• Bronze
Joined: 04.01.2010
I see people doing math where you get 38% equity against villains range but at the end, 3-bet is still profitable.

(As example, take a MP raising 5bb and u're at BU)..

I see all the math but i don't see any explanation about it...Could some math expert gimme that?
• 5 replies
• Bronze
Joined: 03.01.2011
Lack of equity can be made up for by fold equity, or a huge skill advantage in later betting rounds. Having fold equity just means that you can expect your opponent to fold some percentage of the time when you make a bet. If you've seen people argue that you have a profitable bet heads up with only 38% equity against the opponents hand range, it means they think that the opponent will fold often enough to offset this equity disadvantage.

For example, if I have 30% equity against you and make a pot-size bet (P), and we assume you always call, and then we stop all betting and just deal out the cards to determine the winner, my expected value in the hand is
(0.30)(2P) + (0.70)(-P) = -0.1 P
That means I'd expect to lose money making this move, which makes sense because I'm betting a lot without enough equity. But, suppose everything is the same and now I expect you to fold 20% of the time when I make this bet. Then my expected value is
(0.20)(P) + (0.80)((0.30)(2P) + (0.70)(-P)) = 0.12 P
Now the expected value of this bet is positive, even though my equity is negative.

(As a side note, notice that a bet being profitable doesn't necessarily mean it's the best move. It might be profitable but less profitable than checking for example.)

If you're asking where those formulas above came from, they're the standard way to compute expected values that you'd learn in an intro statistics or probability course. You can google "expected value" or something like "how to compute expected value" to learn about it, but basically it's just multiplying the probability of each event (e.g.: winning) by the positive or negative effect on you (e.g.: how much money you win), and adding them up.
• Bronze
Joined: 04.01.2010
Thank you for the answer...Puttin in a simpler way:

Pot is 100\$, i bet 40\$...
I'm risking 40\$ to win a 100\$ pot...

In ten times (10 x 40 = 400)...He has to fold MORE than 40% of the time to make profit?

Is that correct?
• Bronze
Joined: 03.01.2011
If you're making that bet purely as a bluff, then you can figure out the required percentage of the time he has to fold by solving for x in
(x)(100) + (1-x)(-40) > 0
which simplifies to
x > 40 / (100 + 40)
x > 0.28
so 28%

If you don't want to deal with that equation and want to think of it in terms of odds: you notice that you're giving yourself 100:40 odds with your bet (you bet \$40 to try to win \$100), so you need 100:40 odds that he folds (and you win). That simplifies to 2.5:1 odds, so you need him to fold 2.5 times for every time he calls. (And double checking, that gives 1 / (2.5 + 1) = 0.28, so fold 28%).

Bluffs like the one above are an example of how you can have profitable bets even with 0% equity. As you see, if they fold at least 28% of the time, we can make this bet regardless of the hand we actually hold, and we'll still expect to make some money in the long run.
• Bronze
Joined: 04.01.2010
Thanks again bro, i still don't get it 100% but i get the "principle" now....

Thx a lot
• Bronze
Joined: 17.01.2010
Some threads what may help you, its really important to get understand of this things to become good poker player:

http://www.pokerstrategy.com/strategy/bss/1563/1/
http://www.pokerstrategy.com/strategy/bss/1564/1/