"Buy the $100 call, sell the $105" tells you nothing until you know where the stock is, how much it moves, and how long the options last. Delta fixes that. Choose strikes by delta and one rule means the same thing on every stock, at every price, on every expiration.
Delta as a probability
An option's delta doubles as a rough estimate of the chance it finishes in the money. A 0.50 delta call is a coin flip. A 0.25 delta call has about one chance in four, and a minus 0.25 delta put about one in four on the downside. It is not exact, since it ignores skew and drift, but it is close enough to size a trade by.
A $100 strike with 30 days left, against the stock price. The two lines sit close together, so delta works as a quick probability. Raise volatility or days and the gap widens a little; switch to puts and both lines turn negative in delta and flip in probability.
A call's delta sits a little above its chance of finishing in the money, and the gap grows with volatility and time: a 0.25 delta call has nearer a 22% chance. For choosing strikes that gap rarely matters. What matters is that delta turns a dollar strike into odds you can compare across stocks.
Why a dollar rule fails
Take a strike 10% above a $100 stock with 30 days left. At 20% volatility its call delta is about 0.06, a long shot. At 30% it is about 0.15. At 50% it is about 0.28, near the classic short strike. The same "10% out" is three different trades. A rule written in delta adjusts itself: on the quiet stock the 25-delta strike moves in toward the money, on the wild one it moves out.
Call delta against implied volatility for strikes 5%, 10% and 20% above a $100 stock. Follow 0.25 across: it lands at a different strike for every level of volatility. Drag days up and every line rises, because more time means more chance to get there.
The long strike
For a debit spread, start with the long strike. At the money, delta 0.50, is the usual choice: you pay for no intrinsic value you do not need, and the spread sits centered where its vega nets out. Going in the money to 0.60 or 0.70 delta costs more but starts you ahead. Going out to 0.30 is cheap but needs a move just to reach your own strike. Decide how much of the move you want to pay for up front, and let delta name the strike.
The 25-delta rule for the short strike
For a credit spread the short strike is the decision. A widely used starting point is to sell the option nearest 25 delta. Read the delta as a probability and the logic is plain: about one chance in four that the stock reaches your strike, so about three in four that the spread expires and you keep the credit. Sell at 10 delta and you win more often but collect far less. Sell at 40 delta and the credit is fat but you are fighting a near coin flip. Most traders find the balance around 25.
The delta of the spread
A spread's delta is the long leg's delta minus the short leg's. Buy a 0.50 delta call and sell a 0.30, and the spread gains about $0.20 for each $1 the stock rises. There is a second reading. The short strike's delta is the rough chance the stock finishes beyond it. For a credit spread that is the chance of trouble, so one minus the short delta is the rough chance of keeping the whole credit. For a debit spread the short delta itself is the rough chance of collecting the full width.
Net delta of the $100/$105 call spread with 45, 15 and 3 days left. Hover at $100 to read about 0.2 with a month out. Near expiry the hump sharpens between the strikes; raise volatility and it spreads out and flattens.
The spread's delta is a hump, not an S-curve. It peaks between the strikes, and fades to zero on both sides, where the spread is already worth nothing or its full width. Its height is capped well below one, which is the price of the capped payoff: you get some of the move, never all of it.
Width versus cost
Keep the long strike and push the short strike further out. The spread gets wider, the debit rises, the max profit rises faster, and the breakeven barely moves. Widening a $5 spread to $10 costs more but less than twice as much, because the extra width is added further out of the money where the call you stop selling was cheap. The catch is that the full payoff now needs the stock beyond the higher short strike. Go narrow and you pay little, but the most you can make is little too. The width sets the size of the trade; the strikes set its odds. Pick the odds first, by delta, then size with width.
The numbers behind that, with 30 days left and 30% volatility on a $100 stock: the $100/$105 call spread costs about $1.93 for a max profit of $3.07 and a breakeven of $101.93. Widen it to $100/$110 and it costs about $2.94, about 52% more, for a max profit of $7.06 and a breakeven of $102.94.
The maths: delta, the chance of finishing in the money, and the spread
In the pricing model a call's delta is N(d1) and its chance of finishing in the money is N(d2), with d1 = [ln(S/K) + (r + v²/2)·T] / (v·√T) and d2 = d1 - v·√T. S is the stock, K the strike, v the implied volatility, r the rate, T the years left and N the normal curve's cumulative probability. Since d2 is always below d1 by v·√T, the call's delta is always a bit above its chance of finishing in the money.
Worked example: S = $100, K = $105, v = 30%, r = 4%, 30 days (T = 0.0822). ln(100/105) = -0.0488 and (0.04 + 0.045) × 0.0822 = 0.0070, so the top is -0.0418. v·√T = 0.0860. d1 = -0.0418 / 0.0860 = -0.486, so delta = N(-0.486) = 0.31. d2 = -0.486 - 0.086 = -0.572, so the chance of finishing above $105 is N(-0.572) = 0.28.
For a spread, long K1 and short K2: spread delta = delta(K1) - delta(K2). With the $100 call at 0.53 and the $105 at 0.31, the spread's delta is about 0.22. The chance it pays the full width is roughly the short strike's N(d2), 28% here.
Your turn
Find the 25-delta strikes on the AMZN chain, then read short-strike deltas on META and SPY and turn them into probabilities. Notice how far from the stock price the 25-delta strike sits on each name. That distance is the stock's volatility, written in strikes.