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Best of Alan Krigman

Gaming Guru

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Do all the Good Hands You Remember Mean You Almost Won?

21 March 2001

Video poker games have high "hit rates" compared to most other slot machines. Bells, whistles, and electronic renditions of tunes that would drive the average person bonkers if they didn't signal success are activated on over 46 percent of all rounds on jacks-or-better and deuces wild versions. It's almost as good, nearly 44 percent of all tries, on units with single wild jokers. These figures are for players who know what they're doing, of course. And, gilding the lily, are the fairly strong chances of finishing with premium hands -- straights, flushes, or above.

Some of this good news, sadly, is illusion. Roughly half the rounds in which the machines declare players to be winners are really "pushes." That is, bettors get their wagers back but don't actually generate anything as crass as earnings. Further, the profits for most honest-to-goodness video poker hits are modest when viewed alongside the rewards accompanying the admittedly lower-probability boffo combinations on typical reel-type slots.

These factors don't necessarily make video poker superior or inferior to other slots having equivalent house advantages. They do, however, lead to games with different characteristics. In particular, they temper the bankroll swings players are apt to encounter. One result is that video poker buffs who size their bets to their budgets can get long sessions on moderate stakes. True, lots of action for the money isn't as nice as a big score. It's often an acceptable next-best thing, though, since it keeps bettors positioned to grab the prize, offers a hefty dose of the thrills integral to the casino experience, and helps rack up the points every insider knows are key to being treated with respect.

Another illusion fostered by high hit rate draws solid citizens to video poker. The likelihood of surviving long sessions, even when fate is not especially kind, plus the speed at which most folks roar through the game, mean that players see huge numbers of hands during their casino visits. And, it doesn't take too many isolated blockbusters in a long series of results to leave video votaries sure their machines were on the verge of hot cycles, even though they didn't happen to win that day.

I'll illustrate how playing multitudes of rounds during single sittings can encourage such belief. Consider instances of hands "made" on the initial deal -- those that win without discarding and drawing any cards -- at a jacks-or-better game. The odds against receiving such a hand on any round are given in the following list. On this basis alone, you can see that chances aren't outrageous for low-return hands like high pairs, two pairs, or even trips. When all made hands are taken together, the odds against a guaranteed win before the draw are only 3.85-to-1.

Odds against receiving various hands
at jacks-or-better video poker
on the initial deal (without drawing)
high pair
7-to-1
two pairs
20-to-1
three of a kind
46-to-1
straight
254-to-1
flush
504-to-1
full house
693-to-1
four of a kind
4,164-to-1
non-royal straight flush
72,192-to-1
royal
649,739-to-1

Say that a middlingly fast player sees 1500 hands in a sitting. This represents an average of somewhat over eight rounds per minute for three hours. It's well within the capabilities of folks who don't have to agonize over their discard strategies, and whose arthritis takes a turn for the better as soon as their fingers are exposed to whatever the casinos pump into the air.

In 1500 rounds, this person has a greater-than-even chance of receiving at least five pat straights and of being dealt more than two made flushes. Further, the odds against the initial deal yielding over two full houses are a respectably short 1.7-to-1. And at least one four-of-a-kind isn't all that unlikely, either, fighting odds of only 2.3-to-1. Little wonder that even players who suffered defeat believe victory was close at hand. The poet, Sumner A Ingmark, recognized the danger of a relatively few noteworthy events crowding masses of the mundane from the mind when he mused:

Recollections unreliable,
Yield conclusions less than viable.

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.