How to Beat the Bookies with Accumulators & Help Your Account Life | The Neutral Hedge Gambit

Written by Dan Abrams - @DoctorRazzWSOP on Twitter

What’s the only thing better than finding a great value bet that gives you massive expected value (+EV), while taking back some of the profits from the bookies? Finding two or three of them! Trademate Sports specialises in finding these bets for you and giving you guidance on how much to stake on them to optimise your bankroll growth. When done right, their value betting method will produce exponential growth of your bankroll, as long as the variance doesn’t knock you into a downswing. Alex Vella, Marketing Manager of Trademate Sports & part-time Professional Sports Bettor, has been very successful with this method in his own betting, and has limited his variance by staking at 30% of the full Kelly fraction that Trademate calculates for you. Recently, though, I’ve been showing him a different way to limit variance when putting two or three bets into an accumulator, that I call the Neutral Hedge Gambit (NHG). And while it may have a little more variance initially, this method can grow your bankroll much quicker, even if the edges on each leg of your accumulator are smaller than expected.

How does it work?

Normally accumulators are a terrible idea, because the house’s edge on each bet adds together into a larger house advantage. Recreational punters often love to build these kinds of parlay bets, so by doing that you may look more recreational to the books and keep your accounts under the radar for longer. The basic idea of my method is that, when Trademate shows you several trades at the same bookmaker that all have a decent edge, you can combine two or more of them into an accumulator bet with an edge even bigger than for each individual trade. The downside to combining them, though, is that you end up winning your bet a smaller fraction of the time and need to stake a small percentage of your bankroll if you just let it ride. The NHG method allows you to still win most of your value, even when the last leg of your accumulator loses, by showing you how to stake more up front and then optimally hedge against it with a neutral EV hedge bet. This means you’ll win less when all your legs win, but you will still win something as long as only the last leg loses. Even if you have to make a slightly -EV hedge bet at the end, on average you still come out way ahead of flat staking techniques or even fractional Kelly staking (which was designed for making one bet at a time, not for accumulators!). In this article I’ll show you step-by-step instructions for how to stake your accumulator, as well as how to stake your hedge bet, and present some simulated results to show you just how powerful this technique can be.

Staking the Accumulator

To stake your accumulator, you don’t use the conventional Kelly method, but since the NHG method is based on the same principles as Kelly staking, all you have to do is run a couple of Kelly fraction calculations to work it out. It just takes three easy steps to do it:

  1. Calculate the full Kelly fraction
  2. Calculate the parlay Kelly fraction
  3. Divide #1 by #2

parlay example

Take, for example, this accumulator (or parlay) bet Alex was looking at. (Please note that while these are real lines that Trademate alerted him to, this is just an example and the results of these bets are irrelevant). The real odds available to him for the two legs combined were 5.76, while the fair odds were 5.088. This is a very big +EV trade, since the true win % is 1/5.088 or 19.65% and the edge is 13.3%. So for Step 1, you enter the true win % and the real odds of 5.76 into a Kelly calculator, which gives a full Kelly fraction of 2.79%.

Step 2 is just as easy, as long as you understand what the parlay Kelly fraction represents. It isn't an amount to bet, it's an adjustment factor that shows how much risk will be left after hedging. To calculate it, you use the same Kelly calculator with the real odds of your parlay, but plug in the probability of success for just the last leg. You can determine this probability by inverting the fair odds of Leg 2, which in this case gives 1/2.06 or 48.5%. Then, using the Kelly calculator with odds of 5.76 and probability of 48.5%, you get a parlay Kelly fraction of 37.74%.

Step 3 is easy as pie: divide Step 1 by Step 2. So 2.79%/37.74% gives 7.39%. That’s the fraction of your bankroll to stake to do a full NHG bet. I know that’s a big chunk to bet on a 4:1 shot, but remember you’ll be locking up a certain amount of profit if Leg 1 wins, so you win something more than 40% of the time. Still, as with full Kelly, this amount can be very risky if your edges are even slightly off or you have a streak of very bad luck, so it’s much safer to stake at a half NHG amount (which in this case is 3.69%).

Staking the Hedge

If Leg 1 wins, then staking your hedge is almost as simple. Again, the process takes three steps:

  1. Calculate the full Kelly fraction for your hedge
  2. Calculate the hedge factor
  3. Add #1 to #2

Since Leg 2 of your parlay is Begu +3.5 games, your hedge bet would be on his opponent -3.5 games. Alex noted that the best odds for this side were 1.87 at closing, but since they may change over time, you should always use the latest real odds and fair odds to make your calculations. Since the true win % for Leg 2 is 48.5%, the true win % of your hedge must be 1-p, or 51.5%. Combined with real odds of 1.87, plugging these numbers into a Kelly calculator gives you a Kelly fraction of -4.28%. Normally, you’d look at this and say “this bet must be -EV, so I shouldn’t make it at all,” but because it’s a hedge you will just end up staking less than you would if it were +EV or neutral EV.

For Step 2, you calculate the hedge factor, which is the probability of success of your hedge times the potential payout of your original accumulator (as a percentage of your bankroll). The potential payout of your accumulator is 5.76 (the real odds) times your half NHG stake of 3.69%, and 5.76 x 3.69% = 21.3% of your bankroll. The probability of success of your hedge is 51.5%, so your hedge factor is simply 51.5% x 21.3% = 10.9%.

For Step 3, you add them together and bet full Kelly on the hedge (since you're doing it to reduce risk, there's actually LESS variance than by using fractional Kelly here). So add 10.9% to -4.28% and you get about 6.6% of your bankroll, so that's how much to stake on the hedge. Again, if the real odds (and/or fair odds) have changed by then for Leg 2, then use the updated odds to calculate your hedge stake. (Note that you can use this hedging calculation for any bet, not just NHG accumulators, but it’s very important to do with the NHG to reduce your risk and make sure you’re not over-betting).

But how much do you win?

In order to compare how much bankroll growth you can expect when using the NHG to your growth when using more conventional methods, I ran some simulations to see what happens if you bet this accumulator repeatedly over a sample of 5,000 bets. I started with a bankroll of $1.00 and did 10 runs where the staking method (either 50% NHG, 30% Kelly, or flat $0.01 staking) was different, but the results of each leg of the parlay were the same. I plotted the results of the 30% Kelly method and the flat staking method for only one of the runs, which was one of the “luckier” runs overall. In order to fit all the curves on one graph, I used a logarithmic scale for the y-axis, meaning each horizontal line is 10x greater than the last one. On this kind of scale, true exponential growth would look like a straight line going diagonally up.

parlay results

Flat staking by betting 1% of your initial bankroll produced a reasonable return of more than +700% and would have left you with $8.82. For the exact same outcomes, you could have turned $1 into over $277 by using the 30% Kelly staking method. On the other hand, your median ending bankroll when using 50% NHG would be about $30,000, and 2 out of the 10 runs would have grown your bankroll to over $1 Million. I have to think your bookie would limit your stakes a little bit before you win that much, however.

Implementing this with Trademate?

For those of you who have read this article and are also Trademate users, implementing the NHG with the use of the software is quite straightforward. You most likely already have a preset that sends value bets within a timeframe of 0-8 hours before kick-off. So, to make sure you have plenty of time after the first leg of the accumulator to go and hedge the second leg (assuming the first leg wins), I would advise setting up a second preset that sends alerts for games somewhere between 8-24 hours before kick-off. Just note that your 8-24 hours preset should contain a higher minimum edge to give you a bit more wiggle room if the market moves against you.

If you’re still confused about how to implement this method within Trademate Sports, or about setting up new presets, send us a message on our customer support and we can help you out.

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