The Ultimate Guide to Casinos


Risk of Ruin

Those who play casino games are risk takers by definition. They may vary in attitude from overly cautious to foolhardy in the extreme, but the only way to play is to wager, and every wager entails the possibility of loss. Each player must therefore identify his or her own willingness to put a bankroll in jeopardy. On a scale of “zero equals never to ten equals always,” how often are you willing to “go for broke” at a casino?

Perhaps not surprisingly, amateur players tend to rate themselves much more highly in answering this question than professionals. An occasional player might set aside $20 a week as “mad money” and be more than happy to lose it all, 52 times a year, just for the entertainment value of playing online casino games and perhaps gaining some loyalty points to turn into a “free” branded T-shirt. The casinos love such players.

But for the pro or the serious gambler, the profitable sessions must outperform the losing ones with consistency. Those who think of casino games as a livelihood or a sport are focused on winning, so the bankroll must be protected and a reasonable “Risk of Ruin” (RoR) must be as close to zero as possible.

Determining RoR

In both gambling and finance, RoR is not an abstract concept. It is a statistical value, defined as “the probability of an individual losing sufficient trading or gambling money (i.e., capital base or bankroll) to the point at which continuing on is unwise and no longer considered an option to recover losses.” It is typically expressed as a percent or decimal.

In order to calculate RoR, it is necessary to know the probability of winning, the probability of incurring losses, and the portion of the bankroll that is in play or at risk. It is also necessary to know something about the game, including its Standard Deviation or Variance, the House Edge and the player’s Expected Value or Win Rate. One other useful variable is the number of hands/spins/rolls that constitute a session.

Involving logarithmic functions, the mathematics of RoR can be very complex—so much so that most players will use an automated RoR calculator or refer to an RoR table based on random simulations rather than attempt to do the math manually. Once RoR has been determined, it can be extremely useful in two basic ways—to help test earnings goals and to ensure survival.

Applying RoR to Wagering

The first application of RoR is to calculate the probability of a specified profit objective being met before the bankroll will be depleted, regardless of how many hands/rolls/spins take place prior to either event occurring. In many cases, such an analysis can help uncover a flawed strategy or unrealistic objective.

For example, an aggressive player at a European Roulette table might set a goal of doubling a $1,000 bankroll by betting $50 each spin on the colors, Black or Red. In this situation, RoR tables indicate that the probability of going broke before $2,000 can be amassed is 91.5%. In short, the strategy is doomed. A more pragmatic approach would be to wager the entire $1,000 on single spin with an RoR of 52.6%—a virtual coin flip.

Understanding RoR may help goal-focused players quit at levels below their unrealistic objectives and thus retain profits that they otherwise would have gambled away. Alternatively, it may convince some to modify their betting strategies or games, sacrificing the low probabilities of large wins for the high probabilities of small wins.

That leads to the second application of RoR—survival. That aggressive European Roulette player might enjoy the gaming action so much that switching from a long string of $50 bets to one big wager is out of the question. In that case, it could make a difference knowing that the RoR of chasing the $2,000 goal drops from 91.5% to just 7.5% if the pursuit is limited to no more than 100 spins. A lucky streak might ensue during those spins, or at least the losses might be limited to far less than the entire bankroll.