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Best of Alan Krigman
What Can You Lose by Going for the Gold with Their Money?19 January 2000
Over a second rice pudding the other day at an all-you-can-eat casino buffet, a fellow fresser filled me in on his video poker philosophy. He wasn't interested in a modest gain, he said, but would play until either his buy-in was gone or he hit a jackpot.
Most gambling gurus advocate locking up profit whenever possible, rather than giving intermediate winnings back to the casino. But this advice is so often honored in the breach that some obeisance must be accorded an individual's impetus to ignore it.
This particular bettor whiled away most of his wagering time at craps. There, he bought in for $500, put $5 on the line with double odds, placed two numbers, and pressed if a shooter got hot. He happily quit if he was a few hundred ahead at the end of a roll. When he exceeded $200, he added, he'd peel $20 off the top trying for a $1,000 royal at $0.25 video poker.
None of this is unusual. However, he then surprised me, claiming he flouted the statistically-sacrosanct strategies suggested by the sages and aimed almost exclusively at royals. For instance, he broke low pairs and three-card non-royal possible straight flushes with high "expected values." He also never held "made hands" below triplets. This meant keeping only suited high cards, single high cards, or nothing -- in that order of preference. For example, starting with two jacks and three low cards, holding the pair guarantees a minimum of 1-for-1. But he'd toss four cards and hold only one jack, since pairs preclude royals.
I noted there were only six opening hands to consider -- an initial royal; four, three, or two matched-suit high cards; one high card; and no high cards. So I proceeded to pencil out the probabilities of each such onset leading to a jackpot.
On a made royal, you're there at the get-go. The odds starting from matched-suit high cards are 46-to-1 with four, 1,080-to-1 with three, and 16,214-to-1 with two. They are 178,364-to-1 with one high card and 383,484-to-1 with none.
Any such draws could also yield non-jackpot returns. Say you get a five of diamonds and J-Q-K-A of hearts. There's 51 probability of replacing the five with a winner -- 6 percent with a non-heart 10 for a straight, 17 percent with a non-10 heart for a flush, and 26 percent with a picture for a high pair. Similarly, dumping five low cards offers anything from around 20 percent chance of a high pair to under 0.0006 percent of a non-royal straight flush.
A royal is likelier on any hand using this approach than the maximum-expectation strategies advocated by the experts. However, is this player more apt to hit a royal with an equal buy-in? Perhaps not. Higher intermediate returns keep gamblers in the game longer on the same bankroll -- offering more hands and a correspondingly greater overall chance.
Playing optimally, odds against royals are about 40,000-to-1. If the optimum strategy affords an average of 1,000 rounds on some stake, a player has approximately one chance out of 40 of scoring. Instead, say this player pumps his prospects of a royal on any round by 25 percent, to 30,000-to-1. Unless the strategy yields an average of at least 750 rounds on the same buy-in, the chance his investment will grow into the jackpot is less.
Had this solid citizen ever hit a royal? "No," he admitted, "but it doesn't matter since I only play when it's with their money."
Whose money notwithstanding, there's an ideological issue. Going for the gold versus targeting a day's pay and hoping for a bonus. Personal predilection -- why you gamble -- reigns in this realm. Nobody can call one way or the other right or wrong. Except you. When you're heading home. Do you regret stopping when the next bet might have brought a bonanza? Are you sorry you kept playing and gave back the tidy sum you were ahead? Which the more so? It's as the beloved bard of betting, Sumner A Ingmark, blazoned:
Gamblers lacking discipline,
Best of Alan Krigman