*Repost from too long ago.

I created a coin toss simulator (at the bottom) to compare two different wagering methodologies.  But first I’m going to ramble.

Statistics, streaks, can be deceiving, and frequently this feature of statistics is abused.  Services and handicappers that sell picks often either just plain lie about their betting performance, or use statistics over a small subset of games that only act as data in a larger sample size.

You can take any record of picks over a certain time frame, and do a linear extrapolation into future expectation and growth, serving to highlight excellence in picking games.  I went 0-7 in college football two weeks ago, if I use that and do a linear extrapolation through the next 50 years I’ll be losing money at the speed of light expanding infinitely up into the outer regions of space.

Rarely does anybody have constant growth in bankroll, as the only thing absolute is that there will be variation and fluctuation in winners and losers.  But calculating expected growth is a practical application imposing upon a system of random performance.  If a bettor is betting 25% of her bankroll on every play, all it takes is one 0-4 sequence of wagers to lose everything.

Expected Value, to wit:

An example would be a standard -110 wager betting $100.

Expected growth is typically demonstrated in terms of bankroll growth and bankroll shrinkage.  Therefore X (Money wagered) would be expressed as percentage of bankroll.  For the above example, a bankroll of $10,000 at 1% per game equates to $100.  The formula for expected growth:

D = Decimal Odds

p = Win Probability

The Kelly Criterion accounts for such scenarios, and finds the most optimal distribution of bankroll to apply for each wager, given some designated edge.  Kelly is a formula to maximize expected growth, while minimizing risk.

Conversely, flat betting (betting the same amount on each game) defines the edge as immaterial, and embraces randomness and humility.  With either style of managing bankroll, allowing one to stick around long enough to hit a long shot is eminently assumed, in my opinion of course.

Again, Kelly essentially finds the optimal wager for an event that maximizes E(G), from above.  Given an edge, however measured, the “Kelly Stake” can now be calculated as a percentage of bankroll (of course if there is no edge there is no wager).

Conveniently at even odds the stake is equal to the edge.  One thing to keep in mind, Kelly intended each particular stake to relate to each particular moment of current bankroll.  Meaning a $1 winner with a bankroll of $100 now increases the bankroll to $101 and therefore changes the value of the next wager given similar parameters of the wager previous.

Kelly is very aggressive, there is no doubting that, which is why fractional Kelly is more common, in my experience anyways.  I don’t use the Kelly criterion because there is seldom a time where a calculated edge has any actual meaning, and I’m not arrogant enough to think I am smarter than Vegas.  Therefore I bet frivolously and arbitrarily.

The simulator is below, and uses “static” Kelly Criterion, if you will, to compare to flat unit stakes.  Enter numbers in the blue boxes then click simulate.   Its a zip file.  Two excel macro files inside, 0ne is a side by side comparison, the other just allows for the simulation of the specified methodology.

FlatvKelly_Sim