So help me out here,

AsJs vs Kc10c

on Ac 5c 8h

How do I calculate equity? 9 outs to the flush.
Is it theres 44 cards left so 44/100 = 2.22 x 9 ? How do I work out runner runner like 2p or trips, I remember someone doing a post on it before. My maths might be terrible can someone help me out lol

Not sure exactly what you are looking for.

To get the exact answer you need to delineate all the cases (turn/river combos) in which you win and express that as a percentage of all possible turn/river combos.

To get an approximate answer, there are probably many good "rules of thumb" that have been developed over the years.


Here is my attempt to get the exact answer. You win under the following turn/river combos:

1. Exactly two clubs: C(9,2) = 36

2. Exactly one club: C(9,1)*C(36,1) = 9*36 = 324

2A. Need to exclude: 8x8c, Ax8c, AxJc, JxJc (each is 2 combos), so subtotal = -8

3. KK or TT: 2*C(3,2) = 2*3 = 6

4. KT: C(3,1)*C(3,1) = 3*3 = 9

5. QJ (no club): C(3,1)*C(2,1) = 3*2 = 6

TOTAL = 373

PCT = 373/C(45,2) = 373/990 = 37.67676767%

Sorry can you explain I dont understand any of this 9,2? what does that mean 9x2? and why does it = 36? C36,1 where has the 36 come from?

Yeah there are rules of thumb there was one that was like each out you have is like around 2.5% or something i cant remember the calculation that gets u there maybe it was 1.9% and was 52/100, and then there was a way of calculating runner runner like, maybe say ur playing heads up, u have 2 cards opponent has 2 cards, 3 flop 1 burnt, 52-8 = 44, Now say you have K high nut flush draw and ur opponent has flopped an ace. Im sure theres an equation to calculate say running Kings like something like


3 kings left = 3 x (100/44) = 6.8%

then

on the turn 2 x (100/42)= 4.76%

then maybe something like 6.8/4.76 = 1.4%? Of hitting running Kings?

I know this is wrong because 100/42 gives a bigger number then /44 which cant be right because u cant have more equity in later streets, and dont think the last equations right either

Sorry for the confusion on notation.

C(9,2) is the number of ways you can choose 2 items out of 9 items without replacement. C(x,y) is called the Combination function and C(9,2) is sometimes referred to as "9 choose 2".

The formula of C(x,y) is straightforward and is taught in most probability classes in school. You can look it up on the internet if you don't know what it is. C(x,y) is programmed into most modern calculators and computer languages.

Okay, now that that is taken care of. Do we have a fundamental difference in understanding the situation?

Hero (Kc Tc) has 2 clubs. Villain (As Js) has 0 clubs. Flop (Ac 8h 5c) has 2 clubs.

There are 2+2+3=7 cards "known" to us at this point, 4 clubs and 3 non-clubs. The original deck of 52 cards has, of course, 13 clubs and 39 non-clubs. Thus, the turn and river will come from a "stub" which consists of 9 clubs and 36 non-clubs (9+36=45).

You do not "remove" the burn card from the equations since the burn card is unknown. Since you do not know the value of the burn card, it is properly considered part of the "stub" (the set of possible card values from which the turn and river emanate).

From what you have written in your most recent post, you seem to have questions about basic probability concepts rather than poker "theory" questions. There is a Poker Probability forum on 2+2 which may be a better place to continue this conversation.

https://forumserver.twoplustwo.com/25/probability/

Yeah if i scratch my head i can kind of remember this from school, still a bit confused so on point one you say exactly two clubs? So is C(9,2) the probability of a club coming on the turn and river? So its the sum of the 2 out of the 9 clubs coming on the turn and river, the combinations of the 9 clubs that can hit turn and river

Kc10c

Ac 5c 8h

so (2c,3c)(2c,4c)(2c,6c)(2c,7c)(2c,8c)2c9c,2cJc,2cQc, 3c4c,3c6c,3c7c,3c8c,3c9c,3cJc,3cQc,4c6c,4c7c,4c8c, 4c9c,4cJc,4cQc,6c7c,6c8c,6c9c,6cJc,6cQc,7c8c,7c9c, 7cJc,7cQc,8c9c,8cJc,8cQc,9cJc,9cQc,JcQc = 36

So we calculate the sum of combinations for 2 clubs coming because we need to calcualte every single outcome? and then divide by the comination of every other remaning card?

If I am understanding your question, the only way I know how to calculate poker equities (exactly) is to tally all the cases in which you win (ignoring split pots for the moment) and divide by the number of total possible cases.

To determine Hero's equity, tally how many turn/river combos win for Hero and divide by the total number of possible turn/river combos.

Often times in tallying the winning combos, it is important to take care not to double-count certain cases. So I have gotten into the habit of listing the cases very granularly.

To handle the cases where Hero wins with a flush, I separated the cases in which two clubs come (BOTH turn and river are clubs) from the cases in which only one club comes (EITHER turn or river is a club). I have found that it is easy to get the wrong answer if care is not taken when you list cases.

Anyway, as you say one of the ways that Hero wins is if both turn and river are clubs. There are 36 of those turn/river combinations as you listed above.

Do the same thing for winning with a flush when only one club comes. Ditto for trips, two pair, and straight possibilities.

Of course, many times carefully tallying all the winning cases can be a major pain in the ass. So rules of thumb have been developed over the years. Rule of 2, Rule of 4, x% per out, etc.

But these rules of thumb, however useful, only give approximations to the true equity. If you really want to know true equity, you have to (or have a computer) tally all the cases.

Hope that makes sense.

Just do the 2 and 4 rule...9 outs x 2 = 18% with one card left, 9 x 4 =36% with two cards left to come. That is usually good enough, though not perfect. If your opponent goes all in for $50 into a pot of $50 (i.e., you need to bet 50 to win 100), you should fold. 50 is 50% of 100, so we don't have the odds to call. If you only need to bet 30 to win 100, you should call their all in.

If the ratio method works better for you, then consider an all-in on the turn-- there are 46 cards that you do not know. You know 6/52, the 3 flop cards, the 1 turn card, and your 2 hole cards. 9 cards make a flush. You can divide 46 by the number of outs and subtract one. So 46/9=5.11. You need about 4.11:1 odds to call with one card left. If you need to bet 10 into a pot of 50 you can still do so profitably since you're getting 5:1 on your money.

It's good to memorize these numbers for popular scenarios, like open-ended straight draw, flush draws, etc., with a few things to keep in mind. You want to draw to the best hand. Having A7 on an 89T board may not be 8 outs, since if a J rolls off you are beat by any Q or maybe chopping. It is not a strong draw.

Also, in practice, you are rarely facing a flop all-in and simply need to do math. It's usually more complicated. There's usually more rounds of betting, you need to consider how much more money you might make or whether you want to invest more money if your draw misses on the turn and then your opponent bets again.

For runner -runner,e.g, you need 2 clubs, to win after the flop cards are dealt, there are 10 remaining clubs in the 47 card deck, assuming villain’s cards are unknown. If the bet is all in, the win probability is simply

P(win) = P(hit on turn) + P(hit on river given hit on turn) = (10/47) *(9/46) = 4.2%.

Since this is close to 1 out using the 4x.rule, some people say runner, runner is equivalent to 1 out, but that may not be the case for other situations such as needing 2 cards for a straight (TJ..A).

Ah nice, so say you had no pair, and to hit running two pair or trips it would be

(6/47) x (5/4) = 1.38% right?

cheers

Yes

How sure are you on this?