My poker theory math is screwed up, can someone please clear these doubts?

bump

I'll address a part of your question,

Originally posted by maheepsangari
So when BU calls a 100% of CO's river bets and when CO bets the river according to the equation CO need to win 33% of the time, right? I know my conclusion is completely wrong as CO needs 33% of his range to be bluffs and rest to be value so where am I screwing this up?

CO needs 25% of his range to be bluffs actually, in order to make BU's bluffcatchers indifferent to calling or folding.

Eg. If CO bets 50 into 100 pot, and he is bluffing 1/3 of the time, BU should call 100% of the time w his bluffcatchers as its +EV. BU should only be right 1/4 of the time.
If CO is bluffing 1/4 of the time, calling or folding bluffcatchers is the same for BU.

Hope this helps.

Can you show this with an actual equation? Like I showed you how I came to the fact that CO needs 33% folds and BU needs to win over 25% when he calls using the equations I did, can you show me why you say that its 25% and not 33% for CO?

question 1
the 33% is how often opponent needs to fold for your bluffs to be succesfull
if he calls 100% you win more on your value hands so it equals out. but your ev calculation is only shows the EV of your bluffs if you want to see your overall EV you should extend the equation to include valuehands

its the value to bluff ratio that is 33% 25%/75% =0.33

0.25 is bluffs and 0.75 is valuehands

x(1)-(1-x)0.50*0.25 + (1-x)*1.5*0.75=0

question 2
your calculation is right the number is not too low

With a half pot bet

1a. The bettor needs at least 33% FE in order to breakeven on his bluffs
b. Thus, the defender must look to defend 67% of his range to deny the bettor the opportunity to auto-profit on his bluffs

2a. The caller is receiving 25% pot odds on a call
b. In order to make the caller indifferent between calling and folding, the bettor must design his betting range such that the caller's bluffcatchers have exactly 25% equity on a call (75% value, 25% bluffs)

These 2 numbers are not directly related.

If defender knows the aggressor's actual betting ranges or can make a very strong educated guess, his decision is simple.
Call if equity >25%
Fold if equity <25%

If defender is not sure about the aggressor's actual betting ranges, then he looks at his own ranges and defend the top 67% of his bluffcatch range to deny the bettor an opportunity to autoprofit with his bluffs.

Originally posted by mbml
With a half pot bet

1a. The bettor needs at least 33% FE in order to breakeven on his bluffs
b. Thus, the defender must look to defend 67% of his range to deny the bettor the opportunity to auto-profit on his bluffs

2a. The caller is receiving 25% pot odds on a call
b. In order to make the caller indifferent between calling and folding, the bettor must design his betting range such that the caller's bluffcatchers have exactly 25% equity on a call (75% value, 25% bluffs)

These 2 numbers are not directly related.

If defender knows the aggressor's actual betting ranges or can make a very strong educated guess, his decision is simple.
Call if equity >25%
Fold if equity <25%

If defender is not sure about the aggressor's actual betting ranges, then he looks at his own ranges and defend the top 67% of his bluffcatch range to deny the bettor an opportunity to autoprofit with his bluffs.

This really helped clear things up. Thanks a lot.

So the primary purpose of the first equation is to figure out what % the BU needs to defend basically (not just what FE CO needs, just another way of looking at it basically) and work accordingly.

The second equation helps us determine what bluff:value ratio the CO needs and what equity the BU needs to make the river call.