Kenny Rogers’ song, The Gambler, is heard a lot in Las Vegas. (“You got to know when to hold ‘em, know when to fold ‘em, know when to walk away and know when to run.”) Video poker only involves two of these four skills: knowing what to hold, and when to walk away. The “walk away” part is probably the easiest, so this will be tackled first.

Walk on Negative Edges. Machines come with “terms” attached. Among the flat tops they are usually described as something like “9-6-1000” where the first two numbers are the payoffs for a full house and a flush respectively, and the third number is the prize for a royal. The unit of measurement is the “coin,” so the 9, 6, and 1000 are quarters on a quarter machine when a quarter is bet. They are multiplied by 5 when 5 quarters are bet. Poker results other than full house, flush and royal will also receive prizes (down to a “high pair” – jacks or better). These other outcomes are either too rare to make much difference in the payout calculation (even though they may pay better than for a full house) or they are too common to make much difference (because the payouts are so low). So the full house, flush and jackpot define the machine.

The edge on the “9-6-1000” is positive, but just barely, with a payout of 100.07% if the gamer plays perfectly. Other common flat tops are stingier, like the “8-5-800” machine. That machine pays out only 97.3% of what is bet, so the edge is negative. Casinos do not lose money on positive-edge machines because most players make an ample number of mistakes, and lose anyway, some of them miserably.

An approximation of the edge can be calculated by starting with the “9-6-1000” essentially at 100.1%, and subtracting 1.1% of edge for each coin less of a payout for a full house, 1.1% for each coin less for a flush, and each swing of 1,000 coins for the royal causes a shift of about 3%. The table below lists working (weighted average) numbers for many common machines. Most of the stingy bad ones are found in places other than Las Vegas, (like Native American casinos or Atlantic City).

As can be appreciated, some machines are generous. The “8-5-3200” offers a positive edge for perfect play. Most machines do not.

So the first part of the ideal strategy is to avoid playing those machines that offer a negative edge. As can be seen from the flat tops, this is not too hard to discern, as the edge is built into the payoff terms. It is also fairly difficult to find a positive edge on a flat top.

With progressive machines, the jackpot varies, and so it is not straightforward to know when the edge is positive. Nevertheless, the same principle still holds: If the edge is not positive, walk away.

Start with the mathematics of the royal: it occurs once in about 35,700 tries. (To check this, start with the first card (any one of 20 possible cards in a deck of 52). The next one must be 4 of 51, the next, 3 of 50, and so on. The product of five probabilities is the probability of receiving the royal without a draw. Then calculate similar scenarios for the draw of 1 through 4 cards, weighting them by the probability of being in that situation, to draw to the royal. The sum of probabilities attached to the outcome is approximately 1 in 35,700.) Assuming a play rate of 500 bets per hour, at $1.25 per play on a quarter machine, that is $625 per hour bet. Now some part of that $625 will come back in the form of winnings on inferior hands. The expected loss rate for an 8-5 progressive is about $35 per hour net, in between jackpots. 35,700 plays will take a little over 71 hours of perfect play. At minus $35 per hour, that amounts to just about $2500. So, if the jackpot is less than $2500, the player’s edge is negative. This number is the approximate breakeven point (or BE). The BE for one player may be different from the BE for another player due to skill at playing perfectly and the speed of play. If the play proceeds at 700 per hour, the BE goes down to around $1800.

The “walk away” message for progressives, therefore, is to avoid them when the jackpot is below one’s break even point. Each set of terms (i.e., 9-6, 8-5) require a different calculation for absolute precision. In practice, however, the jackpot alone is so much more influential than the rest of the payoff schedule, that the BE’s for all progressives tend to be determined by the speed of play and size of the jackpot, rather than the frequency and size of wins on inferior hands.

Draw to Maximize Winnings. The second part of the ideal strategy deals with knowing when to “hold ‘em.” This is the only decision made by the player, and it is typically made in lightening fast time. The first and most important point is that video poker does not have much to do with real poker, and the strategies are different. The objective is to get a certain hand, not beat another person. The bets are made before the deal. So there’s really little in common with poker other than the hierarchy of winning hands.

Many players have made up strategy sheets to which they refer for the more obscure hands. Books and articles on video poker also provide (proprietary) formats for summarizing the decision rules. In truth, with a little experience and practice, most all of the common situations will not require checking in with a written card. Note that the exact rules may vary according to the terms of the machine.

Maximizing winnings means, first of all, not holding a card in hopes of a hand that has an expected value (prize times probability of success) less than the cost of play. A few points, therefore, are always going to be true, no matter what cards appear on the machine because the value of the reward will either always exceed the risk, or never exceed the risk.

For example:

A few other points are not so obvious. They relate to decisions about how to improve a hand on the draw. Certain of these rules, like the one about not holding a kicker, just relate to the probabilities of succeeding in receiving a card that is hoped for. Each decision involves the three basic elements of a bet: (1) the reward, (2) the cost of the bet, and (3) the physical expectation or “real probability”. On most machines the reward for the lower ranking hands is relatively low in comparison with the bet and the real probabilities involved, so it often makes better sense to draw more aggressively for a somewhat more remote outcome, but with a higher payout.

Certain of the rules tell you whether to hope for a specific, lesser outcome, or skip that altogether and shoot for the royal. These are often non-intuitive, non-obvious decisions for the starting player. For example, suppose you hold a straight flush from 9 to King. Would you stand or would you discard the 9 in hopes of an Ace? On some machines, a straight flush will pay 50 bets ($62.50 on a quarter machine at the $1.25 betting level). Is it worth trading a sure thing of $62.50 for a one in 47 chance (2.13%) chance at the jackpot? How much is the jackpot, anyway? If it is at $2,937 or so, the edge would be neutral. However, if the pot were over $3,000, it would make sense to burn the 9 and hope for an ace to get the Royal.

Here is a somewhat simplified version of a strategy table for an 8-5-progressive machine, commonly found in Las Vegas:

To use this table, imagine that a hand is presented in which one must decide between two options. The first line is between standing with a straight flush or drawing one card to a royal straight flush. The standing decision is higher in the table, so it should be chosen, unless the jackpot exceeds $2,850, in which case the next lower green option, drawing one card to the royal straight flush, is the better choice. Likewise, the choice between a high pair (kings for example) and holding three to a high, unsuited straight (K-Q-J for example) is resolved in favor of the high pair, as that entry is higher on the table than the three high cards in sequence. No amount in the jackpot would alter this decision. The figures and format of this table was developed by noted gambling author Sanford Wong. The values in this table have been truncated to the nearest multiple of $5.