Conan the Librarian: Typical tight aggressive profile that plays about 18% of hands.
Bret Maverick: The v6.0 Advisor. The software author's optimal Limit Hold'Em strategy as derived from lengthy research.
Nicely Nicely Johnson: Tight aggressive preflop, but plays hands passively postflop, keeping pots as cheap as possible until the big hands hit. I have noted in previous trials that this profile has shown routine, minor profitability in some 3/6 environments.
Gypsy Rose: Tight passive pre, playing the same hands as a typical TAG but rarely raising. Tight aggressive postflop.
Lee Jones Hybrid strategy: Programmed in manually. Preflop strategy is taken from Lee Jones' Winning Low Limit Hold'Em. Postflop strategy is a cautious, relatively passive strategy that avoids aggression without a strong made hand or strong draw.
I simulated 500,000 hands for each profile in a 3/6 Limit Hold'Em game with a 10% $4 max rake and $1 jackpot drop (to simulate typical Seattle area conditions: 10% $3 max rake with a $1-2 jackpot drop) plus a $1 toke for every pot larger than $13 (leaving 2 big bets).
For opponents, I used a set of 8 average profiles, of which two or three were TAG profiles and the remaining profiles a bit loose (35% of hands played) but reasonably thoughtful, with one or two programmed to draw regardless of pot odds (typical of some weak players in low limit games).
To properly simulate a typical, not-as-friendly low limit game, I made sure none of these profiles were particularly loose. I also set the simulator to periodically vary the strategy of these other profiles to mix things up. This table saw an average of 3.8 players to the flop. This is not a friendly game, but the idea is to develop a strategy that can beat a sub-optimal low limit game. Any loose low limit game can be potentially profitable despite the rake, but such conditions aren't frequent, and with the current recession, such conditions will become more rare as fish and dead money disappear.
| Profile | Net $ per hand |
|---|---|
| Conan | -0.12 |
| Maverick | -0.08 |
| Nicely | -0.11 |
| Gypsy | -0.09 |
| Lee Jones | -0.05 |
As you can see, all these hands post a net loss over 500,000 hands. As experts say in their texts, these tight strategies indeed cannot turn a profit at 3/6 due to the rake and jackpot drop.
All of these strategies have playable hands that lose money at such a 3/6 table. I believed I could improve the profitability of each strategy by eliminating the starting hands that showed a long term loss over several thousand samples. For each strategy, I decided to improve the starting hand requirements using a simple, crude method I examined data the chosen starting hands and noted only the hands that turned a significant profit (more than $0.10 per hand), eliminating the others.
On average, the following hands showed a profit with each profile: Pairs AA-88, AKs-A8s, AKo-AQo, KQs-K10s, QJs, J10s. All other playable hands posted a loss, including small pairs, suited connectors down to 54s, weak suited Aces, suited Kings down to K7s, suited Queens down to Q8s, suited Jacks down to J8s, and unlisted offsuit Broadway hands.
Each profile had its share of limited exceptions: Maverick and Conan profited with AJo and A10o. Maverick turned a profit with KQo. Maverick and Gypsy profited with Q10s, plus Maverick turned a profit with 10-9s. The Lee Jones profile won with 77. Some also turned a loss with the aforementioned profit hands: 88, A9s and K10s were losers for Nicely. Maverick and Nicely turned a loss with 88 and QJs. Granted, some of these losses could also be a factor of how the strategies played these hands preflop: raising with these hands could be a leak, or maybe the hands are played too passively. But we'll examine the strategy for hands later.
For now, I omitted the leak hands for each profile and ran another 500K test with revised starting hand requirements in the same environment. From here, I'm looking for significant improvements in win rate (or in this case, reductions in loss rate). I also cleaned up the strategies: allowing for more limping behind with draw hands such as Axs and small pairs, knowing the postflop strategy would dump them on the flop if a set or flush draw didn't flop. The original strategies, for some reason, didn't exercise this strategy with limpers in front, curious since most times you limp behind, you will see a multiway flop with the implied odds to draw, or flop a big hand that's way ahead, even if you have to call an extra bet when someone raises behind you.
The results are noted along with the original results below:
| Profile | Original Net $ per hand | Revised Net $ per hand |
|---|---|---|
| Conan | -0.12 | -0.02 |
| Maverick | -0.08 | -0.02 |
| Nicely | -0.11 | -0.08 |
| Gypsy | -0.09 | -0.05 |
| Lee Jones | -0.05 | -0.04 |
Again, all profiles showed a net loss, but certain profiles saw significant improvement in profitability potential, while others barely budged.
While the Lee Jones profile showed the least loss originally, an adjustment of the starting hand strategy netted minimal improvement. This is likely because the starting requirements for the Jones profile were tighter originally than the others, so there was minimal room for improvement. The other strategies had relatively loose starting hand requirements, playing weaker suited Kings, Queens and Jacks in middle position, for example. Once the K7s and Q8s hands were ditched, most of the strategies improved quite a bit, though they still posted a loss.
The biggest net improvment came from the Conan profile, which produced the biggest original loss, but immediately improved to tie for the lowest loser with the Maverick profile, the official software advisor, which also saw a significant improvement, though not as great.
Though these starting requirements were deemed optimal by software designers, they also assume games with a minimal rake, while dismissing lesser games as unbeatable. Bob Wilson himself has noted how a relatively higher rake can turn a normally profitable hand into an unprofitable hand, though stronger hands still remain profitable despite it.This leads me to believe that the key to finding a profitable 3/6 strategy is to take a normal strategy and eliminate lesser drawing hands whose payoffs are reduced by the rake, or at least reduce the circumstances in which they're played to profitable circumstances.
As we see here, by noting the drawing hands that post a loss and eliminating them from the starting strategy, while maintaining a typically solid postflop strategy, you can improve your profitability in games with a relatively high rake.
Now, before we begin trials in middle position, which profile will we use as a strategic baseline? While the Conan profile showed the biggest improvement, I decided to go with the software advisor Maverick. The end profitability was the same, and while it didn't improve as much once the starting strategy was sharpened, it also originated with a small loss rate than the Conan profile. It is also the advisor, which the designers concluded was an optimal strategy, and its solid postflop parameters are fairly similar to the Conan profile, if not nearly the same. And finally, the starting hand selection for the Maverick profile is a bit looser than Conan, which will allow me to run trials for more starting hands directly from the profile, without needing to manually configure a revised profile to test additional hands.
In trials for middle position, late position and the blinds, I will focus on the hand selection for the Maverick profile as our control profile. Later, we'll run tests for the Conan profile in kind, and see if we note any improvements in profit.
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