Daily Fantasy Bankroll Management: Cash Games
This article explores bankroll management through the tool of computer simulation. I do not use any formula that perhaps has flawed assumptions (e.g. normal distribution) but instead use real world data and simulate to see what happens.
To do this let’s first start with a $22 cash game with a $40 prize and assume a hypothetical player wins 60% of time. This implies $2 in expected value for an ROI of 9.1%.
Next we want to examine how large a bankroll needs to be in order to bet 5%, 10%, 15%, 20% etc. of ones total bankroll on this game. This is shown in the table below.
Next we need to find risk of ruin points. In other words, if we play this game over and over again, how often do we lose our entire bankroll due to the normal course of variance, and how does this change based on how much of our bankroll we bet?
To do this I generated random numbers from 0 to 1 and called anything below 0.6 a win and anything above 0.6 a loss. I repeated this 1,000 times and calculated cumulative profit at every point. If cumulative profit ever dipped below zero then I consider it a total loss. I then repeated this 5,000 times and calculated the proportion of trials where a total loss occurred. This is the risk of ruin percentage. The figure below shows this for varying levels of the bankroll bet.
However this assumes we make only make one bet. Of course most daily fantasy players don’t do this but rather make a series of slightly uncorrelated bets each day. Therefore I replicated the above analysis but broke down each bet into a series of 4 bets, each for one-fourth size the original bet, all correlated with each other at 0.5. You can see on the graph below that this reduces risk or ruin considerably. For example, risk of ruin at the 10% level decreases from 9.4% to 2.3% and at the 15% level from 19.8% to 7.5% by splitting up the action.
The table below presents risk of ruin at various levels under both scenarios:
I recommend scanning the above table to identify what levels you feel comfortable at. A few things to keep in mind:
- Risk of ruin grows more or less exponentially.
- The more thinly you slice up your action the lower your risk of ruin is and/or the higher percentage of your bankroll you can get play at any one time. However this assumes you are still winning at a 60% clip. Don’t go making stupid plays just because they are “uncorrelated” to the rest of your action.
- This assumes bet-size stays constant. To more properly manage your bankroll you should approach it from a percentage standpoint and bet less when your bankroll diminishes and more when your bankroll has grown. If done properly, this will make sure you never go broke.
- Finally, this is only applicable for cash games. For tournaments you must wager a lower percentage of your bankroll since you are cashing much less often and downswings will be much longer.