Don’t outplay your bankroll!

Apr 24, 2005 11:50 PM

You’re in Las Vegas for your semi-annual vacation. Generally speaking, you’re a max-coin quarter video poker player. Your bankroll for the week is a few hundred dollars, which is usually sufficient. You’re playing a 99% game when your buddy comes over and tells you about a great video poker machine on the other side with a 101% paytable.

When you get to the machine you find out it’s a $1 machine. Your buddy tells you, "So what? With a payback of 101%, it’s a sure winner!"

You follow your buddy’s lead and are surprised when 20 minutes later your entire bankroll is gone. You walk away muttering that the machine must be rigged.

What went wrong? First of all, a game that pays 101% is hardly a sure winner. More importantly, your bankroll was simply not large enough to play this game. All casino games have ups and downs. The problem with a short bankroll is that if a losing streak wipes out your bankroll, there is no coming back from it.

To help illustrate this point, I created a simulation using a rather unique roulette wheel. I chose this game because of its simplicity.

Most roulette wheels consist of the numbers 0 thru 36. Generally speaking if you bet the odd/even or black/red bets and the ”˜0’ comes up, you get back half of your wager. In my simulation, however, I treated ”˜0’ as an even number, so that betting ”˜even’ repeatedly actually results in an overall payback of nearly 103%. Surely, this must be a guaranteed winner!

Well, not quite. Assuming an infinite bankroll, if you were to play 1,000 spins and bet ”˜even’ each time, you will wind up a net winner around 70% of the time, and a net loser just under 28% of the time. So, was our video poker player just one of the unlucky 28%? Not exactly.

The second simulation I ran started each player off with a bankroll of $100 with a maximum of 1,000 spins. There were four players. The first bet $1 per spin, the second bet $5 per spin, the third bet $10 per spin and the last bet $20 per spin.

With a nearly 103% payback, it would make sense to bet as much as possible per spin to maximize the amount bet and in turn maximize the amount won, right? Again, not quite. In this scenario, the player betting $20 went bust more than 73% of the time! The player betting $10 per spin busted 53% of the time. The player betting $5 went bust a more palatable 27% of the time, while the player betting only $1 almost never lost his entire bankroll.

The problem in this case is that once the $20 player loses five more spins than he wins, it is GAME OVER. While the $1 player never went bust, this player didn’t really maximize the opportunity to play a 103% game. More than likely, it is the $5 player that found the happy medium.

By now, some of the skeptics are saying that what happened in the previous scenario is only because our players didn’t set a GOAL for themselves. So, I set a goal in the next simulation.

The goal of each player, again starting with a $100 bankroll with a maximum of 1,000 spins, was to double their bankroll to $200. If at any time the player’s bankroll reaches zero, his session ends. Also, if at any time his bankroll reaches $200, his session ends.

In this case, the results are not as dramatic, but just as telling. Our $20 player reached the goal 56.7% of the time. The $10 player reached the goal 63.2% of the time. The $5 player reached the goal 71.7% of the time, while our $1 player achieved the goal only 1.7% of the time. Again, we find that the $5 player seems to be maximizing the power of his bankroll.

For those of you who are VERY cynical, I ran a final simulation where the goal that was set was much more modest. The goal for each player was to win a mere $20. Surely, the $20 player has the advantage here because the player will win 51+% of the spins and all it takes is one winning spin for the $20 player to reach the goal. Again, the results are a bit more even than in the past, but the $20 player gains no advantage by betting more. In this final simulation, the $20 player reaches the goal 85.5% of the time, the $10 player reaches it 87.5% of the time, the $5 player reaches the goal 90.9% of the time, while the $1 player reaches it 79% of the time. Once again, the $5 player seems to have the advantage.

The game used in this simulation is for illustration purposes only. Obviously, no such game exists. What it does show is that even if the game is heavily in favor of the player, if you don’t have sufficient bankroll, you will not have the opportunity to take advantage of the game. The roulette game in this article is also a game of very low volatility, with even money payouts and the player winning 51+% of ”˜deals.’ Video poker is not nearly as simplistic. Most versions of video poker have losing hands 55% of the time, with an additional roughly 20% of all hands being a push. As a result, a much larger bankroll is needed for video poker than the roulette game demonstrated here. More volatile games like Double Double Bonus will require even larger bankrolls than your basic jacks or better.