Counting and calculating outs

Mdf1992 said:

Hi All!

When calculating outs and basically calculating the probability that I’ll hit one of the cards that I need on the turn or the river, I’m wondering how many cards are in the denominator? Is it 52? Or is it 52 minus the two cards in my hand minus the amount of cards in everyone else’s hand’s? So let’s say I have 7 “outs”. Do I divide 7 by 52 or by, like I mentioned above, the adjusted number? I’m assuming they just divide it by the full deck number, but wouldn’t it make more sense to adjust?

Thanks!!
Mark

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Nafor said:

Hi Mark,

Cardschat has written a great guide about this:
https://www.cardschat.com/odds-for-dummies.php
Scroll down to part 2 and you'll learn how to calculate outs and adds.

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• outs * 2 to calculate your flop-to-turn, and the turn-to-river odds separately.
• outs * 4 to calculate your odds for hitting on either the turn or river.

Mdf1992 said:

Hi All!

When calculating outs and basically calculating the probability that I’ll hit one of the cards that I need on the turn or the river, I’m wondering how many cards are in the denominator? Is it 52? Or is it 52 minus the two cards in my hand minus the amount of cards in everyone else’s hand’s? So let’s say I have 7 “outs”. Do I divide 7 by 52 or by, like I mentioned above, the adjusted number? I’m assuming they just divide it by the full deck number, but wouldn’t it make more sense to adjust?

Thanks!!
Mark

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ohshootmybad said:

cards in deck - known cards = remaining unknown cards

outs/remaining unknown cards = odds of hitting.

you can also do the rule of 2 and 4, which is a quick calculation for figuring out the odds of you hitting on each street or the odds of hitting on either street.

• outs * 2 to calculate your flop-to-turn, and the turn-to-river odds separately.
• outs * 4 to calculate your odds for hitting on either the turn or river.

it's important to note that you only use the rule of 4 if you're guaranteed to see the river, which only happens if it's guaranteed you will not face any more betting rounds post flop. otherwise, you'll be calculating the wrong odds to for the flop to turn as there is the possibility of you folding on a turn-to-river bet. the only exception to this is if effective stacks are so shallow that you're guaranteed to call a turn bet no matter what hits. majority of the time, though, you'll be using the rule of 2.

going slightly further, the rule of 2 and 4 is very close but not exactly perfect. if you aren't a stickler for being exact, as long as you're over the pot odds with the hand odds (using percentage method), then you'll be fine.

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Collin Moshman said:

I think the replies have gotten to this already, but to clarify the denominator is "Unknown Cards."

For example, at the flop, the denominator would be 47 since you know 5 of the 52 cards.

Nice question, this is an important topic

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Mdf1992 said:

Thank you so much!

So what I've always wondered about the rule of 2 and 4, is that it seems that the examples that are used when explaining it are for example a flush draw. So that would mean you have 9 outs. 9*4 or 9*2 is 36% or 18%.
...as mentioned, you would only use the rule of 4 if you are guaranteed to see the river cards. for example, if you have a flush draw and the pot is 1200 chips. villain goes all in for 800 chips, making the pot 2000. so you would need to call 800 to win a pot of 8800 (you add your call to pot for the percent method), which is ~28%. since you opponent can no longer bet, you can use the rule of 4 which is the odds of you hitting on the turn or river. this gives you a 36% chance to hit and since it's greater than the 28% pot odds, you call.

but lets say, in the same example, you have a flush draw and the pot is 1200 chips. villain bets 800 chips from an effect 20k stack, making the pot 2000. well, now you have to use the rule of 2 to calculate the odds of hitting on the turn because there is still the possibility you fold to turn bet if you miss. remember, the rule of 4 is the odds of hitting on the turn or river, meaning you can completely miss it on the turn and never see the river if you have to fold to a large bet. by using the rule of 4 in this spot, you are miscalculating your expected value in the long run because you only have an 18% chance to hit the turn, which means you're missing 82% of the time and there is a possibility of you not even seeing the river card.

very simple and general rule to follow when using the rule of 2 and 4:

• if i call this bet on the flop, can my opponent(s) bet on the turn? if yes, use the rule of 2.
• if i call this bet on the flop, can my opponent(s) bet on the turn? if no, use the rule of 4.
• on the turn, you can only use the rule of 2 because there is only 1 card to go.

But here's where I'm confused when it comes to calculating equity of other hands other than like flush or straight draws. Can I use the rule of 4 and 2 for things like just having a pair? So if I have a pair of 9s, that means I only have 2 outs, right? The 2 other 9s in the deck. So then my equity would only be 2*4 and 2*2 = 8 and 4%?
....yes, you can use the rule of 2 and 4 for any of your outs.

however, this is just the odds of you hitting an out, but not necessarily winning. so it also depends on your opponent and board structure. so, with 99, you would call if you felt like you were a favorite to win in most situations.

for example, if you had 9s9c and the flop is kd ad 6d, then you probably wouldn't want to call here because a) it's very unlikely you aren't getting correct pot odds to call and b) you could still be behind if you do hit another 9. betting/raising here wouldn't make any sense because you'd only get called by hands that beat you or have a lot of equity. plus, how comfortable would you be firing another barrel if you get called on this flop?

but if the flop was 5c 7s 2h and your opponent bets, then there is a good chance you have the best hand and you don't necessarily need to hit a 9 to win.

Or are you only supposed to use the rule of 4 and 2 for hands that would lead you to definitely winning the pot in the showdown? Like, **could I use the rule of 4 and 2 if I just have 2 random cards? Say 9 and 4?**
...hmmm, i guess i should've read your post completely before i started answering.

honestly, it's just best to use your judgement and ask yourself, "if i hit, what is the likelihood i'll have the best hand at showdown?"

sometimes that can pretty hard if you have something like a king high flush draw because you still lose the ace high flush draw, but there is still a chance you'll have the best hand. so, calling in this spot might not be bad because you only lose 1 other hand. on the other end, if you had a 2 high flush draw, then odds of you having the best hand is very slim, especially against multiple opponents.

it's also opponent dependent. against tight or really good players, i want to call in spots that'll give me the best hand or a really good showdown hand at the river. against loose or weaker opponents, i could include hands like middle flush draws, gut shots + over(s), low 2 pairs, etc because i'll likely have the better hand at showdown majority of the time.

Thanks again for your time!!!

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ohshootmybad said:

above

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