Playing It Smart: Double-or-nothing bonus bets with no edge

Some slot machines can be found with double-or-nothing bonus bets. These games give gamblers opportunities to wager returns they've just received, on 50-50 propositions yielding even money. Players can therefore double their previous payouts, or lose them, by making "fair" bets those on which the house has no edge. Most casino gurus would call this a bargain.

At video poker machines sporting this privilege, chances to double-up usually occur after every winning round. Typically, in operation, the machine draws a card at random and solid citizens pick one from a face-down set of five. The decision goes to whichever is higher, or pushes if the ranks are the same.

At other types of machines, the forms of the propositions also complement the games in some manner. For instance, some Wheel of Fortune slots offer the chance to double-up on the consolation prize obtained by landing in "bankrupt." Bettors taking the shot spin a wheel with equal alternating win and lose segments.

The casinos don't make a big deal out of the double-or-nothing bonus these days. And, not because the bean counters worry about rounds with no house advantage cutting into their profits. Whether fair double-or-nothing bets affect the overall edge on the action depends on the basis the casino uses to calculate the percentages. Whatever the way, the house gets its due from the primary games. Doubling-up is a wash averaged over the long term, so the bosses neither earn nor sacrifice any revenue with it. Casinos would accordingly offer more of these games if they appealed more strongly to patrons. Drawing traffic and increasing the handle is what the business is all about.

In theory, wagers with no house edge should be popular among players. A possible explanation for why they never gained a greater following than they have lies in the dominance of the utility principle over the laws of probability in many forms of gambling. Not only in casinos at the slots and as jackpot side bets at the tables, but more obviously in the lotteries.

Utility holds that many players want to bet amounts they consider chump change or are used to spending routinely, seeking payoffs at levels they covet, or perhaps realize they're unlikely ever to otherwise have at one time in one place. The dollar values of the bets and potential returns appear tangible enough. Probability? What's that? Hey, that pot of gold is just one spin away. Right?

Take 25-cent jacks-or-better video poker as an example. The maximum bet, five quarters, $1.25, is at risk to win $1,000 on a royal. The $1.25 seems like chicken feed for a run at $1,000. Tell people the odds against success are roughly 40,000-to-1 and they look at you like you just arrived from the ex-planet Pluto.

Think about a video poker buff who plays $1.25 and finishes with a pair of queens. The machine proclaims "win! win! win!" But the win is actually a push that returns the person's original bet. Should this "winner" opt for double-or-nothing? The money that would be at risk is $1.25, the same as for a new round and therefore within the individual's comfort zone. But, edge issues aside, many wonder why they should put this money up to win a measly $1.25 rather than bet it on another stab at big bucks?

Alternately, pretend the $1.25 bettor gets a full house. On an 8-6 machine, the return is $10.00. Now, doubling-up costs $10.00 eight times the player's usual bet. It's a lot to lose on one spin, but not much to win, especially since $10.00 represents eight tries at the $1,000 royal. The dilemma deepens at higher return levels. What if the player hit the jackpot for $1,000? Betting $1,000 with a 50 percent prospect of winning $1,000 is statistically seductive, being neutral in a normally negative milieu. But, how apt are folks who usually bet $1.25 to put $1,000 on the line to double it, no matter what the math mavens mutter? Would you? Or would you be among those described in this terse triplet by the rhyming realist, Sumner A Ingmark:

They gripe the house's edge is bruising,
Fair bets, though, you won't find them choosing,
To win no more than they mind losing.