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# Maths of poker thread Watch

1. Presumably there is a non trivial intersection between mathematicians and poker players on these forums. Let's have a thread for discussion?

My initial input: I have been doing a bit of playing about recently. My line of thinking/working is as follows:

-Cash games are easier to analyse, since they're homogeneous in time (assuming we have linear utility functions and bottomless reserves).

-A good first step for analysis would be to investigate what type of action to take pre-flop.

-This will certainly require knowledge of the strength of hands pre-flop.

-Most 'poker maths' is in my eyes bull**** - it seems to revolve around knowledge of your opponent's hand, to then give a probability of winning. Funnily enough we don't know their hand very often in real life.

-So I thought I'd do some Monte Carlo simulation - always good. From this I have a set of tables of the probability of a given hand being the eventual winner given everyone plays the hand all the way through, for a number of players between 2 and 10.

-These tables on their own are quite useful - for example, they give you an indication of the relative strength of hands. However, in reality people tend to fold 'sub par' hands, resulting in higher realised win rates for 'good' hands.

-I wanted to implement this in my model: So, using the existing tables, I produced a new set of tables based on simulations of hands where only hands where the probability of winning based on the initial table exceeds average(win probability)-L, where L is some table 'looseness' factor (which can take either sign).

-This gives a new set of tables which perhaps can be illuminating.

-BUT: what if everyone is playing with these tables? Then I need to iterate the process once again! Or perhaps adjust the looseness. Hmm.

Glad I got that off my chest. Feel free to offer any critique, or post your own musings on this beautiful game...
2. I would post in here, but as poker is haraam and I think my mum stalks me, I'll pass.
3. I tend to not tell my openents something that allows me to have such a advantage - not much sense in doing so.
4. You could read Gus Hansen book. He's meant to be the most mathematical player.

Also, there is a book called Mathematics of poker by Bill Chern. You should download it.

But, has this got any practical applications?

(Original post by Chewwy)
-Most 'poker maths' is in my eyes bull**** - it seems to revolve around knowledge of your opponent's hand, to then give a probability of winning. Funnily enough we don't know their hand very often in real life.
I think it's more calculating EV and trying to make +EV moves
http://www.cardschat.com/poker-odds-expected-value.php

Saying that, in the book the Mathematics of Poker it says you need to play exploitative.
5. Nice thread. I've been playing for over a year now and made a decent amount. I'm not a mathmo but I recently read a few books to see what experienced poker players / poker "theorists" said about mathematics and like Simplicity said, they mainly talk about EV+ decisions, nothing too complicated. But I'm sure there's more difficult stuff which I have no clue about.

Over the past year, it seems clear that a massive portion of the game is about reads; having a good idea of what your opponent has (which develops with experience of the game and the player), what their tendencies are and what their betting patterns mean, so you can play into them. Poker is a game of partial information, so the more information you have, the better decisions you can make.

I was wondering though, if you have information about a player's betting patterns, tendencies etc. (you can get a lot of this stuff for certain players on archives), do any programs exist that work out the best course of action to take in a hand?
6. Theres hundreds of software out there that say what % of hands you beat, what range of hands you beat, what pot odds to call etc - Most require a small payment to use though.
And programmes that tell you betting patterns of your opponent (leading to ladbrokes running an anonymous table new featur)

The maths in poker is all about working out the +EV move when its your turn, obviously the majority of time that is to fold.

The working out probbility is about analyzing "ranges of hands", you saw its bull**** because you don't know what opponent has, if say you have a pair, the pot is 10k and he bets 5k, if you win 51% of the time with your pair, you call the bet. So you work out if your hand will win 51% of the times or not, based on all the knowledge you know and have.

The best book i can recommend is gus hansens aussie millions walkthrough, he analyzes every hand he played, with the odds and explains why he made the decision he did using maths. He's in my eyes the most mathematically poker player out there when it comes to it.
7. Sit and go strategy FTW. Independent chip model, hand equity and push or fold. the first steps to being a highroller
8. (Original post by n1r4v)
Over the past year, it seems clear that a massive portion of the game is about reads; having a good idea of what your opponent has (which develops with experience of the game and the player), what their tendencies are and what their betting patterns mean, so you can play into them. Poker is a game of partial information, so the more information you have, the better decisions you can make.
Not being a keen poker player, I'd imagine that the "massive portion" of the game can only apply when playing with inexperienced players offline. Since a large amount of poker is now online, and good players aren't going to be readable, to get good, presumably a better use of your time would be to understand the mathematics behind the game?
9. (Original post by SimonM)
Not being a keen poker player, I'd imagine that the "massive portion" of the game can only apply when playing with inexperienced players offline. Since a large amount of poker is now online, and good players aren't going to be readable, to get good, presumably a better use of your time would be to understand the mathematics behind the game?
The year and a bit I've been playing is purely online. I've only played twice in real life.

Reads online are massively important. Obviously, if you know more information about your opponent's hand, then you will have a (massive) advantage. The way you get 'reads' from your opponent is usually by analysing their betting patterns. After about 20-30 mins of playing someone online on low stakes, you get a decent idea of how they play and what hands they're probably on. The best online players are excellent at putting others on exact hands.

I'll give you a simple example (of how I managed to save my tournament life)

Spoiler:
Show
I had A7, I made a small raise from late position, "Rambo" called.

The flop came: 5 7 K (different suits)

Rambo made a pot sized bet. This was my first read: I knew from his previous betting patterns that he either had bottom or middle pair, a straight draw (46 / 68) or a flush draw. It would also fit the profile of hands he would call a raise with (suited connectors). I raised and he called.

The turn came: 5 7 K.... 7

So I made trips. Rambo checked, I bet a decent amount and he called.

The river came: 5 7 K 7.... 9

Rambo checked to me again. I was quite surprised at this (it was very uncharacteristic of his betting style). Because I raised him on the flop and bet him on the turn, he must have known I had some kind of a hand. I knew that he either had nothing, or had me beat (re my initial read; it would have completed his straight if he had 68). I was very tempted to value bet him but I trusted my read and gut feeling and he had...

68 of diamonds; one of the hands I had put him on at the beginning (68 + suited connector type).

There are plenty more examples but from my experiences with poker, getting reads (analysing their betting patterns / playing style) is a massive part of poker. I'm sure you can use maths to analyse such behaviour / use some program to analyse archives of data of betting patterns, but it's probably very difficult to model (though such archives were apparently exploited to bust a famous online player called isildur1).

Anyway, I think I'm rambling now; maths definitely has its place but I doubt that the average \$10/\$20 NL player has an inferior understanding of the mathematics behind poker than the best online players in the world (e.g. Tom Dwan / ziigmund). Though of course it would give you a fantastic understanding of what you're doing and an edge over other players. "Reads" certainly have a major place in online poker though.

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