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Do wild cards give you a better chance to win at video poker?

5 November 2012

By Alan Krigman

Gambling gurus rate slots, video poker, and other machines by return percentage. This parameter is the fraction of the gross wager the law of probability says the casinos will give back to players as a whole. It arises because bets pay less than the odds players must overcome to win them.

Round-by-round, return percentage is essentially undetectable. Players lose what they risk or win a multiple of that sum. Even over many coups, nobody really notices. Say a game has 95 percent return. After a million people have each made 100 $1 bets, 100 million decisions with a gross $100 million wager, the house figures it’ll keep close to 5 percent of $100 million or $5 million and return $95 million. But each person doesn’t always lose $5 and get back $95. The $95 million is the net of folks who grab profits big and small, and those who drop varying amounts.

Solid citizens are more attuned to how often they win or lose rounds during their sessions. Frequency, per se, has relatively little monetary meaning unless it’s tied mathematically to the odds of scoring and the associated payouts. Still, casino buffs tend to gravitate toward games in which they believe they get lots of payoffs. Such a conviction may be predicated on experience, as unreliable as casino patrons’ recollections might be. It may also be intimated a priori, from features that seem to imply one game is easier or has more ways to win than the next.

Video poker affords examples of the latter effect. Many variations of this game are available. One dimension of differentiation involves wild cards. The most common forms are:

nothing wild, with 1-for-1 minimum return on pairs of jacks through aces;
joker wild, with 1-for-1 minimum return on pairs of kings or aces or any two pairs;
deuces wild, with 1-for-1 minimum return on three of a kind;
deuces and joker wild, with 1-for-1 minimum return on three of a kind.

The specific probabilities of winning combinations for any of these alternatives depend on the strategies used by the players; that is, what to hold for the draw phase of a round. Optimal criteria are unique, not only to each class of device but also to the payoffs for hands at various levels within a class. Average rates of all hits – including pushes as well as wins – and of losses on typical games, however, highlight the effects of wild cards, and are given in the nearby table.

Probabilities of hits, pushes, wins, and losses for common video poker configurations

  Class of game         any hits    pushes    wins    losses

jacks or better
        average         45.29%    21.34%    23.96%    54.71%
        minimum         44.80%    20.96%    23.83%    54.50%
        maximum         45.50%    21.51%    24.00%    55.20%

joker wild									
        average         44.33%    25.22%    19.11%    55.67%
        minimum         44.13%    25.03%    19.09%    55.26%
        maximum         44.74%    25.59%    19.14%    55.87%

deuces wild									
        average         44.71%    27.35%    17.36%    55.29%
        minimum         44.22%    26.68%    16.84%    54.65%
        maximum         45.35%    28.50%    17.71%    55.78%
deuces and joker wild								
        average         50.38%    28.49%    21.89%    49.62%
        minimum         50.36%    28.46%    21.86%    49.57%
        maximum         50.43%    28.57%    21.90%    55.78%

The probabilities in the table assume players follow the optimum strategy for each class. Values are given of averages, minima, and maxima on the devices studied for:

any hits (anything returned – including pushes as well as wins),
pushes (returns of 1-for-1, players get their money back but don’t actually win anything),
wins (returns greater than 1-for-1, players get back their original bets plus payoffs),
losses (players lose their original bets and get nothing back).

Within each class of game, the maximum and minimum for the various parameters of interest on the games analyzed don’t vary substantially. So, for instance, rates of hits, pushes, wins, and losses were similar on most joker wild machines despite differences in payoff schedules and corresponding optimal strategies. Variations among classes are somewhat greater. As illustrations, video poker with deuces and one joker wild hit more and lose less often than other versions, but the apparently successful rounds involve the highest overall proportions of pushes. Similarly, jacks-or-better games with no wild cards hit at about the same rate as those with a joker or four deuces wild, but more of those hits are actual wins and fewer are merely pushes.

Ingenuous individuals may want to think the bosses are giving them a break with wild-card machines. They should realize that the devil is in the details of probabilities and payoffs together, not singly. Further, optimal strategy differs among games and tends to be more complex with wild cards than on straightforward jacks-or-better games; switching because one variant looks easier to win than another, while ignoring the nuances of the alternate configurations, is therefore fraught with peril. As that irascible inkmeister, Sumner A Ingmark, indicated:

It’s often losers who aren’t scared,
To risk their money unprepared.
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 were focused on those interested in gambling probability and statistics. He passed away in October, 2013.