Hello i would like to know the equation that is used to calculate what value/bluff ratios we need for different sizes. lets say we bet 33% on the flop what ratio of value/bluff do we need to stay balanced? How about if after cbeting flop 33% we cbet turn 60% whats the optimal ratio than?

If all of your value hands beat your villain's calls and all of your bluffs lose to villain's calls, then the ratio is simply the same as the odds/equity villain needs to call.

For example if you bet pot then villain is getting 2-1 on a call. You then need to have 2 value bets for every bluff or roughly 33% of your range needs to be bluffs.

In reality it's not always quite that simple because your bluffs will sometimes have equity and your value bets may sometimes lose or be behind when called.

This abstraction works best when the equity of your hand or the equity required to play is clearly defined (i.e. on the river or in all in situations) and poorly when more betting can occur.

Yeah I get that, thats precisely why I mentioned flop/ turn because these are the streets that I am having most trouble with. Are there any guidelines/tools with which I can at least come closer to solving this?

Yes there is software like GTO+, piosolver, etc. See my response to a similar thread in the theory subforum why the ratio thing isn't really a thing outside of the scenarios I mentioned.

Future betting does make early street EV analysis somewhat questionable. I consider it a first cut look at a math-based decision approach noting that equity realization is an important factor There are several possibilities for (partially) addressing the issue.

.If the bet is all-in or if it is reasonable to assume the hand will be checked down, then the issue goes away.

.If on the turn, you can make several assumptions on what villain may do on the river given a possible action on your part and weight the results by your estimate of occurrence probabilities.

.You can do an implied odds analysis when you have a good drawing hand which considers potential wins (and losses) if you hit the draw on the next street and bet big.

.If villain tends to bet a constant factor of the pot then you can determine on an early street the correct pot odds and equivalent equity you need to make the call that anticipates future bets. The same approach applies if it is you making the bets and villain calling. This approach is suggested with some reservations as it assumes a lot.

Example: It is the turn and TurnPot is 100. Villain over-bets to 150. What equity is needed for hero to make a +EV turn call if villain were to make a bet on the river equal to 1.5 *RiverPot that hero will call?

Answer: The pot into the river with hero calling is 100+150+150 = 400. On the river, villain would bet 1.5*400 = 600. The amount hero would win is 100 + 150 + 600 = 850 and he would risk 150 + 600 = 750. Therefore, his pot odds considering both streets are 850/750 = 1.13. These pot odds require a 47% showdown equity for +EV.

V% = (PS+BS)/(2BS+PS)