## Maximizing Bankroll Growth

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The Kelly Criterion: A strategy for bet sizing to win as much as possible while minimizing your chances of losing too fast or doing so continually.  A proven formula for compounding bankroll growth which was Created or discovered in the 1950s by John Kelly who worked at Bell Labs.  You can find a kelly calculator here or by searching on any search engine.

There is a formula for investing your money which takes into account the percent chance you perceive of an event to occur and compare it to the payout of what you would earn if that event does occur.  In cases where your perceived probability are greater than the implied probability of that payout, the Kelly Criterion tells you what percentage of your bankroll you should risk on this wager or investment based on how much greater your perceived percentage is above the implied percentage based on the odds.

For events where there are only a finite amount of outcomes like a coin flip (2) or the win/loss (2 outcomes when there is no tie possible) or win/loss/tie (3 outcomes) of a sporting event, the formula is X = (pb-q)/b with x being the percentage of your bankroll you should wager on the event, p being your perceived percent chance or true odds that you think the event has to occur, b being the net given odds of an event occurring expressed as the decimal odds of an event minus 1 or net odds, and q being 100% minus what the p perceived percentage of the event is.  So if you think a team has a 40% chance of winning and the odds are 2 to 1 (also can be expressed as +200 in the American moneyline style or 3.0 in the decimal style, the NET odds are 2.0 and the “true odds” or odds you perceive are 40%.   it is x = (((0.4*2)- (-1))/2  (pb-q)/b.   If you put that in a calculator, it spits out 0.1 or 10% of your bankroll.  So if you have 1,000 dollars, then you should bet \$100 on this opportunity.

It tells you that the bet size for compounding your bankroll growth the best, taking safety and speed into account, is \$100.  If you bet more than that percentage per this type of bet, you will eventually go broke.  If you bet less than this, you are leaving some money on the table.  Some people choose to bet half of whatever this number is.  A half Kelly betting method would still see growth, though it would do so slower.  The benefits of this are avoiding uncomfortable or unmanageable downward swings during a patch of bad luck, in the course of applying such a method long term.  But of course you would reduce your upswings during a stretch of good luck as well.

If you do this Kelly calculation, taking into account the true or perceived odds of an event actually occurring and the net payout odds of an event occurring, and your answer is 0 or negative, it is saying not to place a bet on that.  The bigger the edge or difference in your percentage vs the payout percentage, the more it will tell you to bet.  A problem can occur in something like sports betting for example, if the bettor is not good at estimating the approximate percent chance a team has to win or for a player or team to accomplish a certain feat during the game to win a prop bet.  The calculation can only be as good as the numbers you put in so if you think a team has an 80% chance to win, and put that in, the calculation will treat that as the true odds though depending on your ability to predict sports outcomes, it will vary how accurate or beneficial that is.

It is a good talent to be able to predict sports outcomes but even if you could not assign an approximate percentage to them in your head just from your sports knowledge, if you were good with programming or spreadsheets, you could make a model that factors in whatever stats and historical data you think will be-, or whatever stats and data were historically important in determining what happened in games and assigning some sort of numeric or quantifiable value to these factors that can help tell you when someone has an improved percent chance to win or even better, a specific approximate chance to win.  Odds makers and sports books use their own models and factors to develop the odds or line they give you but not only do those often not include all the factors a modeler would deem important but they also are often not even trying to predict the exact outcome of the game, but rather just encourage action or betting to go a certain way that would be profitable to them.

Because there is such a propensity for human error in any activity, one should always be cautious. And there often are unknown factors that you don’t or can’t account for like injuries or someone else cheating.  These are not just reasons to manage your bankroll carefully and patiently but also reasons to be very careful and to re-evaluate strategies for determining your edge regularly. Some people choose to use very conservative estimates when projecting an event’s percent chance of occurrence. Also some people choose to bet some fraction of the full kelly calculation’s recommended stake. If you bet half kelly or quarter kelly, the bankroll fluctuations will be much less severe.