other hands PF, so it makes sense that I made more money over time by betting them hard when I was ahead. In other words, when you think your hand is best, you should bet. This explains why both the BigEP/SmallLP and the Proportional approaches returned similar results*.

Conversely, when I took the SmallEP/BigLP approach, I think was not pounding the opposition hard enough with my big hands in early position. Consequently, I lost a lot of value in those seats. In addition, I think I priced in weaker drawing hands sitting in LP, which allowed them to see relatively cheap flops and then outplay me post-flop because they had position on me. In other words, I let so-called "bust'em" hands go up against my rockets and cowboys for a discounted price.

The constant bet size approach seemed to find a simple, moderately profitable middle ground between these two extremes.

Again, the sample sizes are small, so there is some basic statistical variance still affecting the results. That said, however, I think there is something to this madness. The next step in the experiment should then probably be to take the BigEP/SmallLP approach and try different variants on it. For the initial experiment, I bet 3.5xBB in the first two seats, 3xBB in the middle three, 2.5xBB in the last two seats, and 4xBB from the SB.  For the next round, I may try turning up the gain on these amounts. For instance, in the UTG seat I'm thinking 4-5xBB, and then ramping down to 2.25 or so on the button.

I'll keep you posted.
All-in for now....
-Bug
*Note, however, that the Bet Size Proportional approach probably only works at Rush tables, and there it probably would become exploitable after your opponents gather enough stats on you and are paying attention. If you tried this approach at a "normal" ring table, even the fishiest of players would catch on pretty quickly, and you'd get killed. I think.