The Price We Pay

It’s been almost a year since my initial article on applying the Kelly Criterion came out. I think I’ve made a little headway in helping bettors to understand its impact, but apparently not enough. Many otherwise sharp guys are still singing the same tune they always have, and aren’t following the math. At least one thing we all agree on is that price is king when it comes to sports betting. They may think that a price is only good enough when it’s +EV, but in fact getting a price that’s pretty close to neutral EV can be very useful for hedging. No matter how you use it, line shopping is the key to getting the best price available.

My preferred line-shopping site is They have lots of other great features too, like an arb screen (or a value bet + non-valuable bet screen for those who still think arbing is throwing away profit) and a bonus cruncher to help convert free bets into risk-free money. If you want to try it, please consider using my referral link and tell ’em Dan sent you if you end up subscribing to the Plus account to get all the features:

Fever Dreams

As the annual World Series of Poker kicks into high gear, I’ve been tracking the action through twitter and must admit I’m sort of jealous that I’m not there during this once-in-an-orange-moon Halloween version of the event. This year there are no 115 degree days, or sunsets that creep down below the mountains at 8 pm so that the mercury drops below 100 by midnight (if you’re lucky). All that heat can sometimes make you a little crazy. But, when it comes to sports betting, there’s still a hot debate over which is crazier: risking a big chunk of your bankroll on a huge edge, or arbitraging to lock in a profit (at the expense of giving back some of that edge by betting a -EV line on the other side). It’s an argument as old as the Red Rock mountains.

Luckily, when you look at the issue in the correct way (i.e., the way that will grow your bankroll the quickest), the answer comes into focus. In order to maximize your expected growth you should….

read this article I wrote back in April:


This week the World Series of Poker 2021 started up. If circumstances were different, I would have liked to have gone. It’s been 15 years since I first went, and I’ve met and been beaten by many amazing people out there. Every tournament I played in, I felt I had an edge (and I’m pretty sure I was right). And yet I never cashed, let alone won. The variance got to me. After a few unlucky hands, the last of my chips were gone and I was out. I’m sure if they had let me borrow more chips from someone I could have made a comeback eventually, but that’s not how it works.

That’s not how it works in sports betting, either. In fact, even if you don’t go broke, every loss you take sets you back farther than the gains of every win. That’s how the math works. It’s a tough pill to swallow, even for the sharpest of gamblers, but sip on this article I wrote for the Pinnacle blog and see if you can make heads or tails of it.

Parlay Vous?

With the start of football season came the annual debate in sports betting circles: just how bad are parlays? Adding fuel to the fire were reports of an unnamed bettor who plunked down a $25 free bet on a 16-leg NFL parlay, trying to pick the winners of every Week 2 game. To make matters worse, he inexplicably picked the Lions over the Packers on Monday night! Miraculously, he won the first 15 legs, and then suddenly everyone on gambling Twitter was either screaming at him to hedge (because he probably had $600,000 laying around and a local book who was willing to take that much action on the Packers), or admonishing him for betting a 16-leg parlay in the first place. Why didn’t he just bet the first 15 games instead? Then he would already have won!!

That extreme case notwithstanding, parlays are in fact a double-edged sword. They amplify the hold for the books when you have no edge, because you’re essentially forced into betting larger and larger amounts as one winning bet rolls over into the next leg. On the other hand, when you have an edge on all the legs, your edges add together (approximately) to create a larger overall edge on the parlay. But with greater edge, comes longer odds….. and greater risk. How should you deal with that optimally? Of course, you can simply bet less, according to the simple Kelly Criterion (or a fraction thereof, if you’re smart). But a better way to play is to plan ahead for hedging out of the last leg, assuming you can reliably get low vig lines on that game if you’ve won the first (or first couple) legs. You will usually end up gaining more profit (and greater EG) by taking advantage of your edge on the last leg up front, even if you have to give back some of it to hedge out later. I call this technique the “Neutral Hedge Gambit.”

Originally published in the March, 2021 issue of the TwoPlusTwo magazine, here is my first article explaining why it works and how to do it:

The Swap Equivalent

Recently, the venerable Two Plus Two magazine met an untimely demise. It rarely had sports betting content anymore, but since I had a long standing relationship with them, that’s where I chose to put out my first few articles on sports betting as I uncovered the secrets about expected growth optimization and the benefits of hedging. This exercise eventually led me to formalize a quantity called the “swap equivalent,” and soon after to work out how to use it to calculate an actual cost to variance. Since the 2p2 magazine is no longer operational, I’ll post this article here for now so other truth seekers can see how I derived the swap equivalent. Read on and enjoy!

How It Started

At first, all I wanted to know was the answer to the question “does it ever make sense to hedge?” After mulling it over for a little while, this is the answer I worked out. Some may think it’s just “old wine in a new bottle.” But, if that were true, wouldn’t everyone know these answers already? Originally published in the TwoPlusTwo magazine, this is the article I wrote to try and explain my results. I have learned a lot since then, and in time I will share it all with you.

Why Do We Have To Manage Risk?

Photo by Deep Rajwar on

From the very beginning, we want to win. Famous coaches, venerated leaders, all encourage us to win. That’s why most people take up sports betting to begin with – they play to win the game, at least from their bar stool or arm chair. So, many bettors only focus on how much they can win and not how much they can lose. Sure, they have a vague idea that over-betting is bad and maybe they know about the Kelly Criterion and how to calculate it. But figuring out how much to bet, or risk management, is usually an afterthought.


  • Because it’s lame to think about avoiding loss
  • Because we’ve become convinced that finding +EV is the only thing you need to win
  • Because it’s been drilled into us as sports fans that the surest way to lose, is playing not to lose

Well, that may be true in the NFL (debatable), but it’s definitely not true in sports betting. Figuring out if a bet is positive expected value is very important, but it only takes into account one dimension of how to win in the arena of uncertain events. The other dimension we have to consider is risk.

If it weren’t equally as important to manage risk, then why wouldn’t the best play be to find the largest edge you can and bet your whole bankroll on it? It’s too risky. Eventually you will lose and go broke. Turns out that managing your risk doesn’t just keep you from going broke, it also optimizes how quickly you can grow your bankroll because every time you lose you have less to bet on the next edge you find.

This site will take a deep dive into the math behind optimizing the growth of your bankroll in different situations. Sometimes the answer will be bet less to begin with, but most bettors already understand that. Here, we will evaluate other ways to manage your risk, optimize your expected growth, and win more money by not losing as often.