Why Some Gamblers Need More Luck Than Others

You don't have to spend much time in a casino before you overhear players ardently arguing arcane points such as place versus come bets at craps, insurance at blackjack, or extra paylines rather than larger payouts for more coins at the slots. Eventually, some solid citizen (who's probably just lost) will say something like, "What's the difference? It's all just luck."

Maybe you were thinking the same thing. Perhaps because you just lost (winners think it's mainly skill). Or you haven't a clue as to what an expert might do under certain circumstances, and won't face up to having a higher handicap than necessary. Or your braggadocios brother-in-law won big last month, and it would have to be dumb luck if that jerk could do it.

Luck, of course, pervades all punting parlors. Good luck and bad. But how much? Certain alternatives entail more than others.

Differences in odds among bets form one factor defining the relative importance of luck. The longer the odds, the more fortunate players must be. Bettors who favor low-payoff propositions like red at roulette or pass at craps, with probabilities of almost one half, lean only lightly on luck. Those who invest in longshots like slot machine giganta-pots, with chances less than one in several million, depend direly on destiny.

Differences in "expected returns" for options in games where players make decisions also influence how much luck is required. Great expectations involve little luck, and conversely.

I'll show you what I mean using jacks-or-better video poker.

A player is dealt 3-H, 4-H, 5-H, 6-H, Q-S. Most folks would handle this situation properly. They'd hold the hearts and discard the queen, hoping for a straight flush, a flush, or a straight. Almost nobody would keep the queen and heave the hearts, even though doing so could conceivably lead to anything from a super jackpot royal down to a money-back high pair.

Since there are 2,598,960 possible poker hands in a 52-card deck, starting with something this promising is longshot-league luck. What happens next is another story. The expectation for a $1 bet is a $2.56 win on the four-card straight flush and a $0.52 loss on the single high card. A player needs a lot less luck to make money holding the sequential hearts than the queen.

What if the player gets 3-H, 4-H, 5-H, J-S, Q-S? Hold the three sequential hearts and go for a straight flush, flush, straight, three-of-a-kind, or two pair? Or hold the suited pictures and hope for anything from a royal to a high pair? Most people would consider this a toss-up - the fickle finger of fate. But one choice requires less luck than the other for success.

Both options in this case are underdogs and differ only slightly in expected returns. Further, the range of possibilities is much wider than in the previous example. The logic is therefore more complex and the decision far from obvious. Mathematical analysis gives the answer. Expect a $0.38 loss holding the three sequential hearts and a $0.39 loss keeping the jack and queen of spades. Considerable luck is needed to overcome the adverse odds either way, but the three-card straight flush is marginally less disadvantageous and accordingly the better choice.

True, anything can happen in any particular instance. A player could draw four to a queen and make the royal - the chance is paltry at 1/178,364. Likewise, a player could draw three to a suited jack-queen and hit the biggie - the chance is weak at 1/16,215. Still, luck is a matter of degree and players whose bets and decisions have the best odds and expected returns need it the least.

The immortal Sumner A Ingmark, lyricist whose larks about luck are legendary, may have put it perfectly when he penned:

I know there's luck to gambling and yet,
The more I know, the luckier I get.