Simple math you NEED to know.

I am not a math person. I cannot do simple addition in my head. Whats 18+27? I have no idea what it is and I don't care. That's the kind of math person I am. If you just look at that and "know" like I'm sure many of you can, I hate you. But I digress.

Roy Rounders in his book Poker Math Made Easy really explained much of the math of poker so incredibly well that even a complete math idiot like me finally "gets it"

Lets say you have a nut flush draw on the flop. Nine outs. (I think we can all do that math, if not just memorize flush draw = nine outs, straight draw = eight outs.) What is the chance that we'll hit our card on the turn?

Roy gives us a really really easy formula.

Take the outs, double them, and add 1. So, 9 outs x 2 = 18. Add 1 and we're at 19%. There you go, we're 19% to hit on the turn. (Actual is 19.15) Well shit, we called and missed. Now what chance do we have to hit on the river? Guess what? Its pretty much the same as the first time. 19%. It doesn't change enough to care about (actual is 19.57)

It works from 3-11 outs. At 12 or more outs you need to double and add 2. So 14 outs is (14x2) + 2 = 30% (actual 29.79 on the turn and 30.43 on the river)

Pretty simple stuff, I kind of feel stupid posting about it. But hey, I didnt know that formula and I've been playing poker for years!

I come from a LHE background where everything we do is in x:1 format, 4:1, 5:1, 8:1, etc etc. And i've had a terrible time converting that format to the percentage format we all use in our NL conversations. I just never found a good way to do that.

Well Roy Rounder points out that I'm an idiot, and that its really simple.

2:1= 1/3
5:1 = 1/6
8:1 = 1/9

You see a pattern?

2:1 = 1/3
5:1 = 1/6
8:1 = 1/9

Just add one!

So now we come to the "hardest" part. We know 8:1 is equivalent to 1/9, but whats that in percentage? Well, you could do the math, but just memorize it. Really. I think we all know 1/2 is 50%. We all know 1/3rd = 33%, and we all know 1/4th = 25%. So that takes care of that.

The next part is just some more memorization. Repeat these numbers with me. 20 16 14 12. Read em' again. Say them out loud, seriously. Say them 10 times out loud. 20 16 14 12. This is the hardest part of the whole thing, just do it. 20 16 14 12. If you dont do it I'll just type them here so you're forced to read them. 20 16 14 12. There ya go.

Guess what, now you know 1/5, 1/6, 1/7, and 1/8th.

Want to know 1/9th, 1/10th, 1/11th, and 1/12th? They'll probably never actually come up in any useful poker scenario but what the hell, theyre easy. Repeat these numbers: 11. 10. 9. 8. Hope that wasnt too hard.

Whats the whole sequence then? Can you type it out without looking? Try it. Go from 1/2 to 1/12 without looking. Hint: 20 16 14 12. It's too powerful and too easy to ignore this stuff.

You're getting 5:1 on the turn. So thats 1/6. 1/6 is 16%. (Remember 20 16 14 12?)

Here we go, as hard of an example as physically possible. If I can do it, you can do it. I have top pair with a weak kicker on the river and my villain bets $2 into a $7 pot. I think my hand is good 15% of the time against this villain. Should you call?

Pot odds are 9/2 = 4.5 so we're getting 4.5:1. Convert that over to % and thats like halfway between 1/5 and 1/6 so its halfway between 16% and 20%, call it 18%. Therefore I have to call 18% of the pot but I only think my hand is good 15% of the time. Fold!

There ya go. Thank you Roy Rounders! (20 16 14 12!)

villain bets 2 into 7 totals 9. Might want a little rewording but I know what you mean anyway....

Great post will need to reread a few times for it to stick. I like maths and still struggle with this. The hole fractions/odds/percentages conversion thing will be a lot easier due to this. Thanks!

I thought you were against this in the past? It's the 2 and 4 rule and it's been argued about ad nauseum.

I wouldn't bother adding the 1 or the 2. Basically it won't make that much difference in your decisions. Adding 2 to a calculation that has you at/over 50% anyway is never going to change your mind.

Excellent post though. Always great to bring this up once and a while for the Noobs.

Originally Posted by jyms

Excellent post though. Always great to bring this up once and a while for a refresher for the old farts too.

fyp

I think the second half is about 400% more important than the first. I know the 2/4 rule and its "ok" but I've never seen the second half of my post explained until the royrounder book.

Ok Thanks for the info, I really have to put use of this after flop, but this only works on a cold call and drawing hands? What other situation can I use it in?

This is a great post, I think I am on the verge of getting it, almost.

Can anyone point out where I dont get it?

say I have 4567 rainbow. I know my out are 8.

So , at the table, I think "8 x 2=16+1 =seventeen "

17% chance my card will come ,the same with the river,I get that.

Ive learnt 100/17 is 5.88/1.

Does this mean 1/6.88 is what Im looking at?

You see a pattern?

2:1 = 1/3
5:1 = 1/6
8:1 = 1/9

....and

Repeat these numbers with me. 20 16 14 12

so ,my above 1/6.8 is somewhere between 16 and 14. which is 15% ?

DO I still have people still with me?

So , say it cost me $5 to call , the pot needs to be $34 (6.8x $5 ) or over to make it worth my while?

Damn.

I think I dont get it at all.I seem to be moving further away.

Originally Posted by euphoricism

I have top pair with a weak kicker on the river and my villain bets $2 into a $7 pot. I think my hand is good 15% of the time against this villain. Should you call?
Pot odds are 7/2 = 3.5 so we're getting 3.5:1.

Someone said this earlier, but the pot is $9 when we have to bet $2, so the pot odds are 4.5 to 1. That fraction is between 1/5 and 1/6.

Originally Posted by euphoricism

Pot odds are 7/2 = 3.5 so we're getting 3.5:1. Convert that over to % and thats like halfway between 1/4 and 1/5 so its halfway between 25% and 20%, call it 23%.

We're getting between 20% and 16.7%, so call 18%. Still, a fold.

Originally Posted by euphoricism

There ya go. Thank you Roy Rounders! (20 16 14 12!)

It's a nice post. I like it. I agree with Jyms that we should forgetting about adding 1's and 2's. We can't typically guess villain's hands precisely, so outs can be iffy at times. The extra 1% or 2% we DON'T add in makes our calls more conservative, and more likely to be correct.

But overall, poker math doesn't have to be hard. And I like the quick-and-easy way to convert fractions to percentages. I'm a math teacher, and I will show this to some classes when we run into fraction calculations that use them. Thanks!!

Originally Posted by celtic123

say I have 4567 rainbow. I know my out are 8.

So , at the table, I think "8 x 2=16+1 =seventeen "

17% chance my card will come ,the same with the river,I get that.

Ive learnt 100/17 is 5.88/1.

Does this mean 1/6.88 is what Im looking at?

100 / 17 = 5.88, meaning you have 4.88 to 1 odds.

This is easier with simpler numbers. Say you have a 10% chance to win a hand. This means that 1 out of 10 times you'll win and 9 out of 10 times you'll lose. So the odds against winning are 9 to 1. To do the math your way:

100 / 10 = 10 , then take 1 away => 9 to 1.

Back to your example. For a $5 call, you would need the pot to be just less than $25 (4.88 x 5 = 24.40).

ok, I think I have it. ill use pen and paper with a few scenarios and see what I come up with.

Cheers.

Note that we've been ignoring *implied odds* which are very very important in NLHE.

Originally Posted by euphoricism

Note that we've been ignoring *implied odds* which are very very important in NLHE.

oh, hell, eupho, and next you'll be talking about reverse implied odds - I thought you said you weren't a math guy

implied odds have a basic assumption that you will get a hand to call your effective stack sized raise if u hit your hand. surely the trick is once you hit your hand and you have a good lock (eg trips to TPTK 95% to win assuming no other draws over two cards) to engineer the pot to allow a turn or river call to be mathematically possible to call without being "a bad call" however it is still a loosing call.

Originally Posted by Robb

Originally Posted by euphoricism

Note that we've been ignoring *implied odds* which are very very important in NLHE.

oh, hell, eupho, and next you'll be talking about reverse implied odds - I thought you said you weren't a math guy

I am *thoroughly* incapable of doing the implied odds math. I'm just aware that I *should be*. I'm really, really bad at doing math in my head.

The implied odds thing is easy.

If you're calling $10, and the pot is $30, you're getting 3:1 immediate odds. If you need 5:1 to break even, then that means you need to make 2 x $10 = $20 on a later street to break even since 5-3 = 2.

Excellent post, might need to get a little sticky...

20 16 14 12 11 10 9 8.

Seriously, this post has helped my life more than I thought. I use it more outside of poker than inside, but w/e. I still remember the sequence and use it frequently.

(shameless bump for LuckySlevin)

I do long division in my head in a split second.

1/16 = 0.0625 (half a second)

Originally Posted by iopq

I do long division in my head in a split second.

1/16 = 0.0625 (half a second)

thought half a second = 0.5

glad im not the only one bad @ math here.
this was like the v first thing i learned about poker but i still suck at it.
nice post

Originally Posted by Robb

Originally Posted by iopq

I do long division in my head in a split second.

1/16 = 0.0625 (half a second)

thought half a second = 0.5

LOL!!

Been on a couple months hiatus from poker and beginning to get the itch again. When I was actively playing I was developing an idea that is much in line with the intent of this thread - APPLIED maths.

For some reason I never grew completely comfortable with comparing pot odds with my chance of winning. What I ended up doing was turn it on its head and I inadvertently stumbled into a method that also helps with implied odds.

The basic method is most solid if you are two-way, facing a bet and trying to decide if you want to call a bet - because that closes the action.

Method:
1) Determine my outs in odds notation
2) Apply those odds to the size of the bet I need to call to determine the amount of money I will need to win for calling to be profitable

Alternately - one-liner formula:
Bet size * losing cards / winning cards = amount needed to win for calling to be profitable

Example:
1) Flush draw on the flop - 9 outs
9 card win, 38 cards lose
Odds are 38 to 9 against
Odds are 4.22 to 1 against
2) Bet is $2
$2 * 4.22 is $8.44.
(Alternately: $2 * 38 / 9 = $76 / 9 = $8.44)
If by calling I stand to win $8.44 or more then it is profitable to call.
Included in the $8.44 is the $2 bet by the opponent, which means if the pot was $6.44 before the opponent bet $2 into it - it would always be profitable to call (assuming my outs are good). This can be used directly to make an observation about drawing hands and bet sizes.
If the pot before the $2 bet was $3 then I stand to win $5 and will need my opponent to put $3.44 in the middle on later streets after I hit my flush - and the pot will be $7 - so I would need to win on average a 1/2 PSB for calling on the flop to be profitable.

The interesting thing about this method is that it tells you exactly how much money you will need to win on later streets (through the magic of implied odds) for calling on THIS street to be profitable. The tricky thing is that it is very very easy to fool yourself into thinking something is profitable when it isn't. In the above example if I hit my flush on the turn and bet a 1/2 PSB on either turn or river and get 50% folds and 50% calls - that suddenly turns my flop call into an unprofitable call. It's important to consider that what this method tells you is the average amount of money you need to WIN through bets made by your opponent that you can call or bets made by you that your opponent feels comfortable calling.

This also strongly suggests that once you have identified the average that you must win for the earlier call to be profitable you have to consider that some of the times you will get folds and the actual bet you are looking to make on a later street must be notably bigger than the average you need to win to be profitable.

When you need to assess whether you are able to extract value on a later street it is imperative that you can accurately predict how your opponent will act.

When I apply this method I keep mental track of my deficit - I remember that I'm still out $3.44 for my flop call to be profitable (if I hit), which means that I generally don't bet $4 because I know with any folds at all that makes my flop call -EV - rather I'd bet more PSB or so because even with more folds I'm trying to raise the average EV of the later-street bet to $3.44 or above to keep me overall in the black.

Only accurate reads can tell you whether you are likely to get money out of the hand on later streets, but if you need a rule of thumb I think you could probably do worse than this:
If the bet you need to win on a later street is less than a 1/4 PSB then you will almost always have implied odds that are favourable enough that you should call.
If the bet you need to win on a later street is greater than 1/2 PSB then you will almost always have implied odds that are unfavourable and you should not call. Only really strong reads and a firm belief that your outs are clean should get you into this territory.

For your winning chances the method here is very directly looking at the next street - the flop call may not complete the flush on the turn but may complete the flush on the river. The problem with the river card is that you do not know yet whether you need to pay more money to see it. The simplest thing is to assume that seeing a river card will also cost money and conservatively pretend that you need to hit on the turn to realise the win. As the maths part of this whole thing becomes natural it will be natural to work more factors into it.

Let's say you assess that there is a 50% chance that the turn will check through - if it doesn't check through you'll need to do another calculation as above to judge whether it's profitable to call - if it does check through you get a free 9 outs to improve again. To shorthand the whole thing I'd probably call it 4.5 outs extra on the flop as a chance to not improve on the turn but get a free card to try to improve on the river and redo the calculation with 12.5 outs - something like 2.9 to 1 against and $5.8, which means you'd need to win $0.8 on a later street for calling $2 on the flop to be profitable.

This basic example of modifying the method to work for the chance for a free river card highlights something key - the two basic components are odds of winning and pot odds - any factor that we want to include in the calculation needs to be expressed as either a modification of our chance to win or pot odds. For instance - if we are on a flush draw but it's not the nut flush and we think someone else might have the nut flush draw (or a better flush draw) we might discount our 9 outs down to 8. It doesn't mean that a specific card will make our flush and not make us win - but it does mean that any one of the cards that make our flush may still let us lose. In reality we will need to discount it down further than 8 - probably more like 5 - because if we do hit our card we are not playing for the money currently in the middle - we will expect that we personally go all-in and then lose which makes the outcome while still unlikely even more costly. Capturing that increased loss as less outs is strictly wrong - to get a proper result we would need to calculate multiple possible outcomes - but it's a convenient shorthand to translate any factor that we want to include into a difference in outs.

I hope this didn't get too confusing - as with the original post I think this makes for a simple way to apply the necessary maths to situations.

is this in the stickies?

Awesome stuf Erpel, but let me just see if i get this right....

Post Flop
Pot is $100
Hero is on Flush Draw - 4.11 to 1
Villain bets $50
so..
50 X 4 = 200
so if Hero stands to win $200 by calling (which he does) he should call?

Post Flop
Pot $200
Hero on OE Stre8 draw 11 to 1
Villain bets $80

80 X 11 = 880 = If Hero calls pot contains $360 so fold?

Marbleboy,

It seems you're mixing up a couple of numbers, or maybe I just wasn't clear in how I used them.

In the first example using my method I would come up with the following:
I need to pay $50 and I think my odds of winning are 4.11 to 1 against - I need to win $205.5 for calling to be profitable. $150 is already in the pot to be won, which means I need to win an additional $55.5 on later streets on average for calling to be profitable.

In the second example, using my method and your odds (not the OESD observation as that is 8 outs and your odds seem to indicate a gutshot and 4 outs) I would come up with the following:
I need to pay $80 and I think my odds of winning are 11 to 1 against - I need to win $880 for calling to be profitable. $280 is already in the pot to be won, which means I need to win an additional $600 out of the villain's stack on later streets for calling to be profitable. As an aside the pot after me calling would be $360, which suggests that to win $600 more I would need to win more than one bet.

The method came from me wanting a quick way to assess whether my villain had enough money behind for me to ever be able to have implied odds to call. If you take the amount you need to call and multiply it by the odds against you winning and the amount you would need to win is bigger than the pot and the villain stack combined - it's pretty much never a good idea to call. Everything else sort of followed from that basic observation.

Eupho's post was the best pragmatic explanation of pot odds vs hand odds that I've read. There are a lot of theory posts out there on the web but this is a great hands on tool for calculating your pot odds and hand odds and then comparing the two in a flash. The pattern is so easy between each fractions percentage as the difference between the percentages gets smaller as the fractions get smaller (obv!) - this makes the whole sequence really easy to remember.

Thanks Eupho for a great post. Also thanks Erpel for the implied odds discussion that was also really practical, a really great post - thanks guys.

bumped

Good Post.

Learn
Forget
Relearn
Remember
Forget
I think I have been here before.
Sure enough.

Thanks for the post.

Stickies for sure.

Bad Post

Read
Forget
Junk
Confusing
Useless
I think I have read this before
Sure enough.

No Thanks for your post

Nice bump though Celtic, I think there's a few newer members who can benefit from this post.

Nice post, very useful to introduce the ideas. I already knew about the odds but I didn't knew that formula for the outs. Thanks.

Wow, this stuff is so basic, I'm pretty certain people would call me a donk for posting this. No offence, I have respect for you playing good poker before, without knowing these simple formulas. I guess it usefull for people with limited mathknowledge, but come on, how can this get 5 spades?

non-mensa members itt.

Thanks for the post. Very informative. Im still working on my math.

I hope this is stickied already

Thanks for bumping it, I am a math retard. 20 16 14 12 is awesome.