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Best of Alan Krigman

Gaming Guru

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Intuition in Gambling Can Help, but also Trip You up

11 June 2002

Among the key elements distinguishing adept from inept gamblers is an understanding of the chances associated with relevant phenomena. Proficiency, to a great extent, involves knowing how likely a situation is, and using this information wisely to optimize performance. Incompetency often implies being unaware of the probabilities of pertinent propositions, and acting rashly in the wake of unwarranted confidence or premature pessimism.

This doesn't mean that in any given instance, crackerjacks won't fail and dilettantes prevail. Rather, that knowledge helps gamblers meet or exceed their goals when luck smiles and miss them by less when it frowns. This applies overtly to strategy issues in cases when players exercise decision options. It's also germane to subtler points such as matching bet size to bankroll, quitting at profit or loss levels consistent with the edge and volatility of a game, and maintaining discipline during what seem like extreme but are actually normal hot and cold periods.

Some solid citizens - unfortunately, a minority - prepare themselves for gambling by studying the games on which they risk money and learning what the prodigies calculate offer the best prospects for success. Others just jump in blindly, figuring it's only a matter of luck, so why bother. A third group, perhaps the largest segment, relies on intuition nurtured by experience. There's a lot to be said for intuition, but cautions are needed as well. Casino games in which bets are resolved according to the poker values of hands, and which have a "stud" - no draw - format, illustrate the possible pitfalls.

Three such games have recently become popular (and more are in the pipeline). Caribbean Stud and Let It Ride, which both use five-card hands, are already fixtures at most casinos. Three-Card Poker is fast gaining a following; if it hasn't made its debut at your favorite punting palace yet, it's apt to appear soon.

These games can defy intuition because their five- and three-card formats are mathematically distinct from the seven-card stud and certainly the five-card draw paradigms with which most folks grew up. They therefore have unique statistical attributes which can bedevil bettors accustomed to the more traditional poker models.

The accompanying table shows the odds against hands with winning poker rankings in seven-card stud, Caribbean Stud and Let It Ride - which have similar five-card stud structures, and Three-Card Poker. In all instances, the prospects of obtaining the various hands are fixed by the parameters of the games. Players don't discard and draw; their strategic decisions essentially involve changing the amounts wagered during the progress of a round.


Odds against various final hands
in seven-, five-, and three-card stud poker games

hand
7-card stud
Caribbean Stud
& Let It Ride
3-card poker
royal
30,939.6-to-1
649,739.0-to-1
*
straight flush
3,589.5-to-1
72,192.3-to-1
459.4-to-1
four of a kind
594.0-to-1
4,164.0-to-1
*
full house
37.5-to-1
693.2-to-1
*
flush
32.1-to-1
507.8-to-1
19.2-to-1
straight
20.6-to-1
253.8-to-1
29.7-to-1
3 of a kind
19.7-to-1
46.3-to-1
424.0-to-1
2 pair
3.3-to-1
20.0-to-1
*
pair
1.3-to-1
1.4-to-1
4.9-to-1

The chart shows that "good" hands, especially straights or better, are far scarcer in Caribbean Stud and Let It Ride than seven-card stud. This explains the high payoffs for these results. And, it shows why you can always hope for, but should never bank on, a blockbuster - either to make a bundle at the getgo or to catapult you out of a hole after a cold streak.

The figures also show why Three-Card Poker is deceptive. Flushes are likelier than straights in this game, and both occur much more frequently than in five-card stud. Straight flushes are also more common in the three-card than the other games, and are only slightly tougher to get than triplets. These factors create the impression that Three-Card Poker is gift from the casino bosses. But it's an illusion. Payoffs for hands are offset against the chances, so the house still gets its due. As the artful articulator, Sumner A Ingmark, rhymingly remarked:

Subtle differences in rules throw experts off their pace,
Sages suddenly are fools who run a nescient race,
They forsake their basic tools and finish in disgrace.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.