Volatility in Casino Games
By John Grochowski
When we talk “volatility” in casino games, we’re often talking about electronic games. Reel-spinning slot machines concentrate more of their returns in fewer big wins than video slot machines, which bring more frequent small wins. The reel-spinners are more volatile.
Same deal in video poker. House edges are similar on 9-6 Jacks or Better (99.5 percent) and 9-5 Super Double Bonus Poker (99.7), but Super Double Bonus is much more volatile.
The 2-for-1 payoff on two pair helps keep Jacks or Better on more of an even keel. Super Double Bonus pays only 1-for-1 on two pair, and concentrates more of its return on big four-of-a-kind hands. For a five-coin bet, Jacks or Better pays 125 coins for any four of a kind, while Super Double Bonus pays 800 on four Aces, 600 on four face cards, 400 on four 2s, 3s or 4s, and 250 on any other quads. We can win big money faster on Super Double Bonus, but the lower payoff on the far more common two-pair hands means that without the big hits, we lose much faster. It’s a more volatile experience.
The same concept applies to table games. The house edge on betting odd or even is the same 5.26 percent as betting single numbers. But odd or even brings 18 winners per 38 spins of the wheel, and pays even money. Any single number comes up an average of once per 38 spins, but the payoff is a 35-1 bonanza. Bet single numbers, and you can win big, or lose fast --- there’s more volatility than in playing odd/even.
Sometimes players add their own volatility to games. When players ask me about betting progressions, increasing their bets as they win, I tell them that the main effect is to add volatility. The house edge is the house edge, a mathematical certainty no matter how you size your wagers. But volatility --- that’s different. You can take a steady chug or ride the roller-coaster, depending on whether you bet the same amount on every hand or play a progression.
I remember the first time I ever tried a progression. It was at the Tropicana in Las Vegas , at a time when it had a little less of a threadbare feel than it does today. I started out wagering $5 a hand at a six-deck blackjack table. After two consecutive wins, I increased to $10, then to $15 and $20, adding $5 with each win. After any loss, I brought my bet back to $5. In 45 minutes, I won $300.
It was an incredible feeling. Nothing like that had ever happened to me. In those days, I was strictly a $5 bettor, and I could budget a whole three-day trip to Las Vegas on $300 in gambling money. I’d had winning sessions before, but the big ones were $40 or $50. This time, I’d doubled my stake for the trip in 45 minutes.
Soon, I learned the down side. Betting progressions do bring some spectacular wins, far larger than if you kept your bets flat. But they also turn some potential winning sessions into losers. They add volatility.
I came home with more money than I’d brought, but continued play with my little progression had eroded that $300 win a bit.
When you’re on a roll, a betting progression is a huge bankroll booster. On my modest little progression, winning five hands in a row meant winning wagers of $5, $5, $10, $15 and $20 --- a total win of $55. If I’d bet $5 a hand in my usual style of the time, I’d have won just $25.
That’s the upside. The downside comes when you have more normal short streaks, such as two wins followed by a loss. Keep your bet at a flat $5, and that means two $5 wins and a $5 loss, yielding a $5 profit. On my progression, two $5 wins would be followed by a $10 loss, with no profit at all even though I’d won more hands than I’d lost.
Another problem: Unless you put a limit on the number of increases in your progression, you will always lose your largest bet. On my longest streak at what I now know to have been an extraordinarily lucky session at the Trop, my bet reached $40, with eight wins in a row. Then I lost.
Most progression players use much more aggressive systems than the one I was using that day, increasing wagers more rapidly, but also applying a limit such as four wins, then returning to the minimum bet.
How does it all come out? On balance, pretty much the same. Bet flat, and the winning sessions will be smaller. Bet a progression, and the big wins will be bigger, but the losing sessions will be more frequent. If a flat bettor and a progression player start with the same base wager, the progression player will lose a little more money in the long run because the total of his wagers is larger. Progressions can’t overcome the house edge. They just add volatility.
Even keel or wild ride? Take your pick.
John is the author of six books on casino games, including "The Slot Machine Answer Book."
You can find his weekly column at www.scoblete.com.