# Jacks Or Better: hand frequencies, percentage returns and costing the changes

The payouts on the various hands increase in relation their relative infrequency in all video poker games: in Jacks Or Better, a pair of jacks, queens, kings or aces is the most common of the paying hands and therefore pays the least - just 1 for 1; the royal flush is the rarest hand and so pays the most - 800 for 1. The exact frequency of each of the hands is listed in the chart below, along with the percentage amount that each hand contributes to the overall payout of the game:

HandsFrequencyPercentage
of return
Royal flush403911.98
Straight flush91480.55
Four of a kind4235.91
Full house86.810.36
Flush90.86.61
Straight894.49
Three of a kind1322.33
Two pair7.725.86
Jacks or better4.621.46

(Reproduction courtesy of Winpoker)

The numbers in the "frequency" column tell us the average occurance rate of each hand; straights occur once in every 89 hands, four of a kind every 423 hands, straight flushes every 9148, etc. The "percentage of return" column indicates the relative amount that each hand contributes to the overall payout. For example: Four of a kind is listed as 5.91%, which means that of the overall 99.54% return of this game, the four of a kind hand contributes 5.91%. Remove that hand completely and you'd be left with an overall payout reduced to 93.63%.

You can see from the "frequency" column that jacks or better occurs once every 4.6 hands on average; the royal flush on the other hand puts in an appearance only once in every 40,391. Combining this with the "percentage return" figures, we can get an idea of the sort of payout you can expect over a relatively limited amount of play - which in the case of Jacks Or Better is pretty good: over the course of as little as just a hundred hands you can expect to see each hand at least once, except for the top three - four of a kind, the straight flush and the royal; subtracting those payouts from the total, 99.54 - 1.98 - 0.55 - 5.91, leaves 91.1%. Extending the session to 500 hands we can now include four of a kind - since it hits every 423 hands on average - giving us a still very much "short-tem" payout over those 500 hands of a creditable 97%. Take this a step further and factor out JUST the royal flush and we have an overall "royal-less" game of 97.54% - the straight flush contributes relatively little to the overall return. Although you should not approach your video poker playing career from such a short-term viewpoint - there are plenty of players who play upwards of a million hands over the course of their lives - what this DOES give you is an approximate idea of what you can expect over the course of an hour or so of play.

Leaving aside the frequencies and focusing exclusively on the percentage return column, with a little bit of fiddling with the figures we can work out by how much the royal flush payout needs to improve in order to push this 99.54% game up to and beyond 100% - both online and off there are banks of Jacks Or Better "progressive" games, in which the royal payout increases as a percentage of the players' combined wagering until someone hits the jackpot, at which point it resets to its starting value; it's vital to know the point at which the game hits 100% so that you can start playing as soon as you have the edge. So, let's take a look at the numbers:

The 4000-coin royal contributes 1.98% to the overall return of 99.54%. In order to get to 100% we need an extra 0.44%, and since 0.44 is 22.22% of 1.98 (0.44 / 1.98 * 100), we need to increase the royal payout by 22.23% to squeeze just over 100% - which means the royal needs to reach at least 4889 coins. On a quarter machine, we would reach a 100% return when the standard \$1000 royal reaches \$1,222.

We can apply the same calculations to any progressive game. A very typical variant of the above scenario is Jacks Or Better with the flush payout cut to 5 and the full house to 8 - otherwise known as Jacks Or Better 8/5; if this game includes a progressive royal jackpot it will also eventually push the game over 100%, assuming it climbs high enough before someone hits it. In order to work out just how high it needs to climb, we first need to reduce the flush and full house percentage returns relative to their reduction in the pay lines: flush 6.61 * 5/6 = 5.508, and full house 10.36 * 8/9 = 9.2. We can now add those two new figures together for a new "flush plus full house" total of 14.7%. Substituting that figure for the original total of 16.97% gives us an overall payout of 97.28%, leaving 2.72% to make up with the increased royal. 2.72 is 137% of 1.98, so we need to increase the 4000 coin royal payout by 137%, or 5480 coins, in order to achieve 100% return - and that gives us a required total of 9480 coins. Translated into dollars, that's \$2370 on the \$1.25 machine and \$9480 on the \$5 version.

...and so on and so forth; as long as you know the percentage return numbers, you can calculate the costs / advantages of any set of variations.

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