September 18, 2014

Basics: Edge, Expectation, Variance, & Bonus Hunting


This post is to answer a lot of the newbie questions we get from time to time, and hopefully to establish a clear understanding of what it is bonus hunters and other types of professional gamblers are doing that allows them to make consistent profits. I also want to make sure newbies who are contemplating a purchase of any of our products have the right expectations going into it. 


You will notice I just referred to bonus hunters as a type of professional gambler. This is correct, because smart bonus hunters only play when they have an edge – one created by the bonus money, even though the games they play have a fixed house edge. 

There are several concepts you need to grasp in order to make money gambling. Once you do this (and implement them), the word gambling becomes an incorrect term itself – because if you are playing with an edge you are only gambling in the sense that casinos could consider themselves to be gambling – and it is pretty generally accepted that operating a casino is a sure way to make profits. 

So the first concept is the idea of having an edge. An edge is a mathematical advantage. If you are betting a friend $1 on coin flips nobody has an edge. Now, if you agree to pay him $1.10 every time he wins and he only has to pay you $1.00 when you win, he now has an edge. This particular edge calculates to be 5%; that is every time the coin is flipped his expectation is 5 cents in profit and yours is a 5-cent loss. 

This doesn’t mean much if the game is going to be short. Say you flip the coin 3 or 4 times then quit. Either one of you might very well win all the bets. But if you continue playing, sooner or later your friend will have all your money. It is a mathematical certainty. If that takes a long time, say thousands of flips, you can then divide the amount of money you lost by the number of coin flips and you will find that each flip represents almost exactly minus 5 cents to you. Astonishing? Not really. Long-term results eventually arrive at their expectation. 

In this example your friend had an edge because he was being paid more than even money on a 50/50 chance, but an edge can also be achieved by being paid even money if the chances are in your favor – lets say he knew the coin was biased and he was calling all the flips. An edge can come from any kind of odds. If you are betting on a horse that is paying 5-1 odds and his actual chances of winning are about 25%, you have an edge. Any time the payout is bigger than the actual chances of winning, that’s an edge.

Online casinos enjoy a house edge of varying degrees on every game they offer you. Some are worse than others. Let It Ride Poker for example, typically has a house edge of around 3.5% while Blackjack (when played correctly) only has a house edge of around one-half of one percent, or .50%. That means if you play perfect basic strategy you are expected to lose around a half-cent for each dollar you wager in the long run, and if you play long enough you will find that’s exactly what happened. 

This concept of the edge eventually adding up to exactly what it is supposed to is known as Expectation. And you can bank on it. Casinos do, and they never have any problems meeting payroll. There is no denying math in the end. 

It’s important to understand that there is no way around expectation. You just can’t do anything about it. There is no system of varying your bet size that has any affect whatsoever on it. A long time ago a guy named Martingale invented progressive betting systems, but they are all useless for altering expectation. You WILL experience the worst-case scenario sooner or later, and probably sooner than you think. If you flip a coin 100 times there is a very good chance you are going to see a run of 13+ heads or tails in a row along the way. 

Which brings up the next vital concept: Variance. You will see this term used in our forum a lot, often by somebody who has just undergone a losing streak. Variance is a way of describing short-term luck. Short-term results are erratic; the shorter the term the more erratic they are. If you are going to play one hand against a .50% house edge you certainly aren’t going to lose a half percent of your bet. Your results are likely going to be either a 100% win or a 100% loss. That’s as high as variance gets. The house edge is negated in this circumstance, so much so that it doesn’t even matter (being so small).


As you keep playing the influence of variance is continually reduced while the influence of expectation is continually increased. If you play two hands and quit you will probably either lose 100%, win 100%, or win 50%. Chances are roughly even that you will win 50%. This is a much lower variance than only playing one hand. The more you play the less important variance is and the more important edge is, even what seems like a very small edge.

Variance is affected by the size of the edge in any particular game. All other things being equal, the higher the edge the lower the variance. However, all other things are not always equal! Variance is also affected by the rules of the game. A very low edge game can have a very high variance. A good example is a game where longshots must be hit in order to arrive at the expectation, such as a Royal Flush in video poker.

So you can’t win playing against a negative expectation if you are going to play for any real length of time. Professional gamblers avoid this and put their money into positive expectations only. You must have a bankroll large enough to ride out the natural swings in the game; that is to say your operating capital must be sufficient to absorb the variance.

Bonus hunters have a positive expectation in spite of the fact that the games they play have a house edge. This is because of the deposit bonuses that casinos offer in an attempt to attract action. What this effectively does is create an entirely new game called Bonus Hunting, where the casino customer (who plays it right) actually enjoys the mathematical advantage. Various strategies are employed for milking as much bonus money as possible, and different people have different tolerances for variance. Thus some bonus hunters do better than others.

In the end we’ll all be cashing our chips at that big cage in the sky, at which point we’ll discover that our results equal the sum of our expectations.

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