Math Wiz
Posted by Bill @ 12:51 amHank quotes Abdul and then makes the following comment:
It takes a while to be comfortable calculating odds and outs at the table, but rules of thumb are easy to remember. The above rules allow you to play your draws confidently and profitably. Note that you can profitably call with gutshot draws on the flop in many circustances, which goes against conventional poker wisdom (”and son, never draw to an inside straight”). Of course, your implied odds have to be better than 11:1 unless you have other outs.
I thought it noteworthy because I remember watching a female pro (who I can’t for the life of me remember her name) who said (caution, liberal paraphrasing to follow): “I can’t do all that complicated math in my head. If there’s a lot of money in the pot and I have good cards, I call.”
What works for me may not work for everyone but I’ve always used the following method:
X = number of outs
Y = Unseen cards
Y-X/X = Odds
So let’s say you flop a flush draw.
47 (unseen cards 52 - 3 on the flop and two in your hand) - 9 outs (there are 13 suited cards in a deck, you have two and the board has two which leaves 9) / 9 = 4.2
Some charts list it as 4.1 and if you use the formula of 2x the number of outs to give you a percentage (18%), that’s a little more than to 4.2:1. Bottom line is that if you can quickly do the math in your head; 47 minus 9 is 38 [sorry earlier typo corrected] and 9 goes into 38 approx. four times. You don’t have to be dead on. If it’s 8 outs and you calculate 47 - 8 = 39, 8 goes into 40, 5 times so 8 goes into 39 slightly less than 5 times (4.875 to be exact) but 5:1 is close enough to be a good guideline.
Contrary to popular belief, the vast majority of the time you don’t need to do complicated math at the table. Mostly, it’s rules of thumb.
For a flush or OESD (or Belly Buster) figure 4 or 5 : 1
If you have two pair and you’re trying to make a full house, you have 11:1 odds.
If you have a small pocket pair that you played hoping to flop a set and missed, you need 22:1 odds to call the flop (assuming a full table). Think about that for a moment.
You can figure out the rest of the common scenarios you find might yourself in but the message is that if you figure out the basic odds for a few key situations, you can ballpark everything else. For instance, if you know that 9 outs (a flush draw) is 4:1 odds, you know that you need about 5:1 odds to call 8 outs.
[Update] Wow, I was completely spacing when I wrote the original and some of the numbers/math were off. That’s been corrected.
[Update 2] Richard Brodie points out that the above mentioned poker pro quote is from Maureen Feduniak.
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COMMENTS / 14 COMMENTS
BadBlood added these pithy words on Mar 21 05 at 5:28 am*cough* “47 minus 9 is 36″ *cough* May want to check that one
Good post Bill. I think where most people end up getting more confused is calculating odds of an event happening before the river with 2 cards to come.Taking the flush draw example, the odds of making your flush by the river is (1 - odds of not making flush).
1 - (38/47)*(37/46)
I know you know all this, just a primer for the readers
StudioGlyphic added these pithy words on Mar 21 05 at 9:28 amIs there a compelling reason for someone to calculate the odds of making their hand on the turn or river? The only thing I can think of is where the other guy is all in, and his stack is slightly smaller than the pot.
dmmikkel added these pithy words on Mar 21 05 at 10:18 amIs it the old woman from WPT season 1 party poker million?
Richard Brodie added these pithy words on Mar 21 05 at 3:27 pmThe quote is from Maureen Feduniak.
QL
Bill Rini added these pithy words on Mar 21 05 at 5:06 pmBB,
In keeping with the rule of thumb theme, just divide by two. If you’re on a flush draw and plan on going to the river, your 4.1:1 odds are now approx. 2:1 (1.9:1 is the more exact answer).
Again, the whole idea is to make this simple to do in your head. I don’t think anybody is going to make or break their bankroll on the difference between 2 and 1.9. What you’re looking for is some quick math you can do on the spot. So you might say “Well, I’ve got 9 outs, minus 47 remaining cards, divided by 9, is about 4:1. I plan on going to the river so that’s more like 2:1.” That puts you into the ballpark with very little mental work.
Bill
Bill Rini added these pithy words on Mar 21 05 at 5:50 pmStudioGlyphic,
Let’s pretend that everybody doesn’t play NL
You often need to know the odds in NL so you can destroy somebody’s odds of drawing. Let’s say you and your opponent are deep stacked, you flop top pair with top kicker but there’s two suited cards. You want to destroy the pot odds for anybody who’s thinking about trying to draw out cheap. Let’s say you bet $10 and get a caller. Both blinds fold so there’s $25 in the pot ($2/$3 blinds). A pot sized bet makes it $50 in the pot and it costs $25 to call which offers your opponent 2:1 odds (ignoring implied odds) which is insufficient to draw to a flush. Now, he may still chase after his flush but he’s not getting the proper odds to do so (again, implied odds aren’t being considered here). Though you might eventually lose the hand you should make every attempt to punish him on the turn by making the odds inappropriate for his draw on the turn as well. It’s poker so he could spike his miracle card on the river but if that guy routinely chases 4:1 draws while only getting 2:1 pot odds, he’s eventually going to go broke. Unfortunately he may go broke long after he’s busted you
One of the biggest mistakes I see in newish NL players is not understanding how to use your betting to control the pot odds you’re offering someone. You’ll see somebody open for $10 in $100 buy in NL and get 4 callers (yes, at Commerce this happens as you well know) and they flop top pair, top kicker and they throw out a $10 bet. Well, that’s 6:1 odds you’re offering the next player (the odds get even better for each subsequent player). What hand isn’t worth drawing for at 6:1 odds? Say everybody calls, the last guy is getting 10:1 odds!!! You’re just begging someone to draw out on you. In fact, you’re not just begging them, you’re sending them a formal invitation by offering them such amazing pot odds that they can almost justify calling with any two overcards.Bill
StudioGlyphic added these pithy words on Mar 22 05 at 10:45 amMmm… let me clarify using an analogy.
I have 9 outs for a flush. It’s about 4:1 to get my flush on the turn, but it’s 2:1 to get my flush on the turn or river.So do I care about the latter number in situations where I’m not against 2 or more opponents who are all in (pot being significantly smaller) and I’m drawing to the nuts, or where the pot and the other guy’s all-in gives me 2:1?
Bill Rini added these pithy words on Mar 22 05 at 11:20 amHey StudioGlyphic,
Actually, your clarification confused me even more
Bill
StudioGlyphic added these pithy words on Mar 22 05 at 11:52 pmHeh.
Basically, how useful is it to know the necessary pot odds when you have n outs twice? since you usually have to call a bet on the turn as well as the flop, it seems like unnecessary info unless someone’s all in.
Bill Rini added these pithy words on Mar 23 05 at 6:48 amHey StudioGlyphic,
Let’s make the following assumptions:
1. Not everybody plays NL so the value of knowing your outs on the turn and the river has some value to limit players.
2. Not every hand in NL is an all-in push (despite what you’ve seen at Commerce ). Often you’ll need to know how much you need to bet to discourage a call if your opponent has the hand you think he does. Let’s say, for instance, that two suited cards hit on the flop and you’re afraid that your opponent may try drawing for a flush. You put out a pot size bet and then he comes all in for considerably more than your bet. Now you’ve really got to reconsider whether or not you had the right read on your opponent. You can get away from the hand a little more cheaply if you think he hit a set or was slow playing aces.
3. As was mentioned in the follow up to BadBlood’s comment, divide by two and now you have your approx. odds on the turn AND the river.
So given the above, I think there’s plenty of reasons to know your odds on both the turn and the river. True, in many other cases you’re only concerned with what your odds are all the way to the river but I, personally, think it’s better to know how to calculate your odds to the next card and then being able to derive your odds to the river from that.
Bottom line though is that I, personally, have the odds pretty much memorized. This post was about quick rule of thumb type calculations at the table as was referenced by quoting Hank’s post on rules of thumb. There are more than a few ways to do these calculations.
You can do them (and be more accurate) using the formula BadBlood put out there (i.e. 1 - (38/47)*(37/46)) but I think that’s too complicated for most people (i.e. the mathematically challenged) to do at the table.
You can use the old 2/4 X the number of outs to get a percentage that you then have to convert into odds which is one more step than what I’ve suggested.
You can memorize them but that takes time to learn.
This seems to be, for me, the most simple way to always have access to your odds of making your hand. If you look at most beginning poker books either they provide you with a chart to memorize or they provide a much more complex mathematical calculation which I believe is a roadblock for many newer players trying to learn how to calculate whether or not a call is correct.
So the answer you seek, StudioGlyphic, is that it’s often less useful to know your odds to make your next card in many NL situations but it’s not completely irrelevent either.
Bill
StudioGlyphic added these pithy words on Mar 23 05 at 7:18 pmI think we may still be misunderstanding one another.
I absolutely agree that you must know the odds of making your hand with one card to come, whether it’s on the turn or river. Esp. in limit, but it has its uses in no limit, as well. In live NLHE games you’ll frequently see someone underbet the pot and several callers. You could have as few as 5 outs and still make the right decision by calling.
But I never understood why I’d need to know the odds of making my hand on the turn OR river in limit, since the fact that you have to call a bet on the flop and another bet on the turn makes these calculations difficult. It seems that most pots that will become large enough to chase hands over two cards should be large enough to chase hands one card at a time. Also, as we all know, if our draw is *that* good, we should be increasing our pot equity and/or giving ourselves a shot at a free card by raising.
I guess ultimately what I’m saying is that someone may get confused by the whole “divide by two” thing when trying to figure out whether to call or not with 4 outs and a 5SB pot on the flop.
Bill Rini added these pithy words on Mar 24 05 at 9:55 amUm, StudioGlyphic, I think we agree . . . or maybe not
The one example I can think of off the top of my head is where you don’t have the correct pot odds to call one off but you have the correct *implied* odds if you make your hand on the turn or river.But, in general, I tend to agree. My natural instinct is to look at it one card at a time. Most of the time, if I find myself thinking about the odds of making the hand on the turn OR the river, I’m trying to convince myself to make a call I shouldn’t be making
Bill
Travis added these pithy words on Mar 25 05 at 1:30 pmHi
Nice site. I’m new to the poker blog scene but not new to poker.
I’m essentially playing for a living right now and this year my goal is to meet a great deal of poker players to make new friends and learn from them. I’m trying to create a little community and learn more about the different players who blog. I’d love to get more traffic on my site. If you like my site, would you mind linking to it? Also, I hope you don’t mind but I linked to yours so I can read it frequently.
Travis
ben added these pithy words on Jun 24 05 at 8:10 pmcan u help me calculate the following probabilities/odds — everyone keeps giving me different figures!I am planning a lotto draw for charity. To make it simple , I plan to involve only 1/2/3/4/5/6/7/8/9/0 ;no repeat set ; must be in correct order of draw — ie 3/6 is different from 6/3
The house will draw 5 sets of 2 numbers — eg 1/2 3/6 2/0 /4/9 6/6 9/8
Players must choose 5 sets of numbers —-
What are odds and probability that out of the 5 sets of number chosen, the player will get
1 out of 5 drawn by the house ( 1 in ?????)
2 ” ” ” ”
3 ” ” ” ”
4 ” ” ” ”
5 ” ” ” ”
Pse revert ; thks
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