TwoPaired on the Flop! Odds and a guide to playing them
So I had a hand today in the fake monies vs. a major fish who I've seen all in multiple times with like 29s and J4o, raising all over the place and somehow hitting the nuts on the river. I get dealt QJo on the blinds and EVERYONE calls, so I raise a bit, still nobody folds, and flop comes out QJ6 rainbow. OMGBBQ, raise 2xpot. Alotta folds, 1 caller, and 1 raiser. I reraise, bla bla bla, it ends up I'm all in against a fish and the turn and the river comes down 7 10, and he had 89o, and takes the pot with the straight.
Now, we've all been in this situation before, and I'm sure this has happened plenty of times to people with various flushes and such randomly killing your TPTKs, trips, and top 2 pair hands. Good players will fold to you, bad players will call you, you make money off of both over time if you bet correctly, however, of all these hands, the twopair is often hardest to judge. I offer you your odds and my opinions on the two pair hand based on the following:
The odds of being dealt a pair are 3/51, by way that one card will always be dealt, and there are 3 outs in a 51 card deck to match that card. 5.8%. At a ten person table where you aren't dealt a pair, the odds of someone else being dealt a pair are:
3/51 * 9 hands = 53%.
I keep the 51 card deck simply because the odds of people being dealt any of the 11 pairs around you would take too long for me to figure. Sufficed to say, a bit more than half the time, you'll be fighting a pocket pair.
For a two pair flop to come down, we require 3 seperate numbered cards, ie in our example above, QJ6 rainbow. For the math, we will name these cards H, M, and L, for the high, middle and low cards.
The odds of anyone holding the HH or MM pocket pair when I hold HM is calculated as:
[ (2/47*1/46) + (2/47*1/46) ] * 9 players = 1.67%
The odds of one player holding LL in this situation are:
(3/47*2/46) * 9 players = 2.5%
If you hold HL, it is important to realise you are dominated by HM, and if you hold ML, you are dominated by HL and HM. The odds of another player holding a better 2 pair than you are calculated as follows:
(holding HL) (flop H M L)
The first card dealt to them must be one of two remaining H cards or three remaining M cards (5/47). If it is one of the two H cards, 3 M cards remain. (2/47 * 3/46). If the M card is dealt first, the second must be the H. (3/47 * 2/46). These two are equal, so doubling it we get .55%, * 9 players is almost exactly 5%. (4.9953744)
(holding ML) (flop H M L)
The odds are the same as above, so you are 10% to be dominated here. So, combined, your odds of holding the best hand against 9 players are:
For HM: 100 - 1.67 - 2.5 = 95.83%
For HL: 100 - 1.67 - 2.5 - 5 = 90.83%
For ML: 100 - 1.67 - 2.5 - 10 = 85.83%
So, two pair on the flop seems to be a VERY big moneywinner. With Top 2 pair, you are 96% to have the best hand on the flop, however, unlike 2 of a kind or a flush/straight, there are plenty of outs around your two pair:
Against a pair on board with one overcard, there are 5 outs: 20.3%
Against a weaker two pair, there are only 2 outs: 8.4%
Against flush or straight draws, there can be 4, 8, 9, 12 or even 15 outs (16.5%, 31.5%, 35%, 45%, and 54.1% respectively)
[You of course have four of your own outs to match and make the full house to beat all of these hands: 16.5%]
So from here, your absolute worst option is to slow play your two pair. Two pair should never be checked (unless you are check-raising from poor position) under any circumstance, and I recommend a pot sized bet, particularly against flops showing flush and straight draws. Unfortunately, this often results in you simply taking the blinds, when someone who has made a better hand on the flop can re-raise, and cause you fold, or worse, lose a large chunk of your stack calling a better hand to the river.
Lets stop and do some more math here. First, we need to decide on who our opponents are at the flop. Lets say we have a loose passive semifish type who will call your pot-sized bet with top or middle pair on the board, but has enough sense to raise with three of a kind or better, a loose aggressive player who will raise three of a kind, any two pair, and Top pair, a tight aggressive player who will raise you with top two pair and three of a kind, and occasionally TPTK, and a tight conservative player who you feel will generally just call you down, but will only raise with three of a kind.
If Mr. Fish (loose passive) reraises, you should generally fold. The math here is that you will lose 83.5% of the raises you call here, assuming he has his 3 of a kind for pot x, so of course the magic number is 16.5%, your outs to get the full house. He'll call you alot, this is the kind of guy you want with you on your two pair on the flop.
If Mr. Angry (loose aggressive) reraises, the magic number is of course 16.5%. However, in this case, there are several hands he'll reraise in this situation, and the ones that beat you are the most unlikely of them. Fold if there is good flush or straight draw on the board. I would also fold here if you have a Mid-Low Two pair - having the high card here helps alot, because it means that most of the time, he won't have it. Also, remember if he raised (or called a large call) preflop to indicate a pocket pair. A preflop raise doesn't mean fold by any means - especially on a low board. For instance, on QJ6 rainbow, if my opponent was holding AA or KK, he would vigorously bet this hand as he has a pocket top pair, so don't lose heart, but don't outstay your welcome.
Now here's the thing:
Against Mr. Angry, if you take the pot with a pot-sized bet 50% of the time, get reraised 50%, and fold half the reraises, and split the rest of the pots fairly evenly, you make very little money here. When you are out of position, a good strategy may be to check, wait for his bet, and re-raise to the river, that way it becomes apparent if he makes his hand and you can fold out, or he himself might fold out more often. Examine his pre-flop behavior closely here, you're trying to make sure he has something here and will raise you before you check to him and give him free cards.
If Mr. Tighty Whitey (tight passive) reraises, I generally fold unless he gives me odds, if only to make him play more hands.
If Mr. Rock (tight aggressive) reraises, you have some questions to answer, because he thinks he has the hand. Fold your Mid-Low two pairs here definately, they can be big moneylosers in this situation. Putting him on a hand here is a very good idea, and you can also test the waters with a min-raise (fold to a reraise), or even try to bluff him back down to size with a large raise (which I will rarely do due to it's cost). Calling here says you're nervous that he might have a better hand than you and is generally not a great idea, particuarly if he has position on you (you'll essentially be giving him a license to raise you to the river). Remember, there's good odds still that you have a better hand than him, at least 85%, so don't be afraid to call him and fold out later if the turn and river turn sour, you should make money here, but here is where some of your worst beats will happen. Here also is a good situation to check-raise, as he will often fold to a re-raise if his hand consists of TP with an ok kicker, but be very wary of a tight player that raises here.
Also, I try to fold two pair if I think I might be on TILT for any reason, and if I find this fold frustrating, then I consider myself on TILT and take a break. Raising a low two pair on a flush-draw/straight-draw river is a VERY good indicator of TILT. Again, your two pair hands are your most vulnerable strong hands and are very much dominated by a higher two pair, and also by anyone who has a pair made of your outs, (for instance, you hold QJ on QJ6 flop, hands consisting of QQ and JJ -- your outs to a full house -- dominate you). Pay attention to your opponents, specificially who has been raising and who has been calling preflop to get an indication of hand strength, and the straight and flush possibilities on the board. Also, the beats with Two Pair will come as much as 1/3 of the time, all kinds of fish will call you on a flush or straight draw. I personally made this guide and did all the math to prove to myself that two pair off the flop is a moneymaking hand by the numbers because of a day of fish-infested beats where my KKQQ and QQJJ were both cracked on a flush and a straight.
... that's my guide to the two pair!
Sorry for spelling/grammer, it's late. Take a crack at it!
EDIT majorus:
Section 1: This post was so you and me could both know our odds when playing the two pair, not so I could discuss my bad beat.
Section 2: Betting vs. Pot Size
We know we're the favorite to win here in general, and the pot-sizer is always a good bet, but great poker players maximize their money.
The following is a quick way to estimate your average earnings per hundred hands with a particular betting strategy:
Earnings Ratio = Pot * % fold + (Avg Raise + Pot) * (% Win on call) - Avg Raise * (% Lose on call)
So if say we bet all in here ($25 for the sake of arguement) on an average pot of $2, get folds 80% of the time, lose 15% of the calledhands and win 5% of the called hands, we will take 80 $2 pots and 5 $27 pots, and lose 15 $25 raises. The total earnings over 100 hands? $-80.
Now, supposed we simply bet the pot. Our opponents fold 50% of the time, so we make $100 there, and call with a weaker hand 30% of the time, but have the nuts or complete their draw on you 20%. Here you make $100 + $120 - $100, you make $120 (60 pots) out of 100 hands. The disadvantage of this tactic is it is very weak to reraising, you are put in a position where you have to make a judgement call that can cost you possibly a large chunk of your stack.
Supposed you decide to bet 3 times the pot. Your opponents now call only 30% of the time, winning it 18% of them while you take 12%. $140 in folds, $96 in wins, and $108 in losses = $128/100 (64 pots) hands. Your decisions here are also very clear - against a significant reraise from a tight player, you should fold, and against a call you should continue to raise unless a draw is completed. Of course consistantly doing that will cause you to fall prey to reraise-folds, so a good mixture of large (2-4x pot) and pot-sized raises are recommended.
At 4 times the pot, with 30% calls again and 18-12 loss win ratio you make $116 (58 pots), so from here your winnings start to decrease as you risk more of your stack for essentially the same odds of winning the hand - you will rarely fold out someone who will call a 4x pot bet that will not call a 5 or 6x pot bet with the same hands.
