# Poker Analytics For Beginners and theories — Statistical Arbitrage

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If there weren’t luck involved, I would win every time

Phil Hellmuth

Poker is the ultimate decision theory problem. Poker is a game where you play over a large number of sample aka hands. It is clearly a skill-based game. However, there is a fair role of decision making that takes behind each aspect of a poker round to get the poker analytics right. The questions being discussed are:

And this decision takes place over four parts of each poker round with later ones being optional. Therefore we break the game into Pre-Flop, Post-Flop, Turn and River. The entire game is about these right decision over and over again to be able to win in the long run.

Now what makes this decision problem complicated is the fact that this is an imperfect information game, unlike Chess where we see the entire board, we can only anticipate our opponent’s hands and being a winner’s take all game, we thereby make decisions taking this into account. Additionally, the different rounds of flop add an element of pizazz to the game in form of the variance of results.

# Expected Value

All decision making based on the expected value of the decision. EV is the probability of winning the hand multiply by the size of the pot. If the money/chips we put into the pot is less than the expected value of winning money or chips, we are making the right bet and it’s not if it’s negative and it’s a losing decision.

Let’s look at a couple of resources for poker analytics to get started on this topic, an article and a more detailed deep-dived course for the same.

Another term used in conjunction with expected value is equity. Here, equity is as our winning probability into the pot size and in percentage terms is the same as winning probability.

# Position

Given the need to compute a somewhat accurate guess of our equity before every decision, the position becomes one of the most important aspects of the games. AFAIK, it’s more important than the hands held by the player.

In the below hand played, the user just to our right when I was on the button, bluffed on 9, which I happened to have. By just calling his bluffs, I allowed him to barrel into the pot where I held the equity. This is a perfect example of imperfect information playing in our favour due to position.

# Hand History Example

No Limit Hold’em Rs5.00/Rs10.00
PokerStars
6 players
Formatted by pokercopilot.com: Poker HUD for Mac and Windows

Preflop: ( Rs15.00, 6 players) Hero is BTN with 9♣ K♥
UTG raises to Rs30.00, MP calls Rs30.00, 1 fold, Hero calls Rs30.00, 2 folds

Flop: 3♠ 6♣ 9♠ ( Rs105.00, 3 players — MP: Rs1,715.65, Hero: Rs950.00, UTG: Rs2,981.04)
UTG checks, MP bets Rs100.00, Hero calls Rs100.00, UTG calls Rs100.00

Turn: 7♠ ( Rs405.00, 3 players — MP: Rs1,615.65, Hero: Rs850.00, UTG: Rs2,881.04)
UTG checks, MP checks, Hero checks

River: 9♦ ( Rs405.00, 3 players — MP: Rs1,615.65, Hero: Rs850.00, UTG: Rs2,881.04)
UTG checks, MP bets Rs190.00, Hero calls Rs190.00, 1 fold

Total Pot: Rs785.00
MP shows 4♥ 6♥ (two pair, Nines and Sixes)
Hero shows 9♣ K♥ (three of a kind, Nines)

Hero wins Rs751.64

Screenshot of the play from PokerStars Desktop Client.

In conclusion, to give a sense of how important a button as a position is, this is the graph for one of the biggest losing months. Despite going on tilt and not doing well, it’s really hard to screw up performance over the button.

The graph if from Poker-CoPilot which has been a really useful HuD while playing the game. We will be getting to it as a concept some down the article.

Most important, the hands you hold along with what the board shows up Post-Flop. Especially considering the importance of position and the four rounds of betting, you need a solid strategy in terms of what hands to play Pre-Flop and which ones to continue as you go through the betting rounds.

The current school of thought is around having a range of hands that you open/call or raise depending upon your position. You may deviate depending upon opponents and their plays but having a defined pre-flop strategy helps with discipline and also incorporate aspects of GTO into the play.

The general rule of thumb is you play tight when in early positions and looser over the later ones as you have more manoeuvrability because you can alter decisions based on other’s decision making.

Create your own hand ranges based on your playing history and also read this for more details.

This is an infographic from the guys at Upswing Poker on how to adjust the ranges on the basis of the position.

# Playing Styles

• Rock/Nit: This is very rare in my experience but this is someone who plays very few hands and very aggressively. Think VPIP of ~5–10%, which means, they only play 5–10% of hands dealt.
• TAG (Tight and Aggressive): Has a broader range than a Nit, opening range could be 2–3 times that of a nit with VPIP around 10–15%.
• LAG (Loose and Aggressive): Further evolution over the TAG, the game needs to be aggressive and quite a difficult style to play. VPIP around 30%.
• Calling Station (Fish): VPIP over 40%, passive play. Very difficult to be profitable with such a broad range for a consistent period of time.

Based on the open ranging and other actions such as raise to call ratio to fold, there are broadly three 4 playing styles. To be able to classify, we need two important metrics VPIP(Voluntarily Put in Pot) and PFR (Pre-Flop Raise).

The ideal style switches between the top 3 depending upon the table. Opposite style to the table dynamics is difficult to execute but is true from experience.

# HUD (Heads Up Display )

Besides your strategy and play, HUD is a key tool everyone requires to have a positive win rate over online poker. In addition to this, the fact that other players use it makes it impossible to be able to act/ make decisions without one.

The HuD has two aspects to it, a Heads-Up Display for your poker client to be able to visualise your opponent’s play. This kind of gives you an edge when trying to decide on your opponents’ bluffing instinct. At least that’s what its been really useful for me.

In addition, the other use case for it is to use for maintaining a database of your plays and being able to track your performance over time. In conclusion, with your hand histories, understand your opponents and identifying leaks in your game, you will be able to study and improve the game.

Strongly recommended that you wanna give Poker-Copilot a try, which comes with a 30 day trial period.

Finally learn to choose one of the probable settings for HUDs here

Indeed there are a bunch of metrics used to measure and track your and other’s performance/playing styles. At this time, someone new to the game would be surprised with the gamut of metrics used to understand the game. There are over 222 features or variables available for every hand export including meta-features like player name, table etc.

• VPIP(Voluntarily Put in Pot): Most important metric of all. Single-handedly can tell a lot about one’s looseness which is strongly correlated with the game’s skills.
• PFR(Pre-Flop Raise): Gives a sense of aggressiveness, which is given for any player but too much can be a sign of too many bluffs. This combines well with VPIP to categorise the players. This is the sum of both initiated by the player and when he calls.
• Called Pre-Flop Raise: How many times we called our way into the pot and not initiated the raises.
• Unopened Pre-Flop Raise: The number of times, we were the initiators of the raise
• Flops Seen: For a session, this is an indication of how many flops were seen. Because, every time you put money into the pot, either you or others might have folded pre-flop itself.
• 3-Bet Pre-Flop: This means, this is the 3rd bet in the Pre-Flop round. First being the Blinds, second being a raise on it and then a further raise by you or others. Very strong move, when you believe you hold the strongest hands. Similarly, the other way around is when you folded to 3-bet from your opponent.

## Pre-Flop

• 4-Bet Pre-Flop: This is a further continuation of the previous metric when there is 3rd raise within the same round. 4-bet and 3-bet are useful as means to sometime defend the blinds. The opposite move is to fold to 4-bet by an opponent.
• Squeeze Bet: Quite a rare occurrence but is defined as a Pre-Flop bet wherein a player raises, another one or more call in between before being raised again.

There is an open by a big-blind followed by a raise from TheIntegrated and then a 3-bet from me ( UNNA007).

• Aggression(%): This is the percentage of times, we raised or bet over total instances of flops seen. If we bet 6 out of the 10 times, we saw the flop including calls and folds, our aggression is defined as 60%.
• Aggression Factor: Similar to the first metric but we take the ratio of raise or bet over calls. This could be used alternatively with aggression.
• Check Raised: One of the interesting plays which can happen over the flop, turn or river. Here, the Hero can check the flop, allow the opponent to raise and then re-raise them. Perfect play against an overtly aggressive player against whom, we are sure of an advantage whereas folded to Check-Raise is the opposite, where we folded against such a move.
• Continuation Bet (C-Bet): This is when a Post-Flop bet is continued with our initial raise pre-flop. Thus the name continuation bet, aggressive continuation bet can be used to barrel your opponents out of a weak or moderate hand. There are two more metrics related to it, folded to C-Bet and raised a C-Bet. The second signals a strong flop or maybe even nuts.
• Donk Bet: This is when an out of position player raises before the Pre-Flop Raise. This supposed to have a negative image and is a bit of a complicated move. You can read more here.

## Post Flop

This is where the big bucks are either made or lost. The most important round IMO given it sets up the stage for both river and turn.

# Learnings

The above are the broad categories of the different metrics which can be further broken down by turn, river. Also by whether you raised, folded or called your moves. As can be seen from above, the game has gotten fairly advanced in terms of strategies employed by players.

Most players measure their win rate in terms of BB (BigBlinds) per 100 hands and try to maintain a steady number. You can make more money by either improving the win rate or by moving over to bigger blinds/tables. Subsequently, with a similar win rate, you can leverage higher winnings. By getting a sense of your win rate over a decent sample of hands (~10,000). Grinders can often multi-table to reduce both the variance and to increase winnings.

# Machine Learning For Poker

What makes this an interesting use case for the application of machine learning is the nature of the problem. While a self-playing AI-based bot or player is out of scope. Imperfect information games are yet to be completely solved. A few attempts have been ongoing though, such as Pluribus by Facebook here.

The idea is to more of building a decision support tool to help you aid your game by identifying leaks in your decision-making process. However, the nature of the game, makes for an interesting ML use case, given the urgent and important attribute of the problem. For serious poker players, each hand is important and the time limit on making a decision, limited to 30 odd seconds, makes it urgent.

Also now add the abundance of attributes and metrics to keep track, around 220 odd and you have a complex decision theory problem at hand. Trying to analyse many variables quickly and often conflicting can be daunting and prone to errors. A separate model can use the corresponding metrics related to each round of betting, aka Pre-Flop, Flop, Turn and finally River.

# Conclusion

When tried applying for my hand history analysis, this resulted in giving some very interesting outputs. By running it for very specific use cases, players, tables or positions, a decision tree, in this case, can give some insightful and actionable output.