You're equity would be the % you win vs. a range.

Because we know villains exact hand (Q9) and the number of our outs you can look at my calculation and it's just

# of outs/(# of cards left in deck), as this is giving the probability of us winning the hand.

Well I think your response to my post was pretty rude and I had a reaction to it. Thus I responded with some snide remarks about your insistence on semantics while you yourself weren't concerned with them in your responses. Also my last response was clarifying your mistake in assuming that Equity=B/(2*B+P) is your cost. It is not. It is what you are calling cost RELATIVE to your reward which is a big difference.


In general:


When you're comparing your hand to a range (or range vs a range for that matter) your equity is just the weighted sum of the equity of your hand (or hands) vs all of the hands in villain's range.

To calculate the equity of a single match-up between hands you would do something similar to Brokenstars' method and calculate the probability of winning at showdown using outs or non-outs whichever was relevant and/or easier to use.

Since doing anything more than hand vs hand or hand vs a small number of hands is quite laborious and error prone, most people use pokersoftware called equity calculators.

Hi Johny / Just Grinding. As I say - better minds than mine keep telling me to ignore what's in the pot. I'll accept this advice (thank you!).

Johny - the confusion about my equity is because I made such a bad attempt at outlining the scenario in the first place. I tried to make this clear in post '10' but still made an error (I'm not use to explaining things in this form). But I'll try one more time to explain the 23% equity.

By the turn I have a set versus my opponents straight - I bet 30 and get check-raised shoved on (his total bet is $30 + $47 = $77, so I'm faced with calling off $47 to win $201.50 (two $100 stacks + blinds). my outs are FH + Quads which I think is approx. 23%.

If I had pot odds to call then I've just picked a bad scenario. The thrust of the question was what if I didn't have pot odds to call - should I still call if my loss would be less than the sum I've already invested.

Thanks to the responses I now know that the answer is "No" - "Look at the turn call/fold in isolation - and if I don't have a +EV call then it's a fold".

I think the confusion around 'where does 23% equity come from" is borne from the fact that I stuffed up in my very first post.

Anyway - thanks for clearing things up - much appreciated .....

One last 'Thank You' to Broken_Stars for his post 13 - yes, I agree that the sums stated make it a call - But I'd screwed up my explanation of his shove amount (it should have been $77 not $47).

I call off $47 into the $201.5 pot - which, I think, makes it a -EV call, but I get the point now and appreciate you taking the time to give a detailed response.

You should probably clarify when the opponent made the straight because in your initial post you mentioned the straight came on the river, but here you mention the opponent made a straight on the turn. These are different things and change the calculations.

The second thing you need to clarify if the opponent opened the cards face up and showed you his straight after his c/r.

From what I understand your problem is that you bet some amount on the river and your opponent x/r and you are wondering if it is worth to call the remaining $47. If that happens on the river then you are left with your hand reading skills to determine if your hand is the best hand on the river. If your opponent's hand is face up on the board obviously it is better to fold than call because you know your hand is second best. Otherwise there will be some math involved.

Do the calculation and then we will see if you understand.

47/201.5 means I need 23.3% equity to call

I have 22.78% so should fold

You won't end up having more $ by putting your money in bad. I replied to the following thread about the same subject and showed math, so maybe it will help:

http://forumserver.twoplustwo.com/32...uites-1554975/

Here, I'll do it using an example similar to yours:


$100 dollar stacks. We are now on the turn. Hero and villain have each put $50 in the pot, so the pot size is $100. Villain now shoves. Therefore, the pot is $150 and Hero must call $50, so Hero is getting 3 to 1. Hero has 23% equity.

If Hero folds, then he would have lost $50 on this hand overall.

If Hero calls, then the pot will be $200 and Hero has 23% equity so he will get from the pot 200 * 23% = $46. Hero started the hand with $100 and ends it with $46. So if Hero calls, then in the hand he loses $54 overall ($100 - $46 = $54).

So, if Hero folds, then he loses $50 overall in the hand and if he calls, then he loses $54 overall in the hand. Therefore, folding is $4 better than calling.


The way people usually do these calculations is that they just set fold to equal $0 as follows:

If Hero calls the pot will be $200 and Hero gets 23% of it. $200 * 23% = $46. Calling costs $50. $46 - $50 = -$4. If Hero folds, then he gets $0 from the pot and folding costs $0. $0 - $0 = $0. Therefore, folding is $4 better than calling. This is the same answer we got above.



Also, you could just know that if you have 25% equity, then you need 3 to 1 break even on a call and if you have 20% equity, then you need 4 to 1 to break even on a call, so if you have 23% equity, then you need between there to break even and not worry about the exact dollar amount that either calling or folding is better than the other.

$100 of that $200 was yours at the beginning of the hand. If you are going to calculate profit/loss for the hand overall, you don't count getting back your money as profit.

You actually win $100 23% of the time and lose $100 77% of the time.

($100 * 23%) - ($100 * 77%) = -$54. So you lose $54 overall when you call in this scenario. If you fold, you would have lost the $53 you have already put in the pot.

Finally I see the light! Thanks for this explanation - It was driving me nuts 'accepting' that a fold is correct, without actually understanding why. What I was doing was ignoring the fact that I was losing 77% of $100 rather than (in my mind) 77% of $47.

I get it now - thanks to everyone for the help - I can fold with a peaceful mind :-)

Nice explanation Lego, I should have taken that approach myself. Glad to hear you understand now NotTooEasy.