Posted Mon Aug 25, 2003 9:51 am GMT by kluCAR
If you get dealt pocket pair, what are the odds of catchin at least one of your card and therefore hitting a set or even 4 of a kind?
Is it 1 - 48/50 * 47/49 * 46/48 * 45/47* 44/46 = 0.19? My friends are disagreeing and I want to prove them wrong? Can someone back me up on that? Thanks
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Posted Mon Aug 25, 2003 10:03 am GMT by Dave B
You are right. An easier way to calcuate in your head during a game is 2 cards will give you the set out of 50 remaining. 2/50 is 4% times 5 chances or 20%. You are calculating the odds of catching one each round. The odds of catching one at all preflop is 20%.
Posted Mon Aug 25, 2003 2:02 pm GMT by Adam Marshall
Dave B, that's not quite right as it doesn't take into account the increased chance of hitting your set as cards are dealt (20% preflop is absolutely wrong). klu is right. Since the language is "getting a set or better", you figure out the chance of NOT hitting anything, thus the 1 - (....). It would end up, like Mr. Car said, as...
1 - ( 48/50 )( 47/49 )( 46/48 )( 45/47 )( 44/46 )
Go to maybe 8 decimal places and it comes out to...
1 - .80816326 = .19183674
So ya, about 19%. Almost the same as the chance of finishing a four flush on the turn.
I think Dave's solution is good "at the table" for a quick guesstimate. Since this is one of those questions that is figured out ahead of time, it's good to have kluCar's exact figure. Plus in a home game it's fun to say, "You shouldn't play those low pocket pairs, you only have around a 19.183674% chance of hitting it."
Tell your friends that and they won't question your poker-fu anymore. 
Posted Mon Aug 25, 2003 3:06 pm GMT by Dave B
I think that I am right. Preflop the odds are 20%. 2/50 X 5 chances. The fact that the cards are dealt one at a time does not decrease the likelihood of drawing one of two cards in any one of 5 positions before the flop has occurred.
The odds do not change until the cards are actually revealed. Preflop-20%.
Posted Mon Aug 25, 2003 3:20 pm GMT by Carson Cashman
Well, technically, you don't have five chances at 2/50. The first card of the flop that comes, you have a 2/50 chance of getting your set. There are 50 cards left in the deck, two of which work for you.
Then, the second card of the flop, you have a 2/49 chance of getting your card. This is because there are only 49 cards in the deck now, and so on. As each additional card comes out, your chances of hitting it are slightly improved.
This makes a little more sense if you exagerrate it abit... Lets imagine Texas hold'em is played with 20 cards on the board instead of 5. Imagine you're on a flush draw for hearts. The first 5 cards contain 2 hearts and 3 spades. Then next 5 are all diamonds. The next 5 are all clubs.
Now, there are five more cards coming... Your chances of hitting a spade in these next five cards is much higher than it was on the first five, because now you're looking at 9 hearts left in a deck of 35 cards, versus 9 hearts left in a deck of 9 hearts out of a deck of 50 cards when those first five cards came out.
I hope that example helps. When you're only talking 5 cards on board in a game of hold'em, it doesn't change the odds that much, but it does change them slightly. Long story short, if you miss your outs on the flop and turn, you have a slightly higher chance of hitting on of them on the river, albeit this slight increase in odds in negligable at best. (I don't want to see any of you calling down your gut-shot to the river, thinking the odds are really getting better for you!)
Posted Tue Aug 26, 2003 5:14 pm GMT by Geno
I think some1, and I'm looking at Adam mainly here, should write a nice little program for calculating odds of various situations pre and post flop. Once it's all nicely in place, there should be a section added to include monetary values which would not change the odds but would change the decision....
To explain:
Let's say we use the odds generator to calculate the odds of a flush after being dealt two clubs with 2 more on the flop, turn and river still to come. Odds are just under 20% in real terms. However, the decision on whether to play or not is clearly not based solely on this 1 in 5 shot but on the amount of money it will cost to see those all important next 2 cards. If the call would be 1% of ur stack, the decision is quite different to if it were 15% or 75% of ur stack. This could be incorporated somehow into the proggy which could then spit out either revised odds or a suggestion of how to play the hand.
Obviously, once money enters the equation, the answer becomes very subjective as different players play the same hand very differently even tho the odds are always the same. Also, if the call would be 1% of ur stack with a 5 to 1 shot on, most people will see that as a fair chance and will bet whereas at 15% of ur stack they may not. Worse still, if the call would be perhaps 75% of ur stack and u were short stacked and badly in need of a double thru, a lot of people would re-raise all-in......
Fair enuff, the more I think about it, the more difficult it gets to write as all decision curves vary based on many variables all at once (we haven't even talked about button position, other players' styles etc). However, as a concept it is sound and if it evolved over time it could become the definitive poker machine for the budding player as started by texasholdem-poker.com's very own forum dudes 8)
It may never happen, but I thought of it first in this much detail 
PS. I'm assuming Adam can code here which is probably already a stumbling block..........
Posted Tue Aug 26, 2003 5:54 pm GMT by kluCAR
Odds of hitting a flush on the turn or river if two in a hole an another two on the flop is 3:1. In 3 cases it happens once (not 5:1).
Posted Wed Aug 27, 2003 2:34 am GMT by Geno
Ok, accidental inaccuracies aside...... 
Posted Mon Nov 10, 2003 1:21 pm GMT by cue_ball2163
Now that the odds are straightened out, what is your view upon how playing low pocket pairs?
Posted Mon Nov 10, 2003 8:12 pm GMT by Adam Marshall
In keeping with the "odds" theme, low pairs aren't usually a good idea.
If you have a low pocket pair, you pretty much have to hit your set. With low pocket pairs 22 through 66, there is a very low chance that you'll have an overpair. Also, if you don't hit your set on the flop, you'll be out most of the time if a bet comes your way. The chance of hitting your set or better on the flop is something like 1-( 46*47*48 )/( 50*49*48 ) which is a crappy 0.117551 or 11.8%. That doesn't take into consideration that you may hit your set with a 3-flush on the board or with the other two flop cards pairing. You need to be able to seriously affect the pot odds. This favors no limit games, but makes low pocket pairs a poor choice in limit games.
I wrote something about the chance of flopping an overpair based on what pocket pair you hold. Did that get deleted?
Posted Tue Dec 16, 2003 10:08 am GMT by JimTheBullet
Greetings all, I just registered today and I have a couple of things to add to this thread.
Firstly, on the subject of low (anything up to and including 99 in my view is low) pocket pairs. I have always taken the view that there are two ways to play them, which way you choose will depend largely on position and whether anyone has raised in front of you.
Most people will just call the big blind when they have a low pocket pair as they take the view that the odds of hitting a set are not good so they think they have a low chance of winning the hand. But, in my view, there is a flaw in the logic here. I agree there is a low chance of hitting the set and therefore of having the best hand but having a low chance of the best hand is not the same as having a low chance of winning the hand.
Let me explain a scenario. Say you are on the button in a 10 player tournament and the blinds are 10 & 20, everybody has around 1000 tournament chips and the blinds are called by 3 people in front of you. If you call the blind you are getting 4.5 - 1 (3 callers, the small and big blind) which is likely to increase to 5 - 1 when the small blind calls the big blind. Now, is that good odds? Of course not because as we have seen the odds of making the set are 7.5 - 1. True, the implied odds you get will be big but even if you do make your set it is almost certainly not the nuts (you have a low pair, therefore an overcard is likely) and it is very likely that at least one of the other players will have a lot of outs to beat your set with either a flush or a straight. On the other hand, if the flop comes down, say, AJ6 and you didn't hit the set you will HAVE to fold to any bet as there are 2 overcards to your pair on the board (although I have seen poor players hold on to the pocket pair with the overcards on the board a ridiculous number of times). So in my view, although it is a low risk strategy I think just calling with the pocket pair is a weak move which relies far too heavily on hitting cards to be profitable.
My alternative method is to raise with a low pocket pair, providing nobody has raised in front (the issue of somebody raising in front of you is much more complex and your reaction would have to be based on a number of factors, including your knowledge of your opponent). Take the example above, and imaging you have 77 in the hole. 3 people call the big blind in front of you and you are on the button, it is 20 to call and everybody has around 1000 chips. Let us say that instead of just calling you raise to about 80 (the exact amount of the raise would again vary according to your knowledge of the players who originally called), what is likely to happen now? Most of the time the blinds would fold (beware if they don't) and you would get called by either 1 or two of the original callers. lets keep it simple and say one called. You now have some valuable information that you did not previously have about your opponents hand. Your opponent has something that he can call with, he probably doesn't have a big pair(AA, KK, QQ) because he would have raised originally or certainly reraised your raise. He is likely to have a weak ace, A7 maybe, or perhaps two high cards with no ace, maybe suited, bear in mind that he is likely to have some kind of drawing possibilities, many people would have called your raise to see a flop with suited connectors for example.
Now, how do you play the hand after the flop? Bear in mind you have position in this hand. If the flop comes down AJ6 you would have been forced to fold, as we have seen, had you just called before the flop. But now, even if your opponent has an ace, he will be worried about his kicker because he is putting you on a big hand such as AK, AQ or AJ. Your opponent therefore may not bet the top pair. If your opponent doesn't bet it then bet it strong, if he does bet it raise him about 3 times his bet (e.g. if he bets 100, you put in 400) to scare him away. Your opponent will only call you or raise you if he has two pair in this spot, if he reraises get out of there, if he calls then think about whether he is calling for a draw or whether he has perhaps the second pair. The point about this play is that your bluff is very, very feasible. It is not just a random act with no evidence to back it. You raised before the flop so a strong ace is a very feasible hand for you to be holding, had you called before the flop then you are much less likely to get away with representing the ace in this way. The best flop you can see in this type of hand is one where you make your trips with rag cards. For example, say you have 77 in the hole and the flop is 972. This will look like you missed the flop to the other players as there are no high cards to back up your raising hand and hopefully the guy who has A9 will generously give you all his chips thinking his top pair, top kicker hand is strong.
Basically, if you show aggression with pocket pairs before the flop you have 2 ways of winning the pot. You can win it with a bet or raise to any kind of raisers flop and you can potentially clean up if you do hit trips on the flop. I have analysed these alternative methods over time and found that the aggressive method is more profitable in the long run although it undeniably has a higher variance. You can get into trouble if you misread your opponent as being on a draw when in fact he is trapping with two pair. Bear in mind that as soon as there are overcards to your pair it is a hand that can be easily laid down if somebody shows aggression.
The other thing I wanted to mention was to do with odds calculations. Somebody posted a suggestion here that somebody could write a program for calculating outs and suggesting strategy. I have started work on just such a program and I have a fairly good idea of where I am going with it. Unfortunately, I don't have a good enough PC at home to do the development work and I am a bit busy at work at the moment to get it done. I will let you all know if I ever get it to the stage where it needs to be beta tested.
Wow, sorry for the long post guys!
later
Jim
Posted Tue Dec 16, 2003 10:37 am GMT by Dave B
I totally agree w/ much of what you said. However, if I am on the button w/ low pairs w/ one caller on the flop after a strong bet and he bets 100 TC after the flop w/ 2 over pairs....NO WAY I am raising 3 times his bet. I started w/ 1000 TC, I have committed 80TC toward a 300TC pot. If he bets 100 and I raise I have put in 1/2 of my stack toward a pot where that puts me to 1200-1300TC if I win. The risk reward just isnt worth it.
If the player has been stealing a lot of pots, I may reraise to 200 just to gather more info, but then I still have 700TC if he reraises.
Now....if I have 3 times his stack..say 2000TC to 650 before the hand starts, I may go all in if he bets 100. Even if he has a top pair, he likely wont want to stake his entire stack and will fold. If he calls and I lose, I am still in a decent position for the rest of the tourney.
Posted Mon Jan 12, 2004 5:15 pm GMT by jim nayzium
someone on here stated 20 percent is 5 to 1....
Isn't 20 percent technically 4 to 1?
I like your low pair strategy...especially in tournament play vs cash play...
Posted Mon May 31, 2004 6:09 pm GMT by snoogins47
I definitely agree with the aggression on low pocket pairs, moreso in NL than in Limit.
Flopping a low or middle set is a very hard to read hand. Even moreso if you raise pre-flop... well, to many people. If you consistently do it, your betting after the flop may set off warning bells everywhere.
And btw, somebody mentioned flopping a set with a higher pair on the board.
If I'm on 22, and the board is 2 J J... i'm feelin pretty damned good about my hand, especially if there are two aggressors before me, and ESPECIALLY in a raised preflop pot.
In a raise pot preflop, the only hand you have to worry about, for the most part, is JJ. No matter what, you've got the third best hand at the moment. One is very unlikely, mathematically (JJ) and the other is pretty much a long shot as well, probably even more so, as 3 of the 2s are accounted for, and most people would not hesitate to dump J2 preflop.
Posted Wed Jul 07, 2004 2:56 am GMT by snoogins47
After re-reading through this thread a bit...I have something to add
Much of whether or not I will take the aggressive stance preflop with a low or mid pair has to do with the looks of the hand.
Though I don't have any hard and fast numbers to back this up, as I'm not one of those pokertracker junkies myself, it seems to me that middle pocket pairs tend to eke out a nice +EV either in heads-up pots, or in large multi-way pots (as in 5+ people)
In the heads up situation, a middle pair will often hold up, even if an overcard or two flops. And with something like 8s or 9s, it's not all that uncommon to hold an overpair, which will obviously put you in a strong position.
In the large family pots, you're playing to make your set, and that's about all there is to it.
In the middle-sized pots, (3-5 people) you're in a sticky situation. Your middle pair may very often get beat if it doesn't improve, and you're typically not getting favorable odds to make your set.
Of course, this changes with the type of game you're in, situations, players, blah blah, typical postscript goes here ;P
Posted Wed Jul 07, 2004 7:52 am GMT by Ben4040
All of this was very interesting to read. I have always raised with pocket pairs of any kind if no one else has raised the pot before me. Jim and Dave both made good points. I think facing a significant bet with a low pocket pair with two overcards on the flop it would be very hard to re-raise your opponent, unless you had a significant amount of chips that you could afford to bluff or you were pretty sure your opponent didn't have a hand.
Posted Sat Jul 10, 2004 11:24 pm GMT by suprastyxx
why is it that when we are calculating odds we have to calculate the odds of NOT hitting our hand instead of calculating the odds to hit it?
Andrew
Posted Sun Jul 11, 2004 3:17 pm GMT by snoogins47
A few reasons:
First, it's not a big difference. 80% of not hitting it, pretty obviously means 20% that we will.
Secondly, it's just typical conventions to put the bigger number in front in odds... if you're the favorite, you'd say you're a 4:1 favorite. If you're behind, you're a 4:1 dog.
Third, knowing I have a 65% chance of MISSING my flush draw makes me a lot less apt to chase than if I thought "Man, I make this over a third of the time!" ;P
Posted Sun Jul 11, 2004 5:04 pm GMT by suprastyxx
ok, so it doesn't matter which way you calculate then its just preference basically. i always wondered if you got a wrong percentage if you did it the wrong way.
Thanks for the answer
Andrew
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