Hi...
I'm new to the forums but am a math guy and I usually play by the odds (though not always) depending on the table. I prefer 6-player games for that reason.
Anyway here is my take (and sorry for the length of the post as I just kept rambling)
Dealt to klitkat [Qc Th]
*** FLOP *** [Ah Ts 4c]
A 6-bet preflop probably means a high pair or 2 big cards, or a
bluff, but with a weakish hand like QTo I would generally credit the hand.
So at this stage (ignoring T4)...
You're behind against Ax, KK, KQ, QQ, QJ, JJ, TT, and 44. While it's possible the raiser could have a smaller pair it's pretty likely he (or the other limper) has one of these so it's a good idea to assume you're behind here and base a decision figuring you have to improve to win the pot without
bluffing.
If opponent has AA you need runner runner (see bottom).
The odds from the rule of 2/4 are only that you improve your hand not that you'll win the pot so reads are critical in figuring the real odds. You might have 5 outs to improve your hand (3 queens and 2 tens) but against certain hands not all of them will help you.
For example, if opponent has QQ, TT, AQ, AT then you only have 2 or 3 outs which means a 4%/6% chance to hit the card on the turn or 8%/12% by the river. At best this translates to about 7.3:1 (at 12% you win 12 times out of 100 so you lose the other 88 times so your odds are 88 against 12 or 7.3:1). Your real odds would usually be worse in this situation since you're unlikely to get a free card here.
Otherwise you have 5 outs which means roughly a 10% chance to hit the card on the turn or 20% by the river so at best you'd have a 4:1 shot
if the turn is free*.
Since you're up against 2 players, you might already be drawing dead since even if the turn misses the raiser and helps you, the other limper might improve from it also. As a charter member of the paranoia patrol I view the odds above very conservatively if I'm not heads up. To call the bet, not to raise, I might assume the 7.3:1 odds against me increased by half to maybe 10:1 or even 15:1.
*** TURN *** [Ah Ts 4c] K♠
This wasn't a good card since now Kx and QJ also has you beat. But at least you picked up a gutshot straight draw though any player with a queen or jack also has one. Remember that if a queen falls on the river you might have 2 pair but it could have given someone the straight. So the fact that you had around a 4*3=12% chance of picking up 2 pair by the river it might actually cost you money against hands like JJ, QQ, QJ. This is where playing by the odds is really tricky.
You can't expect someone to hit a runner runner straight of course but it's something I keep in mind after I see this flop, especially if I think an opponent has a hand like KQs or QJs where he might have a fairly decent chance of hitting runner-runner to a good hand.
As the above posters mentioned any of the 4 jacks gives you a straight, but there is also a flush draw now and a J♠ might give someone a flush which beats you so rule #7 of the paranoia patrol says to only use 3 jacks as outs in this case. The difference is pretty small though (8 outs vs 9 outs or about 5.3:1 vs 4.6:1) so in most cases it wouldn't affect my betting too much. At worst I might just call with a straight if the J♠ came instead of raising.
Something else to consider is that someone might already have the straight (QJ) and you are drawing to a split pot which potentially cuts the odds the pot is giving you in half. If the pot is 1000 and there is a 200 bet you are getting 6:1 pot odds which migh be worth calling. But if you are drawing to a split pot then you are betting 200 to win 600 which is only 3:1. While a split here is unlikely, it happens a lot in Omaha so it's just something to keep in mind when figuring what odds you really need.
*** RIVER *** [Ah Ts 4c Ks]
J♣
OK you would have made the runner-runner straight and won the full pot if you stayed in. But I wouldn't look at it that way since you made the right decision considering the odds as you miss it the vast majority of the time. We always look back and think of the pots we could have won but rarely look back and think what a great fold. Anyway, look at it as getting to see how your opponents play AK and KK!
Now if you want to figure out your chances of hitting runner runner from the flop, there are about 1,100 possible combinations of turn+river cards (1,081 actally) so count the number of combinations that works for you.
KJ -> 32 possibilities
QT -> 12 possibiliies
QQ -> 3 possibilities
TT -> 1 possibility
That's a total of 48 ways you have of hitting runner-runner. (am I missing any?)
So you have a 48 out of around 1100 chance of hitting a big hand by the rivver which is about 4.5% (or around 21:1 which partly explains why I get beat by runner runner so often in limit games). This is only worthwhile if you are looking to figure the odds of making a hand at the river when you see the flop. This is the same for the rule of 4 which also looks at both cards. When you think about it though, runner-runner is both cards helping you while the rule of 4 is the chance of just 1 of the 2 cards helping you.
So if you have 5 outs on the flop, then your chance to get 1 card to improve by the river is 4*5=20% so figure that half the chance of hitting that big hand is already in your rule of 4 odds so add 4.5%/2 to get 22.5% which lowers the odds from 4:1 to about 3.5:1. It might not seem like much but it really comes into play when you have a suited hand and/or overcards where you get more outs and more runner-runner possibilities. For example, if you have 3 of a suit on the flop there are an additional 45 ways of hitting the flush (about a 4.2% chance).
Hope this helped - sorry for rambling!
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* BTW this is a rule of thumb and works for typical hands but fails for certain hands with lots of outs.
