Ok

I need to learn about the mathematics of poker. I am finding it impossible.

I want to know a simple way of calculating stuff. I have been given 1,000,000 different mathematical equations and methods and all sorts of crap that makes no sense, but, I have a feeling it will make sense if I can put the bits together.

Firstly, pure and simple, how do I work out a ratio on the flop?

I know that if im drawing, say I have a f/d, then I have 9 outs to make it.

So I take the amount of cards I can catch to win and divide them into the amount of cards left in the deck.

On a 6mx table in which I play, there are 10 cards dealt out to other players, 1 burnt, 2 in my hand and 3 on the flop, leaving me with 52 - 16 = 36 cards available.

To work out my ratio I divide 9 into 36 and get 4 to 1. Am I 4 to 1 against or for or what? and is the 4 to 1 statement correct?


Next when im turning my ratio into a percentage, I get confused. Ive been told so many ways to do it and wonder if one way is more accurate than another or something.

I take 4 to 1 and simply add the two numbers together then divide 100 by the number I get and that is the value of 1. So 4 to 1 is 4 + 1 = 5, then divide 100 by 5 and thats 20. So the left is 4 x 20 and the right is 1 x 20 thus = 80%.
80% of wat tho? how am i against or for or wat?

Another thing, should i be estimating my opponents range and doing these calculations for them to determine how much they will draw out in order to size my bets correctly (something im trying to grasp)

there is more but i need to refine my questions a bit first, so can i make this the official "teach telford09 maths" thread?

The easiest way to calculate the chance of hitting your outs is to use the rule of 4 and 2. On the flop, count your outs, and multiply by 4, and that's about the percentage chance you have of hitting the draw by the river. So, if you flop a flush draw you have 9 outs.

9 x 4 = 36

So you have around a 36% chance of hitting the flush by the river.

Same on the turn, except multiply by 2, so you have about an 18% chance of hitting the flush on the river. It's not exact, but it's close enough to make better decisions at the table.

If you want to work out your pot odds, you take the amount already in the pot and compare it to the amount you need to call.

For example, say you are heads up and you flop a flush draw. The pot on the flop is $100 and your opponent pushes all in for his last $50. Should you call, assuming that if you hit the flush you'll win the pot?

Pot odds = 100+50 : 50

=150:50
=3:1

So you are getting 3:1 on your money. To calculate the equity % you need, divide the right side by both sides added together and multiply by 100 (to convert to a percentage).

1 / (3+1) = 0.25

.25*100 = 25%

So you should call if you have a 25% chance of making the winning hand by the river. According to the rule of 4 and 2, you have approximately 36% chance of making the flush by the river, so this is a profitable call.

thx for taking the time to write this m8 but i still am confused.

shud i be calculating equity the same way u have, every time i make a call on the river?

or the flop or turn for that matter?

To calculate pot odds, just use a calculator at first. After a while you will know almost all of the odds for the certain bet amounts at your regular stake.

At 10nl a standard preflop play will go like this. UTG raises 3.5xbb ($.35), BTN calls 3.5xbb raise ($.35), SB/BB fold ($.15)

So on the flop the standard pot might be $.85. UTG cbets for 2/3 the pot ($.55)

To calculate the pot odds press this into the calculator : 1.4 (total pot) / .55 (amount to call) = 2.5:1

2/3 (66%) bets of the pot = 2.5 : 1 OR ~29%.

You can profitably call an OESD (8 outs) or FD (9 outs) here, if you are only taking odds into account.

still dont get it

you have to use pot odds every hand,



until you are able to make ninja moves lol

ok so if i have a flush draw on the flop i need 3 to 1 odds to call correctly?

You are on the right track - however you do not remove the burn cards or cards in the other players hands as you do not know what they are. The only cards you subtract are the ones that you know - your hole cards and what is on the board.

so if you are on the flop and want to know what are the odds of hitting your flush on the turn:
You know of the 2 cards in your hand and the 3 on the board - that is 5 known cards
Unknown cards = 52 - 5 = 47
9 cards will give you the flush
So the odds of hitting your flush on the turn are 9/47 = roughly 19%
this number is hard to use when trying to figure out pot odds etc, so you want it in terms of odds rather than a fraction
In terms of odds it is 47 - 9 : 9 which is 38 : 9 (when talking odds we look at the number of times we hit v the number of times we miss, as opposed to fractions where we talk the number of times we hit v the total number of times (which is hit + miss))
Or very roughly (and good enough at the table) about 4 : 1 to hit your flush on the next card

if someone does a 2/3 bet pot....and you have at least a 66% chance of hitting. call. i think thats right. as long as the two %s =


and if im wrong well...thats why math isnt big into my game. or im doing it not even realizing it

what exactly don't you get, how to calculate your equity, how to calculate pot odds, or how to calculate your chance of hitting a draw?

2:1 odds = 66:33. 2/3 bet pot = 2.5:1. That would mean that you have to have 20 outs to improve by the river, 20 outs = 67.5%.

how to calculate equity.


is ur equity not the same as your chances of hitting a draw?

do i make the same decision like.....

if im layed 2 to 1 on the flop with top pair, i add 2 and 1 to get 3 then divide 1 by 3 to get 33%. does this mean i need 33% equity at least to prof+ call? or is there any rules that say i shud raise here?

if im layed 2 to 1 on the flop with an O/E do i have to have 33% equity to call AAAAAAAAHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH HHHHHHHHHHHHHHHHHHHHHHH

That's what I was trying to figure - about the only game I can think of where you will be >60% to improve would be omahahahaha in which case you could call any size bet because you are a favourite.

Im not amazing with the math either, but pretty sure its 8 outs if ur on a flush draw.

I would work on your addition flush draw is 9 outs, open ended straight draw is 8

From here you can use the rule of 2 and 4.

On the flop, assuming you are behind, and you need to improve, you figuring out your equity is easy. OESD, you have 8 outs. To figure out what your equity is, and what odds you need to call, you just multiply your # of outs by 4.

4x8 = ~32% equity. So you will need ~2.2:1, to call on odds alone.

On the turn, assuming you are behind, and you need to improve, to figure out your equity you multiply your # of outs by 2.

Obviously here this is completely situational / villian dependent. Based on his stats or past are you likely ahead with TP? Do you plan on calling down with TP or are you satisfied getting it in vs. his expected range? If you are getting 2:1 on the flop (pot sized bet) and you have TP, you are typically good @ 10NL, so you can profitably move to showdown, which is encouraged at micros. Of course this is 100% situational.

repost

im in the same boat as you, a bit confused with odds (just made a post about it), but ive been reading "small stakes holdem" and figured an easier way to explain it would be
- im going to use an example someone else posted already but try to re-word the pot odds part -

say you flop a flush draw, you have 9 outs (9 cards that can make your flush)
since you have 2 more cards (the turn and river) you use the x4 method

odds:
9x4 = 36, so just remember you have around a 36% chance to hit your flush
your odds are 36%

pot odds:
now lets say the pot is 100. guy before you raises 50, so now the pot is 150
to call, you have to put in another 50 right?
so, you call (50) / the current pot + your call (150+50) = 1/4. in other words, IF you call, your call will only be 25% of the pot.
your pot odds are 25%

so to sum it up, if your odds > your pot odds, you're in a good standing to make a call. and in this case 36% > 25% so you would call

there's more stuff in this book too about implied odds and reverse implied odds but im still learning so i cant really help you there

Correct, and essential to understand.

Basic example. I shuffle the cards, pick the first card off the top, and turn it up. What are the chances it's a heart? 1/4 (also expressed as 3 to 1 against). That's because there are 4 suits in equal proportion. Okay, simple.

Same example. Shuffle the full deck. I burn two cards, then turn up the next card. What are the chances that next card is a heart? Same solution. We have no info about the burn cards, so they have no effect on our probability calculation. The same would be true if we dealt out a bunch of cards to other players, burned them, or threw them out the window. Any given unknown card has a 1/4 chance to be a heart.

Any cards which have not been exposed for your eyes to see must be regarded as "unseen" (hence part of the theoretical "deck" of cards that you're drawing from), unless you have some logical way to deduce what those "unseen" cards may be.

One possible example of deducing what the unseen cards are would be if the flop came 227 with two clubs. If a whole lot of players saw the flop, one player made a pot size bet and then *several* players called before you, you *might* conclude that there are other players with clubs in their hands, so your flush draw will be less likely to come in, and less likely to win if it does come in but you don't have the nuts.

There are 13 cards of a particular suit. A "flush draw" implies you've seen 4 of your suit (in hand and on board). 13-4 = 9 unseen cards which would complete your flush. 9 outs on a flush draw.

--------------------------------------------------------

P.S. Note that "the rule of 2 and 4" is a handy little trick to help figure an *approximate* probability of hitting a draw... but it's not a clear explanation of the math behind the calculations for someone who is struggling to understand the basics.

The BASIC fact is that a player with 9 outs and 47 unseen cards has a 9/47 chance to hit their flush on the next card.

IF they miss that, but they have one more card to draw (river), then they have a 9/46 chance to hit the flush on that card.

To figure the chances that they'll hit the flush with two cards to come (you've got a draw on the flop), you actually have to calculate the odds of NOT hitting on the turn or river, and subtract that from one. That's 1 - (38/47 * 37/46).

Doing this kind of calculation on the spot is not practical, which is why players typically remember the odds for the most common situation, or use good approximations to help their memory, like the rule of 2 and 4 mentioned above.

150/50 = pot odds of 3:1 (you need at least 25% equity in the pot to continue)

haha oops, guess I was wrong there, it is 9 outs.

The above is wrong. If someone bets 200 into a 300 pot, there's 500 out there for you to win. You're considering a call of 200, so getting 5/2 odds. You must win 2 times for every 5 times you lose to make the call good... so 2/7 = 29% is a good enough chance to call.

Note that, unless the opponent bets MORE than the pot, he is ALWAYS laying you at least 2 to 1 odds, so you can not lay down any hand that's better than 1/3 to win! And even if the opponent bet a million dollars into a pot of ZERO, you're getting 1 to 1 odds on your call, so you can NEVER fold a draw that's better than 50% to hit. *(see note at bottom)

There's be a lot of misinformation in this thread, including the claim there are 8. Then there's this somewhat confusing explanation, which however did arrive at a correct estimate of the odds needed to call.

This was expressed in a strange way. If the pot is 100, the opponent bets 50, then the caller is getting 150 for his 50 call, so he's getting 3 to 1.

Going a step further, yeah, if the odds the pot offers are 3 to 1 then you must win 1 time out of 4 to break even. Why? Well, when the odds are 3 to 1 against you, clearly if you played 4 times, won $3 once, and lost $1 three times, that would break even. Add 3 losing trials to 1 winning trial, that makes 4 trials total, and you must win 1. That could also be expressed as 1/4 = 25%.

So the answer given "25%" represents how good your odds of winning must be to make a call good, getting 3 to 1 pot odds. It becomes confusing (to me at least) to express this as "25% pot odds," or to imply that the player is aiming to win a 200 chip pot, since that includes his own money.

Then again, anyone their own conceptual model to understand it, if it helps them arrive at the right answer.

*note: When I said you can NEVER fold a draw that's better than 50% to hit, or never fold a 33% shot getting 2 to 1, this does NOT consider situations on an early betting round where you face possible future betting on another round... that is, you might know on the flop that you're getting 2 to 1 from the pot, and you're better than 1/3 to win by the river... but if your opponent can bet enough on the turn to prevent you from seeing the river, then you do not have an automatic calling situation. That's especially true if you don't expect to get paid anything more after hitting your draw (no implied odds if you obviously hit).

Right this is what I have grasped so far...........

To work out my pot odds I take the amount in the pot and divide what I need to call into that.

so .... pot is $1, they bet $.50 so total is $1.50, i need to call $.50 so my effective pot odds are 3 to 1.

True or False?

If in any given situation I dont have the correct pot odds to call profitably, I must be able to extract the money I am losing by calling and missing, when I actually make my hand.

True or False?

In any given situation, if I can estimate the % my opponent folding and I can add this to my hand equity to form my overall equity when betting a draw.

True or False?

Any help appreciated

thx