Hello,

I would very kindly ask if anyone could clear up something for me. I am pretty much lost on the topic about the value to bluff ratio on the river(or basically any street) when betting.

If we (Hero) bets the pot on the river we have to construct our range in a 2:1 ratio, where 2 are our value bets and 1 are our bluffs -> that way we make our opponent indifferent between folding and calling with is bluff-catchers. Since by our bet size we are offering villain 2:1 odds on a call and cause our range is created in 2:1(value-bet to bluff ratio) the villain does not care if he calls or folds and neither do we.

Now, this bluffs to value bets ratio is also called Alpha, right?

In other literature (MoP) alpha`s formula is S/S+1 where S is a fraction of the pot when bet. Then (1-alpha) or the calling frequency for the player that has been bet into with alpha ratio of bluffs to value bets is 1/1+S.

So for example: I want to make you indifferent between calling and folding on the river. So I will bet with alpha % of bluffs and you will be calling me with (1-alpha).

I decided to bet the pot. Alpha = S/S+1 = 50%
So when I bet the pot on the river I will have half the time bluff and half the time a value-bet.
Now you have to be calling me with (1-alpha) or 1/S+1=50% because if you are not calling half the time I can just bet every time.

The idea seems to be similar then pot odds thing but the construction for both ranges is different. Here by using alpha we have 1:1 ratio of value bets to bluffs on a pot sized bet and not 2:1.

Could someone please explain this, I am very eager to learn and I am very confused now xD

Cheers

Alpha is the ratio of bluffs to value bets, not the % of your range that consists of bluffs. Here, α*[# of value combos] = [# of bluff combos].

You might want to re-check the definition of or formula for alpha. If you bet pot on the river with nuts and air, then a 2:1 ratio will make bluff-catchers indifferent. A 1:1 ratio will let bluff-catchers all call profitably.

Thanks for responding guys. Can any of you provide me with the correct definition of alpha. I would very much like to get this right. Will could you give a postflop example with certain bet size in order for me to understand this correctly. Ty in advance

I have come across some game theory lectures from MITpokerclass and watched some on their youtube channel. https://www.youtube.com/watch?v=VHcr...VVSeMw&index=8
This is Matt Hawrilenko`s video and my "alpha problem" is explained by him just they way I though it was. So this is wrong as Rei and Will said. In video 21:22 - 22:46 he says so.
Can you tell me whats right? I am confused and want to learn the proper way.
Cheers

alpha is the amount of bluffs you should have for each vbet. so for a = 1/2, you should have 1/2 as many bluffs as vbets, or in other words, 2 vbets for every bluff, or a 2:1 vbet:bluff ratio.

Thanks alot!

BOOM.

my brain hurts and I'm so confused when i see the word alpha.

so when we pot, the optimal value to bluff ratio should be 2:1, or 1:1?

If we hv value to bluff ratio of 1:1 villain call down super light right?

Half pot bet:

https://www.youtube.com/watch?v=j98QFH_Dc9A (25:34: bluff to value ratio for half pot bet: 1:2 according to this link)

http://www.runitonce.com/chatter/gto-simplified/ (optimal bluffing freq: 25%; which means 3:1 value ratio when we bet half pot)

The confusion is in the different way these terms are applied.

When you BET pot, then alpha is 1/2, which is correctly interpreted as "you should have 1/2 as many bluffs as value bets", or "you should have 1 bluff for every 2 value bets"

When you CALL a pot sized bet, (1-a) is also 1/2, but that is correctly interpreted as "you should call 1/2 of the time as to not be exploited (by any two cards)"

For a half-pot bet, alpha is 1/3 (1 bluff per 3 value bets), and (1-a) is 2/3 (defender calls 2/3 of the time to avoid being exploited)

Another question:

Does this optimum bluff to value-bets ratio only apply vs. an observant villain (one who will observe and exploit your weaknesses)?

In other words, if you play on an anonymous site (or zoom poker vs. a huge player pool), do you still have to place so many bluffs? After all, no one will notice and exploit you.

No you don´t. They don´t notice stuff like that. But still, understanding this concept give you the tools to let you know in what spots you can exploit your villains.

If you have reads on the population you should obv adjust your strategy. But be aware that if the population folds to much you will get exploitet.. In general you start with a balanced approach and than apply you reads on the population to get a decent gameplan vs unknown opponents..

So you have population reads right? i.e the population plays x spot y way. In some spots you think the population calls too much, some spots maybe you think they fold too much. And then in some spots you think they call/fold approx correctly.

So lets say you get a river spot and you have the nuts/air (specifically your valuebets always win and never get XR for simplicity sake).

$100 pot, you bet $100 (allin). You'll have 1 bluff for every 2 valuebets right?

So your EV (assuming this spot they call correctly--50% of the time):

So 33% (1/(1+2)) of the time you're bluffing. When* you're bluffing you get called half the time and lose and the other half they fold and you win. So of that 33% of the time your EV with bluffs is (.5*100)+(.5*-100) where 100 is the pot you win when they fold and -100 is the bet you lose when they call.
So for your bluffing section it would look like .33*[(.5*100)+(.5*-100)]=0!
So when you're bluffing, you dont lose, you break even. That is the point of them bluff catching you--to make your bluffs break even.

So 66% of the time you're valuebetting.
They call 50% and fold 50%. (.5*(100+100)+.5*(100)). When they call you win their bet and the pot.
So your valubetting section looks like .66*[(.5*(100+100)+.5*(100))]

Together add them up, and that accounts for the exchange of $ for every situation. Notice that if you didnt bluff, and instead checked and lost your EV wouldn't change! Id recommend doing a math tree of exactly what amt of $ exchanges with what frequency and sub*frequency (of my bluffing range this happens this often etc.)

Sorry for the long winded reply, maybe that helps some folks internalize what's going on and why.