# Outs question

• Bronze
Joined: 09.12.2014
Hi,

On a board of 3s5c5d

Hero: 3c 3d
Villain: Jd Jh

Why would I say villain has 4 outs instead of 3?
Villain would make 3555 and have 5's full of jacks which villain would only need 1 of the 5's
Two remaining Jacks would also give 355J which would give villain jacks full.

I guess we're assuming it's either one of the remaining 5's which would count as 2 outs + 2 jacks which is total of 4 outs.
• 8 replies
• Bronze
Joined: 09.12.2014
What I don't understand is how math works in this hand, if I put this hand in equilab it displays villains equity to be 16.7%.
Out of 45 cards that are known we know 4 of them help us and 41 doesn't, but equilab calculates we are going to see both streets?
• Bronze
Joined: 01.05.2012
Originally posted by dddq8842
I guess we're assuming it's either one of the remaining 5's which would count as 2 outs + 2 jacks which is total of 4 outs.
Hi dddq8842,

You are absolutely correct, villain has four outs in this example, as you already explained: The two remaining 5's, which would give him 555JJ, and the two remaining J's for JJJ55, both of which beat hero's hand.

And yes, Equilab obviously calculates the equity for the entire hand, so it includes both remaining streets. You may have heard of the rule of thumb for (approximately) calculating post-flop equity on the fly, simply multiply the number of outs by 2 for one more street, or multiply it by 4 for two more streets. In this case it's 4*4, so it's pretty close to Equilab's more accurate result of 16.7%.
• Bronze
Joined: 09.12.2014
I seem to understand it as a whole but I want to know the math how it adds up to 16.7% by the river
Known cards: 7 cards
Unknown cards: 45 cards
Outs: 4 cards
4/45 cards will improve villains hand = 0.08
4/44 cards on the turn: 0.09
Or
Flop 41/45=.91
40/45=.91
Take away each result from the above from 1 and it should add up as our total equity.
Which I feel this is sort of bit off from the numbers equilab displayed.
Correct me If I'm wrong I'm not a big fan of math
• Bronze
Joined: 01.05.2012
Well, I'm embarrassed to admit that I'm pretty crap at math myself, so I'll have to leave it to someone else to explain how the probabilities add up. I'm afraid I can't really help you besides providing that rule of thumb I mentioned, which should be enough in most in-game situations. Your initial assumption about the outs is correct, though.

And as far as I know, programs like Equilab calculate their equity by literally simulating millions of deals in a matter of seconds, so they wouldn't even need any mathematical formulas for these results.
• Moderator
Moderator
Joined: 27.01.2013
I guess you just calculated that either villain hits on the turn or then you hits on the river? It is a little bit more complicated because you have a re-draw to quads.

So you can either hit turn and river cannot be a 3, or then you miss the flop but it cannot be a 3 and then you hit OTR.

I used ((4/45)*(44/45))+((40/45)*4/44)) <---- hit AND any card but 3 OR any card but our outs or 3 AND hit OTR

I hope that I'm not very much mistaken.. It is possible that I calculated it wrong but just got the correct % with luck
• Silver
Joined: 12.10.2011
Hi

It's fairly simple actually and la55i has it almost spot on although you should have 43/44 as the second term, not 44/45. Remember there's one less card in the deck OTR. The difference is so small that the result will be almost the same, but still it's not 100% correct

To maybe make it a bit more visual...

There's basically 5 things that can happen, 2 of which result in villain winning:
a. Villain doesn't hit
b. Villain hits turn, you miss river
c. Villain hits turn, you hit river
d. Villain misses turn, hits river where turn is a 3
e. Villain misses turn, hits river where turn is not a 3

 code: ```a = 41/45 * 40/44 = 82.83% b = 4/45 * 43/44 = 8.69% c = 4/45 * 1/44 = 0.2% d = 1/45 * 4/44 = 0.2% e = 40/45 * 4/44 = 8.08%```

(a, c and d aren't strictly necessary for the calculation, but added them just to make it a bit more clear)

So villain's equity here is basically b + e which is 16.77%.

So if you would put that in one equation, you would get:

 code: `Villain's equity = 4/45 * 43/44 + 40/45 * 4/44 = 0.167676767676... = 16.77%`

Note that a in the above example is not the same as hero's equity. a only denotes the cases where villain doesn't hit. Hero's equity is of course 100 - 16.77 = 83.23% so the difference should be obvious, namely that we still need to add c and d (the scenarios where villain hits but still loses) to reach hero's equity.

Hopefully that clears things up a bit
• Bronze
Joined: 09.12.2014
Hi,

Listing the possible outcome for each street made it clear.
Thank you TJ.
• Silver
Joined: 12.10.2011
You're quite welcome sir