Preflop Strategy and Playing Style

*The painter ChatGPT “A poker player in a Texas Hold’em game, suspiciously eyeing their opponent, trying to detect a bluff.”

Preflop Hand Ranges

Most poker books will argue that beginners enter too many hands preflop and should narrow their hand range so that their VPIP is around 20%. In fact, in the games I play, I feel like many players have a VPIP of around 60%. If the poker books are correct, then narrowing your hand range so that your VPIP is around 20% will give you an advantage against these players. The reason why many players don’t do this may be because the claim is not believed or is actually incorrect. Therefore, the purpose of this article is to verify the validity of this claim by performing a Monte Carlo simulation using the hand range table for each VPIP from the previous article.

Simplifying the Rules

In actual Texas Hold’em, decisions are made after the preflop for the flop, turn, and river, so winning or losing is not determined solely by preflop choices, but it seems difficult to handle this at present. Therefore, the decision to win or lose and the allocation of chips will be made on the assumption that the remaining players pre-flop will check in all subsequent rounds.

 Also, if you consider 4-bets or 5-bets, almost all loose players will be forced to fold, so you may come to the conclusion that you should 5-bet every hand. Therefore, for the purposes of this verification, we will assume that a 3-bet is equivalent to an all-in. Specifically, let’s assume the blinds are 10/20 and each player has 180 chips. A 1-bet is a fixed raise of 20, a 2-bet is a fixed raise of 60, and a 3-bet is a fixed raise of 180 (if an ante is assumed, the stack is 180 + ante).

 Under this assumption, by using a Monte Carlo simulation to calculate the expected value when competing between players with various hand ranges, we can verify which ranges have an advantage. In order to eliminate differences due to position, the dealer button is rotated among players during the simulation.

Configuration Example

The actual testing program allows you to set the pre-flop strategy to a certain degree of discretion, but we estimate that the following settings for each player type will give you a good idea of ​​what the strategy will be like. “1%, 2 players” represent hand ranges of only AA, KK, and QQ.

	3bet/3bet	2bet/3bet	2bet/2bet	1bet/2bet	Fold
Loose Passive	1%, 2 players	10%, 2 players	20%, 2 players	66%, 6 players	otherwise
Loose Aggressive	10%, 2 players	20%, 2 players	66%, 6 players	—	otherwise
Tight Passive	1%, 2 players	10%, 2 players	20%, 2 players	—	otherwise
Tight Aggressive	10%, 2 players	20%, 2 players	—	—	otherwise

What I’m interested in is whether playing tight aggressively will give you an advantage when all other players are loose-passive. Another question is whether a tight-aggressive setup has an advantage when these player types are mixed. Unlike a Nash equilibrium strategy (which not many players would be able to copy exactly), this is a fixed strategy, but in reality most players play in their own preferred style, so it may be more useful for amateur players to use.

Result

I tried to implement it, but the calculations were very heavy, perhaps due to a flaw in my implementation or because it was simply impossible to implement such a Monte Carlo simulation in JavaScript. It takes about 30 seconds to 1 minute to perform 10,000 simulations, and the results obtained from 10,000 simulations are far from convergent. Nevertheless, certain trends are visible, so I will briefly explain my thoughts on the results.

 The list of experiments to try is:

1. 1 tight aggressive vs. 5 loose passive
2. 1 tight aggressive vs. 5 loose aggressive
3. 1 loose aggressive vs. 5 loose passive

and we will calculate the expected value for antes of 0, 5 (0.25bb), and 10 (0.5bb). An ante here is assumed to be a compulsory entry fee that is put into the pot and is in a form that can be collected by the winner. When the ante was 0, the result was:

1. Tight aggressive players have an expected advantage of about +15bb/100 games.
2. Tight aggressive players have an expected advantage of about +20bb/100 games.
3. Loose aggressive players have an expected advantage of about +7bb/100 games.

Overall, it seems that tight aggressive has the highest expected value, which proves the assertion in poker textbooks is not wrong. Since the betting is done pre-flop, the profit may seem small, but keep in mind that since the bet is multiplied many times after the flop, you may actually be in the black by 100-200bb/100 games.

 However, if there are antes the results look quite different. With an ante of 5 (0.25bb) the results are as follows:

1. There is not much difference in expectations between tight aggressive and loose passive.
2. There is not much difference in expectations between tight aggressive and loose aggressive.
3. Loose aggressive players have an expected advantage of about +7bb/100 games.

In this case, tight aggressive is just as good as loose passive and loose aggressive, but loose aggressive may end up being the most advantageous playstyle. If you set the ante to 10 (0.5bb), there is no benefit to playing tight and tight aggressive players will lose to loose passive players. Of course, this is the expected value at the end of the preflop, and the influence of the ante may tend to decrease if you increase the bet after the flop. However, the value of your hand can change drastically on the flop, and you can fold if you’re slipping, so it’s quite possible that the advantage of tight aggression is no longer there.

 In fact, the game I play has a 0.25bb ante, which may be why tight aggression doesn’t seem like a strong option. The rules of the game are designed to favor loose players, which may result in loose-aggression being the most advantageous playing style. The reason why the majority of players have a VPIP of nearly 60% may not be because the participants are all beginners and unable to play tightly, but rather because the rules of the game are simply designed to favor loose players.

 Also, the fact that the simulation does not converge even after 10,000 times (even in setting example 1., +15bb/100 games may result in a loss) means that in real life, even after playing 10,000 times, it is possible that you will not be able to earn any profit equivalent to the positive expected value. There may be times when being patient and playing tight can be difficult to realize the benefits of, so there may be a good reason why many people refuse to listen to poker books that insist on keeping VPIP at around 20%.

Appendix

I’ve included the program I implemented. Note that the calculations are heavy and it takes a while to converge, so it may be difficult to see what I’m trying to say unless you repeat it several times.