Opponent Modeling in No Limit Texas Hold 'em

Opponent Modeling in No Limit Texas Hold 'em

by Evan Ettinger

Purpose:

The purpose of this project is develop a No Limit Texas Hold 'em opponent modeler than can be adaptive over a period of poker play. Data from live real money poker games will be used to generalize from.

The Rules:

No Limit Texas Hold 'em is sometimes refered to as the Cadillac of poker. It is widely regarded by most to be the only pure form of poker left. Each player is dealt two cards face down called their "hole cards." A round of betting then takes place followed by the flop where three community cards are dealt face up in the middle. Another round of betting takes place followed by the turn, where another community card is dealt face up. Again the players bet, and then the river, the final community card, is dealt face up. The showdown then occurs when the remaining players make a final bet. The winner is determined by the best five card poker hand from their two hole cards and the five community cards. For example, the best possible hand (a.k.a. "the nuts") on a board with As Ks Qs 8d 4c would be the hole cards Js and Ts giving the player a royal flush.

Here are the poker hand rankings:

The beauty of No Limit Texas Hold 'em is that a player can raise any amount they wish. The only restriction is that a player's raise amount must be at least as much as the previous bet or raise in the same round. For example, if the first player to act bets $100 then the second player must raise a minimum of $100 (a total bet of $200). If a bet is raised to more than the amount of an opponent's stack, that opponent still has the opportunity to call the raise, but can only win as much as they can call. For example, if one person bets $100 into an opponent whose stack only totals $50, the opponent may still call and then is said to be "all-in", however, the opponent can only win $50 for a total of $100, not the entire $150 (the remainder $50 is simply returned back to the first player's stack upon the all-in call).

Modern Hold 'em poker games have a betting structure utilizing what is called a "blind structure." In the blind structure a button is passed around the table one seat at a time counter-clockwise after each hand. The button is called the "dealer button" and thus the game is played as if that person was the dealer even though they may not physically be dealing. The two people in the seats directly to the left of the dealer are said to be in the blind positions. The person immediately to the left of the button must put in the small blind which is typically 1/2 or 2/3 the big blind. The person two spots to the left of the dealer must put in the big blind. Each blind is put into the pot before the hole cards are dealt. This structure replaces the commonly known ante structure and has the purpose of increasing pot sizes and encouraging more play. For example, a common blind structure for low no limit games is $1/$2 blinds where $2 is the big blind and $1 is the small one. After the hole cards are dealt, betting begins with the person to the left of the big blind who then must either call the big blind, fold, or raise as described above. When betting comes back to the small blind, if no raise has been made, the person can either fold and forfeit the small blind or call the difference between the small and big blind. Finally play is returned to the big blind and if no raise has yet been made, he/she has the opportunity to raise or he/she can simply check and let the flop be dealt.

The following are features that I propose to examine as salient variables involved in classifying players:

5. Percentage of times player has a top 10 hole card hand (i.e. AA, KK, AKs (s here means suited not spades), AQs, QQ, AK, JJ, TT, KQs, AQ) when calling or making a preflop raise (view histogram)

6. Percentage of times player has a top 25 hole card hand when calling or making a preflop raise. (view histogram)

10. Percentage of time a player makes/calls a raise on the river (view histogram)

11. Percentage of time a player sees a flop from early position on hands of 10 players (the first three spots to the left of the big bind) (view histogram)

12. Percentage of time a player sees a flop from on hands of 10 players (the next 3 spots after) (view histogram)

13. Percentage of time a player sees a flop from late position on hands of 10 players (the last 3 positions, including the small and big blind) (view histogram)

The following are features that I propose to examine as salient variables in predicting the play of players:

14. Percentage of time a class bets upon a flush draw on the flop (i.e. the flop has 2 or more cards of the same suit and the player's hole cards are also suited of the same suit).

15. Percentage of time a class bets upon an open ended straight draw on the flop (i.e. the flop has cards that when combined with the player's hole cards makes a 4-straight, e.g. 2c 3s 4d 5c).

16. Percentage of time a class goes to the showdown with a top 5 hand given the board on the flop (note: top hands will be evaluated such that if a 4-flush is on the board without the A of that suit, having the A will be considered as having one hand and hands such as A2 vs A3 will not be considered as different hands).

17. Percentage of time a class goes to the showdown with a top 10 hand given the board on the flop.

18. Percentage of time a class goes to the showdown with a top 20 hand given the board on the flop.

19. Ratio of stack to bet size when a class bets/calls on a flush draw on the flop.

20. Ratio of stack to bet size when a class bets/calls on a open ended straight draw on the flop.

21. Percentage of time a class goes to the showdown with less than top pair on the flop.

22. Percentage of time a class goes to the showdown with less than second pair on the flop.

23. Percentage of time a class goes to the showdown when the board pairs on the flop.

The first course of action will be to place the players into n-classes by k-means or some other EM type grouping algorithm. The hope is that by grouping the players on the first category of variables, the second category of variables will be distributed similarly within classes. Thus, conclusions can be drawn about a players play based on what class they fall within. For example, a person who is in a class that only sees 10% of flops can be assumed to be playing hands that are very strong starting hands, and thus we can weight our probabilities for which hand the opponent has towards the high end of the spectrum. We will use Skalansky's and Malmuth's hand groupings to value the 169 possible starting hands. Their table labels what are to be considered the top hands and furthermore groups these hands by their strength. Group 1 is the strongest and 8 is the weakest among hands that can even be considered playable. Their table is as follows:

This table clearly does not list all the hands possible, but instead is supposed to be an outline of which hands are playable. Group 1-3 are always playable no matter what the game conditions or type of player. A tight player such as the one described above who only sees 10% of the flops probably has a hand in one of these three groups. These groupings are also organized in such a way the the first hands listed in a grouping are stronger than those that are listed later. Thus, AA is the strongest hand and is slightly stronger than KK (and in fact is a lot stronger when AA plays KK "heads up", which means 1 on 1). To reiterate this is not a complete list of the playable hands, but only an outline. Hands like 52s are implied to be at the low end of group 8, and A5s is obviously stronger than A4s but all are placed in group 4.

The variables in the first category are more general categorical variables that can be used to seperate the players into classes, however, the second class of variables listed are those that can be used when needed to make predictions about the opponents play given the current situation on the board. The combination of these two types of variables should aid in an attempt to model opponent poker players.