Texas Hold’em Rules
See the following article.
Operation Manual
Specify the game settings and press the start button to start the game. You can only press the start button once, and if you want to change the settings, you can reload the page by pressing the refresh button on your browser and reset the settings. The meaning of each setting item is as follows:
- # of Players (Fixed/Float): Specify whether the number of players sitting at the table is fixed or float. In the case of float, players will leave or join at a certain probability.
- # of Players: Specifies the number of players at the table. If you selected float in 1, this is the initial value.
- Initial Chips: In this game, the strength of the opponent changes depending on the amount of chips that the player has. If you want to increase the difficulty, set this amount higher.
- Winning Probability: Specifies whether to display a simulated probability of the player winning.
- # of Simulation: Specifies the number of simulations to be performed when estimating the probability of winning.
- Opponent NPC: Set whether to randomize the strength and personality of the NPCs you will face, or specify them. If you specify them, NPCs other than the specified strength and personality will not appear.
- NPC Level: If you selected “Specified” in step 6, specify the strength of the NPC you will face.
- NPC Risk Aversion: If you selected “Specified” in step 6, specify the risk aversion level (aggressive/passive) of the NPCs you will face.
- NPC Style・・・If you selected “Specified” in step 6, specify the play style (loose/tight) of the NPC you will be face.
To play, press the start button to start the game, then just click Raise, Call, and Fold. The raise is calculated by multiplying the bet (the maximum bet amount among players) by x (the value in the combo box). Specifying x1 will result in a minimum raise. When a round ends, you automatically move on to the next round, so the game continues indefinitely. Since no data is saved, refreshing or closing the page will mean you have to start over from the beginning. The ♢ in the Order column is a symbol that represents that player’s turn, and when ♢ appears in your column, you press a button to progress through the game.
If the number of players is fixed, the opposing player will leave the game when their chips fall below half the user’s and be replaced by another player. If you select “Float” as the number of players, enemy players will randomly leave the table if they lose chips or play too many times, and new enemy players will randomly appear. The probability is about 3 to 7 people. If you go all-in and defeat all the enemies, the number of players will increase again from 2 to a little at a time. During the showdown, hands are announced and the abbreviations are as follows: HC: High Card, 1P: One Pair, 2P: Two Pair, 3C: Three Cards, ST: Straight, FL: Flush, FH: Full House, 4C:Four Cards, SF: Straight Flush (including Royal Straight Flush).
NPC Specifications
The specifications of the NPC players are as follows. For a detailed explanation, see the following post.
The settings for each level of NPC are as follows:
- Level 1: \(\small \delta = 0.8,\lambda = 4\), # of simulation for probability evaluation:30
- Level 2: \(\small \delta = 0.6,\lambda = 3\), # of simulation for probability evaluation:100
- Level 3: \(\small \delta = 0.4,\lambda = 2\), # of simulation for probability evaluation:300
- Level 4: \(\small \delta = 0.2,\lambda = 1\), # of simulation for probability evaluation:1000
- Level 5: \(\small \delta = 0,\lambda = 0\), # of simulation for probability evaluation:10000
The NPC’s risk aversion is the \(\small \gamma\) value of the CRRA-type utility function. The NPC style is set by the parameter \(\small s\), which represents the bias of subjective probability, as follows: Loose1:0.1, Loose2:0.2, Neutral:0, Tight1:-0.1, Tight2:-0.2.
The Name column of the NPC player displays the level, risk aversion, and style parameters, where Lv is the level value, g is the risk aversion value, and s is the style index, which represents 0: Loose1, 1: Loose2, 2: Neutral, 3: Tight1, and 4: Tight2.
Similar Games
There are several games similar to Texas Hold’em. Since they were easy to implement, I tried making the following two.
- Short Deck Hold’em: Texas Hold’em played with 36 cards, excluding cards 2 through 5. The strength of flushes and full houses is changed to flush > full house. Straights can circulate, and KA678 also counts as a straight.
- Omaha Hold’em: Each player is dealt four cards. Players must choose two cards from their hole cards and three cards from the community cards to make a hand. Since 4×11+5=49<52, a maximum of 11 players can play.
In Omaha Hold’em, if you set the difficulty level to high, the processing may become heavy due to the simulation calculations. Other than that, it is the same as Texas Hold’em.