Overview
In the previous article, I wrote about a player who was playing a Push or Fold event without knowing it, and in my article on optimal heads-up all-in I mentioned that I wanted to develop a game where players could choose between All-in or Fold. I have actually developed an alpha version, so I would like to introduce it to you. Although it is a simple game, I think it is enjoyable because the NPCs make relatively human-like decisions. Games in which you can only choose All-in or Fold pre-flop are called All-in or Fold (AOF) or Push or Fold (POF).
The rules differ from regular Texas Hold’em as follows:
- All players have two pre-flop decisions to make: All-in or Fold.
- The stack is reset to a fixed amount each time (the stack that increases or decreases after a win or loss is not used as is, and the same stack is always used in the win or loss).
- The number of players seems to be usually 3 or 4. If there are 2 or more players, it seems like the game becomes more of a game of luck.
- Other rules are the same as Texas Hold’em.
Since everyone except the player is an NPC, if you leave the player’s stack with some leeway and don’t reset it, the player will be able to see how many chips they have earned. If a player has more chips than the specified stack, their strategy is the same as if they had the specified stack (because their Effective Stack is the specified stack).
I implemented several models for the NPC opponents, including those discussed in previous articles. Specifically, they are as follows:
- Calling Station: Always all-in
- Random: Folds with a certain probability, but does not consider hand strength
- Fixed Hand Range: All-in for the specified VPIP amount in order of highest probability of winning
- Preference Order Model: Various hand ranges can be specified depending on the model parameters
- Game Theory Optimal: Going all-in with the theoretically optimal hand range
and 2. are relatively weak opponents, and on average you can win if you choose your cards reasonably well. This is a model that goes all-in in order of the highest probability of winning, as discussed in the article “VPIP and Hand Range,” so that a certain VPIP is reached. 4. is the All-in or Fold version of the “Pre-flop Player Model” that was mentioned in a recent post, and the player will select their hand according to their order of preference. is a model that uses the hand range calculated using the CFR calculated for the “optimal heads-up all-in”. This model currently only works for two players, but I plan to expand to multiplayer in the future (I’ll be writing a post exploring this in the future). Here are some links to related posts:
The Developed Game
The link to the game I developed is below. The basic settings are the same as those of a regular Texas Hold’em game. However, due to the nature of the game, it is difficult to vary the number of players, so I have made it so that the number of players can only be set to a fixed number.
The default setting is Game Theory Optimal for NPC models, but when I played against them, I found they weren’t very strong (though they weren’t weak either). I think this is because with two players, it’s relatively easy to remember the hand ranges, and if you choose the optimal range, it just becomes a game of luck.
Future Extension
The game seems too simple to play on a PC. If it could be made into a mobile game that could be played on a smartphone, it could become a game that can be played to kill some time. It will also be a good way to practice Push or Fold in Texas Hold’em. There are already several similar mobile games, but it would be possible to differentiate it by adding unique behavioral models to the opponents. It will take some time to develop a mobile game, but I intend to develop it in the future.
Also, in previous game implementations, the UI was in a format that displayed the internal structure of the program almost as it was, so it may not have looked like a game UI. This time I made it a little closer to the game’s UI, so I think I’ll be modifying the game screen to this format in the future. Screens for games like Texas Hold’em and Omaha Hold’em may also be slightly easier to play if they are used in this way when implementing NPC models.
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