Math question

[SeanC]

Hey,

What's the mathematical method for determining flop probabilities (such as flopping a pair, draws, undercards to an overpair, etc.)?

Thanks.

[RobNottsUk]

You can use basic probability (like outs over 3 cards extending 2 card to come flop to river calcs), for rough calculations. But if you want to be cuter about it, then combinatorics are best.

c(50,3) = 50! / ((50-3)! * 3!) is the number of flop with 2 known hole cards. The number of subset combinations meeting your criteria over your total possibilities gives you the exact probability.

There's a number of books covering the sort of Poker Maths now, I have "Science of Poker" by Mahmoud. I think one of the best ones, has been produced by 2+2 forum users; though I've only skimmed it in a bookshop not read it properly yet.

[SeanC]

[ QUOTE ]
You can use basic probability (like outs over 3 cards extending 2 card to come flop to river calcs), for rough calculations. But if you want to be cuter about it, then combinatorics are best.

c(50,3) = 50! / ((50-3)! * 3!) is the number of flop with 2 known hole cards. The number of subset combinations meeting your criteria over your total possibilities gives you the exact probability.

There's a number of books covering the sort of Poker Maths now, I have "Science of Poker" by Mahmoud. I think one of the best ones, has been produced by 2+2 forum users; though I've only skimmed it in a bookshop not read it properly yet.

[/ QUOTE ]

Thanks. Could you give an explanation for dummies on how that equation works? [img]/images/graemlins/smile.gif[/img] I don't know [censored] about combinatorics, so I'm going to have to do some Googling.

[RobNottsUk]

Say you have AK, then there's 2x3 ways of flopping tptk or better, with 49x48 other hand combos possible in the other 2 cards. It's easier because you don't care about order the cards appear, just the 'sets' which meet your criteria out of the total probabilites.

I really think that book I mentioned, has the stuff in it, at the level you're trying to work out, and it's not an expensive one...

[SeanC]

[ QUOTE ]
Say you have AK, then there's 2x3 ways of flopping tptk or better, with 49x48 other hand combos possible in the other 2 cards. It's easier because you don't care about order the cards appear, just the 'sets' which meet your criteria out of the total probabilites.

I really think that book I mentioned, has the stuff in it, at the level you're trying to work out, and it's not an expensive one...

[/ QUOTE ]

I see. I'm going to look over some open, online college courses on combinatorics, which will help.

Unfortunately the book you recommend has some pretty terrible reviews:

http://www.amazon.com/Science-Poker-Dr-M...6750&sr=8-1

I'd have to look through it myself before buying, as I know I can simply get the math information online.

[RobNottsUk]

Rolf Slotboom's review on his site is reasonably fair. The main fault IMO is the lack of explanation of 'reverse implied odds' and over emphasis on 'pot equity' simulations. The writing is mostly technical, concise and precise, and to the point and some concepts are brilliantly explained (ie. implied odds winning zone).

Do you want a non-flowery educated explanation of the maths you're asking about with worked out examples, or are you looking for a general poker book to improve your play?

Most players just aren't very interested in grubby 'details', and whilst Jerod's book is highly regarded, I couldn't see this stuff explained flicking through it in bookstore; as noone has suggested "Maths of Poker" I'm guessing it's not covered in detail, with space taken up by more advanced concepts.

So reviews or not, it's the best I've seen for covering this though "Killer Poker Maths" may be more palatable and may cover it, I have not studied that book.

There's some threads in the Omaha8 section of forum, covering probability using combinatoric, and one question asking about liklihood of holding AAnn with some debate on a common approximation technique for multiple opponents.

[Gabethebabe]

if you have Excel, you can make a spreadsheet with which you can make lotsa calculations.
Construct it like this:
Cell H2: No of cards in the deck
Cell H3: No of outs remaining in the deck
Cell H4: No of card that remain to draw
Cell H5: No of outs you want to draw
Cell H6: Chance that you draw these outs.

Paste into cell H6 the following formula:

=FACT(H2-H4)*FACT(H3)*FACT(H2-H3)*FACT(H4)/FACT(H2)/FACT(H3-H5)/FACT(H2-H3-H4+H5)/FACT(H5)/FACT(H4-H5)

Nou you can make calculations.
For example. I have KK and my opponent has a weak ace. What is the chance that he flops one ace?

Cell H2: No of cards in the deck = 48 (52-4 hole cards)
Cell H3: No of outs remaining in the deck = 3 (3 aces)
Cell H4: No of card that remain to draw = 3 (the flop)
Cell H5: No of outs you want to draw = 1

And out flops the answer.

[SeanC]

[ QUOTE ]
Rolf Slotboom's review on his site is reasonably fair. The main fault IMO is the lack of explanation of 'reverse implied odds' and over emphasis on 'pot equity' simulations. The writing is mostly technical, concise and precise, and to the point and some concepts are brilliantly explained (ie. implied odds winning zone).

Do you want a non-flowery educated explanation of the maths you're asking about with worked out examples, or are you looking for a general poker book to improve your play?

Most players just aren't very interested in grubby 'details', and whilst Jerod's book is highly regarded, I couldn't see this stuff explained flicking through it in bookstore; as noone has suggested "Maths of Poker" I'm guessing it's not covered in detail, with space taken up by more advanced concepts.

So reviews or not, it's the best I've seen for covering this though "Killer Poker Maths" may be more palatable and may cover it, I have not studied that book.

There's some threads in the Omaha8 section of forum, covering probability using combinatoric, and one question asking about liklihood of holding AAnn with some debate on a common approximation technique for multiple opponents.

[/ QUOTE ]

I actually do want the gritty details, and this Mathematics of Poker book looks very promising. I'm having to brush up on my calc, but I think this will answer a lot of my questions...

Thanks for the reply, though.

[SeanC]

[ QUOTE ]
if you have Excel, you can make a spreadsheet with which you can make lotsa calculations.
Construct it like this:
Cell H2: No of cards in the deck
Cell H3: No of outs remaining in the deck
Cell H4: No of card that remain to draw
Cell H5: No of outs you want to draw
Cell H6: Chance that you draw these outs.

Paste into cell H6 the following formula:

=FACT(H2-H4)*FACT(H3)*FACT(H2-H3)*FACT(H4)/FACT(H2)/FACT(H3-H5)/FACT(H2-H3-H4+H5)/FACT(H5)/FACT(H4-H5)

Nou you can make calculations.
For example. I have KK and my opponent has a weak ace. What is the chance that he flops one ace?

Cell H2: No of cards in the deck = 48 (52-4 hole cards)
Cell H3: No of outs remaining in the deck = 3 (3 aces)
Cell H4: No of card that remain to draw = 3 (the flop)
Cell H5: No of outs you want to draw = 1

And out flops the answer.

[/ QUOTE ]

Awesome, thanks!

[Flip-Flop]

I wouldn`t bother with MoP yet if I were you, you not gonna understand anything.
You need to learn the basics first and the cheapest and fastest way is to read some of the Wikipedia articles, everything is there and well explained, start the search with probability in general then poker probability etc etc.