I began studying casinos about four years ago after my employer sent me along with its top national salespeople to Las Vegas for an incentive trip. At this point I’d never seriously considered casino gambling as a hobby as I was far too occupied with my own investment portfolio and career. But after my first trip to Las Vegas, I became fascinated by all aspects of the city, including a quest to find ways to beat the casinos. Today, after refining my strategies and gambling process, I’ve become a winning player by focusing on video poker, sports betting, and couponing. Two beatable games I’d like to add to my repertoire are blackjack and holdem’ poker. Today, I also play on a team with another player, and below I describe the rationale behind our gambling bankroll.
Like many aspects of risk management, there isn’t an exact bankroll requirement, just degrees of risk. A small bankroll is usually riskier than a large bankroll. After deciding which games we’ll play, the size of our bankroll is a function of our risk preference, profit goals, and time constraints. Since each game has a different volatility and expected sequence of returns, we account for these factors too. We believe that by diversifying by type of game, we will decrease the impact of any single game and thereby lower the individual game/session risk to our bankroll. In investing parlance, we are happy to take systemic risk, but we’ll attempt to decrease individual risk as much as possible thru diversification. Much the same as an investor will diversify their portfolio by type of asset. maturity, and a mix of individual holdings, we will play several types of games on our bankroll to achieve the same effect. We view our gambling bankroll as a portfolio of risks the way an investor views their investments as a portfolio of securities.
It’s worth pointing out that unless we are playing games with a positive expectation, no amount of bankroll will help us. A gambler who plays for fun is willing to pay the casino and might win sometimes and lose other times, but if the recreational gambler plays without regard to playing advantages, the player will eventually go bust. Just as the blackkack player who sits at a blackjack table without counting the cards and making corresponding bets will eventually lose no matter how big their bankroll is. For the recreational gambler, a bankroll determines the likelihood of how fast or slow they will bust as the house edge grinds them down. Any casino game gives a mathematical edge to the casino. This can be calculated mathematically, and players can consult the Wizard of Odds website to determine the return on any casino game. We are not recreational gamblers, we only play casinos games were we have an edge and it can be proven mathematically.
We are playing for advantage, and we have picked our games, so how do we calculate a bankroll requirement? Different games have different degrees of granularity. Video poker can generally be played for quarters, 50 cents, dollars, and other denominations. These denominations will guide our bankroll requirements. We have determined we will play video poker mostly for dollars and sometimes for quarters. We have also determined that we will only play video poker when our expectation is at least $10 per hour with an average hourly expectation of $20 per hour. We will only play 9/6 Jacks or Better progressives and 8/5 Bonus Poker progressives. With this information, we can decide how big our bankroll needs to be.
We can consult the Wizard of Odds website section on buy erythromycin gel for acne. His methodology is described if p is the probability of ruin with 1 unit then p2 is the probability of ruin with 2 units, p3 is the probability of ruin with 3 units, and so on. With the known probabilities for the outcome of each hand an equation could be set up to solve: p=sum over all possible outcomes of pri * pri, where pri is the probability of hand i and ri is the return for hand i. We can use the table’s listed in the Jacks or Better section to see that our goal of at least $10 per hour expectation can be earned when the cashback rate is at least 1% and accounting for strategy errors. With a $20,000 bankroll, we can handle almost any swing at dollars. With a $20,000 bankroll, we would have 5 royals worth of bankroll at the dollar level with a base royal of $4,000.
With our $20,000 bankroll, we can work backwards to determine the size of our sports bets. For our arbitrage bets, the size of our bet will be determined by how much the casino will let us get down while staying under the reporting limit. We’ve never come up against a betting limit. If we find an advantage on a stright up sports bet, we use a kelly bet sizing method. We plug in the variables such as our edge, as determined by comparing prices to a market such as betfair, along with the probabilty and bankroll. The cheap erythromycin determines our bet size.
What do we do with our bankroll while we aren’t gambling? When we aren’t gambling, we invest our bankroll in a portfolio of gaming investments such as stocks, bonds, and options of other casino companies.