In control variate technique we have to calculate $$b=\frac{\text{cov}\{{X,Y}\}}{\text{var}\{{X}\}}$$ where $X$ is a payoff from standard call option and $Y$ is a payoff from for example barrier option. Why we have to estimate $b$ before we use this method and we cant use payoffs which we use during pricing? Or maybe I can first calculate the payoffs for these options, then based on them, calculate the option price, and finally calculate $b$ using the same payoffs and change the price of the barrier option accordingly?

In control variate technique we have to calculate $$b=\frac{\text{cov}\{{X,Y}\}}{\text{var}\{{X}\}}$$ where $X$ is a payoff from standard call option and $Y$ is a payoff from for example barrier option. Why we have to estimate $b$ before we use this method and we cant use payoffs which we use during pricing? Or maybe I can first calculate the payoffs for these options, then based on them, calculate the option price, and finally calculate $b$ using the same payoffs and change the price of the barrier option accordingly?

EDIT: My current problem: I try to calculate value of Up and out call option using MC simulation. I use three methods: 1) standard Monte Carlo, 2) anthitetic variates MC, 3) control variates MC using standard call option. The correct price in BS model is $1.3341$. My three methods (with the same parameters and number of simulations equal $100000$) gives me these results:

1. MC: $1.3621$

2. Antithetic MC: $1.3763$

3. Control variates MC: $1.3703$

Is it normal that using standard MC I get the best price?