@wxytrader it’s very straightforward, you just need to abstract yourself from “probability” for a moment.
1. a call spread and put spread with the same strikes is the same thing in terms of the payoff - you make money linearly from k_low to k_high and are flat outside of this range. You can draw that on a napkin and prove to yourself that it’s true.
2. the premium for call spread and put spread are going to add to the difference between strikes, with a spread that has higher moneyness having bigger upfront premium. Again, you can prove it to yourself by taking two calls and using put-call parity to convert each price to a put with the same strike.
3. the only “miracle” here is that your upfront premium is discounted by the interest rate which is why if you combine two spreads in a box, you’re guaranteed to make roughly the prevailing funding rate. If you take a market price of that structure (it’s called ze box), you can take the difference between strikes, divide by the premium and, after multiplying by appropriate year fraction (eg 1 month box you’d multiply by 12) you will back out interest rate.