Most of the time, when placing bets, we focus on finding opportunities with positive expected value (EV). This approach ensures that, in the long run, we make more money than we lose. However, when it comes to free bets, the strategy should shift slightly because the expected results formula changes.

### Understanding Expected Value (EV) for Normal Bets

For a normal bet, calculating the expected profit follows a straightforward formula:

**Expected Profit = win_probability * to_win + push_probability * 0 + lose_probability * amount_risked**

In this equation, the "amount_risked" plays a key role in determining the potential loss, as it's the amount of money you're staking. If you lose the bet, the full amount risked is gone. However, with a free bet, there's no risk since you aren't putting your own money on the line.

### How Free Bets Change the Equation

With a free bet, the "amount_risked" is effectively $0. This changes the expected profit formula because there’s no personal financial loss if the bet doesn't hit. Here's the adjusted formula for free bets:

**Expected Profit (Free Bet) = win_probability * to_win**

Since there's no loss associated with the bet, the only thing that matters is the potential winnings. This key difference allows for a more aggressive strategy, and it means you should be aiming for longer odds with your free bets to maximize potential gains.

### Example of Two Bet Options

Let's consider two different betting scenarios where we have a $100 free bet to use.

**Bet 1: The 49ers are -250 against the Rams**

The No-Vig line for this bet is -303.6, implying a 75.2% chance of winning. In a standard betting situation, this would be a relatively safe pick, as the high win probability aligns with a positive expected value. However, for a free bet, the expected profit looks different.

- Win Probability: 75.2%
- Odds: -250
- To Win: $100 / 2.5 = $40

For this bet, the expected profit would be:

**Expected Profit = 0.752 * $40 = $30.08**

**Bet 2: A 4-Team Parlay at +1000**

Now, let’s consider a riskier option. We could place a 4-team parlay with odds of +1000. The No-Vig line suggests the implied probability of winning this parlay is 8.33%. While this seems like a long shot, it's actually a more profitable use of the free bet.

- Win Probability: 8.33%
- Odds: +1000
- To Win: $100 * 10 = $1,000

For this bet, the expected profit would be:

**Expected Profit = 0.0833 * $1,000 = $83.30**

### Why Bet 2 is a Better Use of a Free Bet

Even though Bet 2 has a much lower probability of hitting, it offers significantly higher potential winnings. Since there is no risk of losing your own money with a free bet, placing it on a higher payout option like the parlay can yield much better results. In this case, the expected profit of Bet 2 ($83.30) is substantially higher than Bet 1 ($30.08), even though the parlay is far less likely to hit.

The key takeaway here is that free bets are unique in that they eliminate downside risk. As a result, taking a more aggressive approach with longer odds can maximize your potential profits without increasing your financial risk.

### Conclusion

When using free bets, the standard approach of playing it safe and focusing solely on positive EV may not be the best strategy. Instead, * it's often better to seek out longer-shot odds*, like parlays or high-payout underdog bets, where the potential return outweighs the lower win probability. Free bets give you the flexibility to go after bigger wins without the downside of risking your own money, so take advantage of them strategically to maximize your profits.