It had to happen. In many ways it was a miracle I'd avoided them for so long. Ten months of serious poker without once thinking about the bet niore, numbers. Ten months without doing a single mathematical calculation. How had I achieved this? Why, by ignoring such delicacies as pot odds, or, any kind of odds at all, it was a miracle I was making a profit at the tables.
But I knew they - the numbers, those evil things I never understood - were waiting for me. They lurked as sure as J-4 is known as "full employment" (because, if you play the hand you'll always have a day job).
Although I had tried to convince myself that poker was as much an art form as it is a science - something that could be felt and played intuitively, rather than with cold science as one's right hand man - the evidence was starting to suggest that embracing the numerical world inside poker might be a wise thing to do. The numbers knew this and just sat there, waiting. They, those imponderables I had seen me gain an O level, knew that intuition will only take you so far.
In my case, the physical evidence was impressive, I'd made a profit online without going broke, or even getting anywhere a situation where I may flatten my roll. However, ignoring the math (I knew) would only take me so far. Poker without maths is like bacon without eggs, salt without pepper, Fred without Ginger.
I buried my head inside books, spoke to knowledgeable friends of mine. Then I understood how far I could go (or not) by ignoring my numerical friends.
A friend said to me "Your basic understanding of the game is ok but, your bets a disproportionate to the pot. Sometimes this is a good thing, because you confuse the opposition, but after a while experienced players will recognise that you haven't the first idea about pot odds.
So to pot odds. To the world of percentages and rapid calculations. To a world I don't think I'm ever going to understand. I learn that pot odds is the relationship between the size of the pot and the size of a bet. If there is $10 in the pot and $2 is required to call, then the pot odds are 5/1.
This means obviously I stand to win $10 for a $2 stake. Easy?
Now for the illumination. The books tell me that the pot odds the more value you are getting for your call. I realised while reading this that I already knew all this to a degree, it was something that had been intuitively absorbed. Then I went on to read that pot odds are only half the story and that I needed to know my hand odds. What? This is the statistical likelihood of making my hand. To do this I read an example that if I had an up and down straight draw post flop then I needed to divide the 39 cards that wont complete my straight by the number (8) that will.
That figure is a little under 5, which means that every time you play the hand you will make that hand only once from five hands on average. So, if the pot is offering better odds than of you hitting the card or cards you need to complete your hand then you "call". If th pot is offering less, you dont. The more you make the right decision based on the math you will (long term) be making profit in these situations.
I have a decent grasp of math in the real world but how do people expect me to do these kind of calculations on every street whilst playing online to a strict and very short clock.
Then, my angel from above came down to me in the form of a post on an online forum about poker odds. In this post, the guy explained "the easy way" to do that math. Forget dividing X by Y and follow a simple rule of what (apparently) is knowN as the "4 and 2" rule.
If you have a situation like the one above (up and down straight draw, post flop) all you need to do is multiply the 8 "outs" by 4 post flop and by 2 post turn. So post flop 4x8= 32, 32 is roughly the percentage of the time you will complete the hand after seeing both the turn and river. Or in other words 1 in 3. Post turn you do the same calculation but multiply your "outs" by only 2. 8x2=16. You are roughly going to complete your hand around 16% of the time.
Ever since I read, "and had time to digest my newly given poker tools" I didn't play every hand to mathematical perfection but I did see a rise in my bankroll. That little bit of mathematical knowledge did go a long way. But then I started reading about implied odds and quickly became depressed again.
Art or mathematical science, it seems that there' no evading the numbers in poker.
Do the math!
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5 comments:
Harrington's book on Strategy for No Limit Poker Vol. I explains very well the Pot Odds from a layman's point of view. It is 4x or 2x, but then to get more accurate figure for the odds he gives you Soloman's Formula. It is worth reading.
Ahhh! The MATH! Well buddy, as a Math teacher, I can tell you one thing: Math is nothing and is everything. Easy right?
1)EVERYTHING: You're in the BB (at 4000) and checked to see a flop with 98s. Only SB called and the flop comes JsTs2c and SB goes allin for his last 30000 (makes the pot 40000 with the blinds and antes). Now, you have a flush draw and openended str8 flush draw to booth...gives you 15 outs. So you do your little 4x thing and figure you're actually 60-40 (3 to 2) favorite here! Since it costs you 30000 to win 40000, you're getting 1.33 to 1 pot odds. Auto call right? 3 out of 5 times you'll win 40000 and 2 out of 5 times you'll lose 30000. So you call of course, right?
2)NOTHING: But wait, 3 to 2 really? The 4x thing is nice to have an idea, but, the real odds here are 54-46, not 60-40. And, you blindly count any spade as an out...is that correct? Are you drawing to the nut flush? No. What about the str8 cards? Could he be making this move with AK? what if the Q hits? Is the Q really an out? Lets use the worse possible outcome...he shoved with AsKs...how many outs have you got now? 4 outs! Count'hem...4!!! That puts you at 17-83...oops! So where are you at...really? And remember that since he's allin, there are no implied odds here. So, do you call or not?
The point here is this: be careful with MATH...if you rely only on outs that give you the nuts, you'll never make a blunder. But then again, you'll play too tight. So you could count outs that don't give you the nuts as 0.5 outs...So in the previous example, 4 outs for the nuts, 11 other outs...gives you 9.5 outs...which puts you at 37-63...Basically, i would consider this situation as a 50-50 thing. So then, Math doesnt matter at that point...it's all about how the guy played, your stack, your position in the tourney, bla bla bla..
One final thing. As if you're not depressed enough about the whole math business. careful with implied odds...this is an imperfect science. If a guy bets the pot and you have the nut flush draw which doesn't quite give you the right odds to call...you figure that implied odds give you the reason to call. Really? Don't you think he'll slow down if the flush does hit? In some clear flush or str8 drawin boards, it's better to either fold or raise there...but callin not quite having the odds is a bad EV play most of the time.
Final thought: and this goes for everyone...if you havent read all 3 of Harrington's books...DO IT NOW!
Well anyhow...I suck so, don't rely on what I said too much lol
Hi guys, great replies.
Very informative Franky, I love your depth on this subject.
I just threw this in there for a reference to not ignoring the math.
I know all you guys obv know the math but I just wanted to throw something up here as a quick read and got a bit carried away,lol.
Toally agree on both posts about the Harrington books. Ive got em all and love them too.
The thing is I think you missunderstood what I was saying in the post.
I agree you are likely to NOT have so many outs as you think in some situations.
I posted this as a quick guide to anyone who has problems running the math quickly as you only have a short time limit online.
This 4 and 2 calculation is a guide to calculating your chances of completing the hand you are looking for, and not the chances of taking down the pot.
But thanks again for the reply.
Very well explained and totally right in what I call ghost out cards.
The problem with the 4x 2x "rule" is that the 4x is based on your staying in the hand for BOTH the turn and the river, and does not allow for someone making a huge bet after the turn which forces you to fold. In otherwords, it gives you a false starting point for calculating the pot odds.
As far as calculating pot odds & EV is concerned, 2x is much more accruate as it is your chance of hitting on the next card and will save you making a call for the wrong reasons.
The 4x can really only be used if calling all in after the flop with no possibility of further betting after the turn and river.
As for Soloman's Formula, pass the calculator...!
While we're on Math...here's a fun thing I question my students about...
Follow, step by step:
0=0
Good so far?
0=(1-1)
Still good?
0=(1-1)+(1-1)+(1-1)+(1-1)+.....
No problem yet?
0=1-1+1-1+1-1+1-1+....
Hang in there
0=1+-1+1+-1+1+-1+1+-1+....
here's the twist
0=1+(-1+1)+(-1+1)+(-1+1)+.....
which means
0=1+0+0+0....
so
0=1 right?
Silly but funny!
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