The Math of the Odds Boost

Let’s play a game. I have a stack of 50 $20 bills. Let’s assume you also have $1,000 worth of $20 bills. We flip a coin, you call heads or tails, and we bet $100 per flip. After one flip, one of us is going to be up $100 and the other one will be down $100.

If we keep going, do you think eventually one of us gets all the money the other guy had? Statistically speaking, it’s highly unlikely. In order for that to happen, one of us would need to win 10 times more than they lost. Considering a coin flip is as true a 50/50 proposition as you can get, that would require an unlikely statistical anomaly. The more we flipped the coin, the more likely the peaks and valleys would smooth out over time. After hours of flipping, we would both probably end up right around where we started with $1,000 worth of pictures of Andrew Jackson. 

Now let’s assume in order to make it fair, we hired a person to flip the coin for us. We have to pay this person 5% of any winning wager. Now instead of betting $100 to win $100, the winner still profits with $95, but the flipper takes $5 every time. The flipper doesn’t care who wins, because they get 5% from the winner either way. Let’s play this out a bit further. I win the first flip and you win the second. Without the 5% fee, we would be right where we were in Example 1, with $1,000 each. Unfortunately, we both had to give $5 of our winnings to the flipper when we won. Now instead of $1,000 each, we both have $995. If we decided to continue to play for an hour, we would both likely end up with around the same number of wins and losses. Let’s say we could flip that coin 200 times in an hour. It is a true 50/50 proposition, so we both ended up with 100 wins and 100 losses. Remember we lose $100 when it comes up opposite our call. We win $95 when we are right with $5 going to the flipper. We flipped the coin 200 total times, meaning the flipper now has 200 times $5 or $1,000 of the money we combined to have in play. That would leave each of us with $500 of our original $1,000, even though we had the same exact number of wins and losses we had in the first example. This is the business model of sportsbooks. In this example, they are the flipper and that is why the house always wins eventually. 

But what if the house is not interested in winning? What if they were more interested in making you feel like a winner so you stay at their book and keep betting more? What if they offered you a bet where the more you did it, the more money you would be expected to win? What if I told you, this is exactly the case with odds boosts? Now do I have your attention?

Sportsbooks are in the business of making money, but you have to spend money to make money. The model relies on having winners and losers, but having enough of both that they can get action on both sides and take a cut no matter what the outcome is. In order to do that, they need people to use their product. In order to entice people to do so, they offer odds boosts to help you beat them. I know it sounds crazy, but think about the alternative. They could spend billions in advertising and hope that those ads bring in business OR they could just give the money directly to you, the gambler, with the expectation that eventually you will make enough bets that they take a piece of to earn it back. So let’s take a look at how this works out. 

Remember our coin flip example? We’re going to tweak the rules again here for Round 3. We are still betting $100 a flip. This time, instead of winning $95 and losing $5 to the flipper, the payout is going to be $120 to the winner instead of $100 split 95%/5% between you and the flipper. If I win the first flip, I would now have $1,120 and you would have $900. If you win the second flip, we would both have $1020. Remember we each started with $1,000 and each won one flip and lost one flip. Yet because of the odds boost we are both now profitable coin-flip bettors. Let’s continue to play this out. If we flipped the coin 100 times, we would both win about 50 flips and lose about 50 flips. On the 50 losses, we would lose 50 times $100 or a total of $5,000. On the 50 wins, we would win $120 each flip times 50 or $6,000 total. At the end of the day, we would have a profit. Our winnings of $6,000, minus our losses of $5,000 would leave us with an extra $1000 each above where we started. On a 50/50 proposition after 100 flips, we would both have grown our initial $1,000 bankroll into $2,000 for a 100% profit each. 

Expected Value

The difference in the three examples can be explained by a concept called expected value. You may have heard the term +EV before and this is what that is referring to. In the first example, you have an expected value of zero. The bet is a true 50/50 proposition, and you get paid out even money on your $100 bet, meaning you bet $100 to win or lose $100. If you flip the coin twice, you would expect it to land on heads once and tails once. If you constantly call heads, you would expect to win one flip and lose the other. In a small sample of two flips it is possible that the coin lands heads twice or tails twice. If your sample size is big enough though, you would expect the number of times heads and tails come up to be exactly the same. Each win is +100 and every loss is -$100, so at the end of the day you would expect what we saw in the first example. Both people would have the same amount of money in the end because they expected value was zero and they both won as many times as they lost. 

In Example 2, you would have a negative expected value. Every time you lose, you still lose the same $100, but now when you win you only win $95 with the flipper (the sportsbook) taking $5 as his cut for hosting the bet. That means if you win one flip and lose the next for $100 per toss, you would expect to end up with $195 on $200 wagered. So per bet, you would expect to lose $2.50 every time the coin is flipped. If you only flipped the coin once and won, you would be up $95. Remember though this is a small sample size. Over the long run you would also expect to win as often as you lose on a true 50/50 proposition. If you flipped the coin 100 times in this example, you should expect to be down $250 at the end of that 100 flips. You would still lose the same 50 flips at $100 per flip or $5,000 total. When you win 50 times in Example 2, you get $95 each win, or $4,750. $5,000 in losses minus $4,750 in winnings would equal that expected loss of $250. Why would anyone want to play by these rules if the expected outcome is you slowly losing your money until the entire bankroll is depleted?

Now let’s take a look at our third example and the only +EV situation. In this example, every time you bet $100, you win $120 if you are right. When you guess wrong, you only lose the $100 that you bet. Assuming the same two flips with one landing on each side of the coin you would have won $120 and lost $100 for a $20 profit. A $20 profit on two flips would mean you won $10 per flip. That means per $100 bet, your expected value would be $10 per flip. If you flipped this coin 100 times at +$10 EV per flip, we would end up with $1,000 as we did in Example 3. If we flipped the coin 500 times, we would expect a profit of $5,000 ($10 times 500 flips). Remember in this example we still won only half the time. On 100 flips we won 50, but still lost 50. The difference is due to the payout we made a profit on $10 per flip on average. 

When a sportsbook offers you a profit boost, this is exactly the situation they are putting you in. You are now expected to make a profit on these boosts over time. Remember, you are not going to win every odds boost bet you make, but that is not the point. You do not need to win every one of those bets in order to end up growing your bankroll. You just need to win enough of them so that your profit on the wins covers your losses with money left over. In a small sample you could win or lose a bunch of bets in a row, but over the longer term you should end up around the break-even percentage that the true odds of the bet have. If the book is willing to pay you out more than you should be receiving on those true odds, then you should end up with more money than you started with. If every one of these bets is +EV, you want to make as many of them as you can, as often as you can, for as much money as they will allow you to bet in order to grow your bankroll the fastest. If you make 10 bets, each with an expected value of +$10 per bet, you should expect to grow your bankroll by $100 (10 bets times $10 each bet on $100 bets). If you make 100 of them, you should expect to grow your bankroll by $1,000 (100 times $10 per bet on $100 bets). 

No matter what book you look at or what state you play in, they are all offering these odds boosts on a daily basis. Without knowing anything about the sport or the teams, blindly betting nothing but +EV situations at the end of the day will help you grow your bankroll. Seasoned sports bettors can find and take advantage of +EV situations without needing odds boosts, but it takes time to learn how to capitalize on those for someone new to betting. These odds boosts offered by the various online sportsbooks are an easy way for new players to start to get a feel for the game and build that bankroll by staying in situations where every bet they make is expected to be profitable. Use them to start to learn how sports betting markets work, while also building up your bankroll as you begin to understand how to find +EV bets in the broader market of available plays. If you combine this odds boost strategy with the bonuses these sites offer on your first-time deposit, you will be able to double your bankroll faster and with less downside risk. You are not always going to be on the right side of games you bet, but as long as the payouts have positive expected value, you will be able to grow the bankroll in the long run.