The Mathematically Optimal Way to Use Your $250 ESPN BET Sign-Up Bonus

ESPN BET is now live in 17 states, and thousands of users will be rushing to jump in and claim their ESPN BET promo code for $250 in bonus bets.

But just take a second. Don't rush. And make sure you're using your $250 bonus bets in the optimal way.

First, make sure you click sign up, even if you have an old Penn account, and not login. Input your same email, and then you'll be prompted to login.

How do ESPN BET bonus bets work?

It's fairly simple. You keep any profit from the bonus bet, but not the bonus bet itself.

Say you put $100 worth of bonus bets on the Steelers to beat the Browns at +160:

• If the Steelers win, you profit $160 in cash ($100 x 1.6) but you don't keep the $100 bonus bet.
• If the Steelers lose, your bonus bet just goes away.

Learn about American odds first if you're unsure what +160 means.

So what's the optimal way to use your ESPN BET promo?

Many users feel like they need to "lock in" cash from their bonus bets by betting a big favorite at -200. But that's not what the math says.

The mathematically-optimal way to use bonus bets is on plus-money wagers between +300 and +500. Because you're not getting your stake back with bonus bets, you'll always get more expected value betting something at longer odds than a big favorite.

A brief detour on expected value…

Expected value is just probability multiplied by profit. If I flipped a coin and got paid $2 for every heads and $0 for tails, the EV of every flip is $1 — $2 x .5 (since there's a 50% chance it lands on heads).

You're still winning either $2 or $0 on every coin toss, but the EV is $1 because over 1,000 flips, you'd expect to win 500 and lose 500. That would result in $1,000 over 1,000 flips.

OK, now back to sports. There's a lot going on in this chart below, but it's just like the coin toss example. If you bet a $50 bonus bet on each of these lines — -250, +250 and +500 — you're going to get more expected value the higher you go (again, we're just multiplying the probability times the win amount to calculate the EV).

If you go even higher, you can get even more expected value, but in sports betting, you only have a finite number of bonus bets.

How much cash can I expect to win using this method?

Over a large sample, bonus bets turn into cash at about a 70% rate if you use them optimally. So with $250, you'd get back about $175 in cash.

But if all your bets lose, you can get back $0. If they all win, you can get back much more. You'll have big swings betting at +300 to +500.

3 ways to use ESPN BET bonus bets on Tuesday

If you suffered through the math or just skipped it, you've now gotten to the good stuff. Here are three games that check the optimal bonus bet boxes:

• Between +300 and +500
• Two-way markets (meaning there is an available bet on the other side; if you bet on aliens to invade earth at +500 but there's not a "no" offered, that's probably a bad bet).
• It's one of the better prices, or the best price in the market (if ESPN BET has the underdog at +325 and the best price at any sportsbook is +330, that's a good bet).

If the lines have moved or you want to bet something else, of course feel free — these are just the mathematically optimal rules to follow.

Bet 1: Wagner +400 vs. Rhode Island (CBB Tuesday)

We've got a good number to target at +400, and ESPN BET has the best price in the market.

Bet 2: Central Michigan +320 vs. Ohio (CFB Wednesday)

CMU travels to Athens to take on Ohio in Wednesday night MACtion, with the Chips priced at +320. Again, ESPN BET has the best price in the market at +320, with most other books between +290 and +305.

Bet 3: Titans +250 vs. Jaguars (NFL Sunday)

ESPN BET has (tied) for the best price in the market on this game, and there's no market more efficient than NFL. It doesn't quite hit the +300 mark, but