Having some trouble calculating certain odds.. plz help

Hi, Im pretty new to holdem, and the way i usually calculate my odds on the spot is simply using 2% per out per card im going to see.. very basic.. What Im having trouble with is trying to calculate the chances of 2 specific cards showing. like if i hold 2 3 5 and i need a 4 and then a A or a 6 to complete my straight. I know that gives me 12 outs, but thats not 24% chance if i just see the turn or 48% if i see both the turn and the river.. (roughly..) because that would mean 2 A's could show or 2 6's could show and it wouldnt complete my hand. So how do i calculate this out properly??

ALSO, calculating hand strength preflop.. Ive been told, for example, AJo vs AKo is roughly 30% for AJo to win.. and I was told that its because AJ only has 3 outs to win, 3 J's x 2% x 5 cards to come = 30% (i think its really 29%, but that way is accuate enough for my taste..) Now, I think thats pretty simple, but what if you are comparing two completly different hands like 89s vs A2o, and I dont completly understand how its 71%-29% in the previous example, because that doesnt consider chances of straights.. and it is possible for AJ to hit a straight and AK to not hit it.. does that not come into play when calculating preflop?? thats what confusing me.. and on the last note, is knowing how to calculate preflop hand comparison even a neccesary skill, and do people ever use this in game? its just stated on TV, but flop changes everything, and when playing you never completly know what someone has.. So thanks everyone very much for your input... greatly appreciated.

EDITED- After thought, with the AJo Vs AKo example, im guessing straights aren't considered because they both need 3 cards to hit a straight, so that cancels it out, but what about a matchup where 1 hand needs 3 cards to hit a straight, and the other needs 4.. does that change things?? and what about comparing more than 2 hands preflop.. and I still dont know if this is even a neccesary skill to be able to calculate it, but I would just like to understand how its done.. :/

well you need to think that you got like 24% to get 3 cards to help on your straight on the turn.. lets say that the A come up on the turn. now you need the 4... 4x2 8% to get... if the 4 come up on the turn... you have 16% to get an ace or 6... I think that's it.. you can't know the exactly percentage... but let's wait some math's experts.

The chances of you hitting 2 required cards ( a runner-runner) are VERY slim. You shouldn't really be counting on these, and its really not a skill you need to learn. You've only got a 'drawing' hand if your one card away from your made hand, so these are the outs you need to calculate.


When you talk about gutshot straights, with just 4 cards out of 47 to make your hand, your in long-odds territory (6/1 ish). If your talking about specific odds for drawing 2 cards to a straight, I'd say your looking at about 36/1. And its HIGHLY unlikely your getting 36/1 on your money as far as pot-odds.
Hope this is right, and I hope it helps.
If you're getting a free or cheap turn card, then by all means take it and see if it helps your chances. But dont get involved in a hand simply hoping to improve. Most people will fold a 'drawing hand' to a sturdy enough bet, so calculating how likely it is to pull a card on the turn that will IMPROVE you to a drawing hand by the river is fairly pointless.

If you need runner-runner and they beat the BEST option you have is fold. I believe the only thing calculated in the AK vs. AJ hand is the probability of the second hand hitting their J. Since pre-flop no cards have been dealt neither has straight draws. I do think that suited cards get an extra 2 percentage points due to less cards needed for the flush to occur. But again no flush draws pre-flop.

Google up "Pokerstove". It will get you all the probabilities you are looking for. If you are looking for more advanced stuff including flop hand strength, look into "Pokerazor".

As has been stated, knowing your equity when you need runner runner is a pointless skill to have. Knowing general preflop equity (dominations and one over one under against a pair is 25-30%, underpair is ~20%) can help but knowing equity against ranges is generally the more important skill to have.

To quickly go through the runner runner math:

Assume you have 78o, the board is A62r and need a 4 or a 5 on the turn, and the one not turned to come on the river. The odds of a 4 or a 5 coming on the turn is 8/47 (52 cards in the deck - 5 known cards; if you know your opponents hole cards, this becomes 8/45) . Given that one of them comes, there are 4 cards you want to come so the odds that you river that card is 4/46 (or 4/44). To find the probability that both of these events occur, you multiply them together to get 1.48% (or 1.62%).

in addition to what WurlyQ said above, i'd like to point out something else.

it seems that you must have misunderstood the concept of "outs". in this case, you would have 12 cards that would somehow slightly improve your hand. Those are not outs because even if you hit one of them, you still do not have a good made hand. Cards are outs for you only if you think that hitting them will make your hand the best. For the example, even if you hit a 4 on the turn, you still do not have a made hand and now you would be needing to hit your outs - namely an A or 6 on the river (and even then, depending on which cards are in your hand and which are on the board, your hand may still be beaten by a higher straight or a flush if one shows).

So here is the math for your specific question:
options for the turn:
A) an ace or 6 comes - chance 8/47
- now you only need a 4 on the river, and the chance for that is 4/46 (you have seen one more card, remember). the total chance for this is 32/(47*46), or under 1.5%
B) a 4 comes - chance 4/47
- in this case you would need an ace or 6 on the river - chance 8/46. guess what, the total chance for this is the same as above, under 1.5%
C) any other card comes - chance 35/47
- here it doesn't really matter what the river will bring, you are not in a good shape. there are exceptions, of course, like getting both the turn and river be 3s to the 3 in your hand and you win, but those are outside the scope of the current analysis.

so you will be good in under 3% of the time total, when either A or B above happens, and then you get another lucky card on the river. (the difference between my number and WurlyQ's above is because he somehow forgot you could also make a higher straight, with a 5-9 or 9-10.)

basically - if you only need one card, but have chances to hit it on EITHER the turn or the river, then you could (approximately) add the probabilities. if you need specific things to happen on BOTH the turn and the river, you need to multiply the probabilities of the events.

pokerstove (as suggested above) will do the math for you - but it is only really useful as an analysis tool after the fact. you should be much better if you knew some approximate ways to do math while at the table, and it seems you have the basics of that good luck!

i think you should just download an "outs" chart and kep it close while playings. or better yet make one yourself.