Kelly Criterion Formula: Optimize Your Betting
How Much To Bet
As every seasoned gambler knows, winning comes hand in hand with losing. The objective, however, is always to win slightly more than you lose to come out ahead in the end. And while there are many ways to subjectively guess how one should go around bankroll betting optimization, none has really held up to the true genius of what is widely known as the Kelly Criterion.
What is Kelly Criterion?
The Kelly Criterion is a formula used to calculate bet sizes for people looking to make a sustainable profit over the long term. This is important to think about because imagine a scenario where you have a rigged coin toss that gives you a 60% chance to double your money instead of just a 50% chance to double your cash. Sounds great, right? It is pretty good bet in fact, one that would make you want to gamble a fair amount on it's outcome. But, if you were to place your life savings on this gamble, you'd be completely bankrupt and homeless 40% of the time. And that simply isn't worth it, let alone even mathematically sustainable in the long run.
Meanwhile if you bet too small on this favorable proposition, you simply won't be making as much money as you could potentially stand to gain long-term. With that in mind, there clearly has to be an optimized middle ground between these two polarized options.
It's important to note from up above that even with these situations that are theoretically profitable for the gambler, these also aren't situations to bet the farm so to speak. You always need to bet in moderation and in line with how much of an edge you think your gambling proposition has in addition to other factors which will include how much money you have at stake and what terms the casino or gambling counterpart are offering you.
In strict mathematical terms, the Kelly Criterion is written out like this:
[(Multiplier – 1) * (Chance of Winning) – (Chance of Losing)] / (Multiplier – 1)
Multiplier – 1 is going to equal your multiplier (for example 2x for a chance to double your prize would then be subtracted by 1 to give you a value of 1 for this field). Meanwhile your chance of winning and losing are written as a decimal value between 0 and 1. Always lean towards conservative values that underestimate your perceived chance of winning. You can make computations for this bet relatively easily with this above equation or even use pre-built Kelly Criterion Calculators if you wish.
What does Kelly Criterion mean for me in layman's terms?
It's important to use short cuts for estimating many situations to ballpark what is correct since you won't always have a calculator handy to compute exactly what is correct. Or you simply won't know how profitable bet is other than that it is profitable, which will require estimation by default anyway.
The simplest bets deal with one doubling their money otherwise known as 2.00x bets in the decimal world or +100 with American betting. And in cases like this, your edge actually dictates the percentage of your bankroll that you should put at risk in doubling your money, which makes for a very easy short hand.
For example, if you have a 1% edge on doubling your money, you should probably consider wagering roughly 1% of your gambling bankroll on this proposition. Meanwhile if you have a 99% edge, meaning that you are all but certain to double your money, you should risk approximately 99% of your gambling bankroll on this outcome.
And by extension, you can do some quick mental math to determine roughly how much to put at risk with other novel situations, such as a 1.50x bet or a 3x bet. Depending on how profitable you estimate your skill to be in a situation relative to the profit at stake should dictate approximately how much you put at risk again.
Adjustments to Kelly Criterion
Of course, it must be said that of everything so far that you must use your own judgement when it comes to any of these situations and your personal finances, livelihood, preferences and all else can't fit into that simple equation. That's where Kelly Criterion adjustments come into play.
What has been discussed so far is the classic form of Kelly Criterion, otherwise known as a “1x Kelly Criterion”. This is your bread and butter strategy for making money long term with moderate risk exposure. However, if you have a very aggressive appetite for risk, you can try what is known as a “2x Kelly Criterion” whereby your bet sizes are doubled compared with up above. For instance, if you have a 1% edge on a 2.00x bet, you don't risk 1% of your bankroll but rather 2%.
The consequences of utilizing a 2x Kelly Criterion is that it will dramatically raise your risk of ruin which can actually deplete your bankroll and actually cause long term damage to your overall financial success. But the increased risk can bring increased rewards, so it will be up to the user to determine what is correct for them.
On the flip side, you can have more conservative betting patterns like 0.5x Kelly or 0.25x Kelly. These will almost ensure long term capital growth with your bets but may come at the cost of forgoing a larger amount of profit in both the short and long term. To each their own.
Kelly Criterion On MintDice: Real Life Example
MintDice uses Kelly Criterion for it's gambling endeavors. Also interesting is that with it's skill games, players can also use Kelly Criterion to their advantage as well. So, in a sense, it's Kelly Criterion meets Kelly Criterion!
For this discussion, we will focus on BitRocket, a Bitcoin game of skill and luck but Kelly Criterion can apply in some ways to almost all MintDice games in different ways depending on the game which is beyond the scope of discussion in this blog.
With BitRocket, from the casino's perspective, the house edge is well known to be at 1%, since it is mathematically designed this way with a Provably Fair algorithm. MintDice also knows their precise investor bankroll which currently sits around 400 BTC or $4,000,000 at the time of writing. Finally, MintDice operates at a 1x Kelly Criterion schedule. Given all these pieces of information, the maximum win, specifically on BitRocket, is $40,000 per game. Interesting, if you'll note, is that if a user were to win $40,000, the bankroll would then draw down to $3,960,000, making the new highest bet only $39,600. This self adjusting system protects MintDice and it's investors from ever going bankrupt and also maximizes returns when it is winning.
Meanwhile, on the player side of BitRocket, users can deploy their skill sets to win Bitcoin from other users by being the last player to cash out. If they estimate their edge to be also at 1%, it is then up to them to figure out which bet size to use. Let's take a user who also likes using the traditional 1X Kelly Criterion and has a gambling bankroll of $1,000. This user should likely bet about $1,000 * 0.01 or $10 per game to maximize their chance of winning long term. This number will have to adjust upwards or downwards based on the risk the expose themselves to with BitRocket and as they start winning or losing, respectively.
As with everything related to gambling, make sure you make your own informed decisions. This is simply a Kelly Criterion guide and is not meant to create your decisions for you. View this guide as something strictly for entertainment purposes only and always consult with a financial advisor before taking on any risk.