The Hazard of Short Pay Machines

            Last week, I glossed over the cost of playing less than full-pay machines.  This week, I'm going to jump into this topic a bit further.  Full-pay machines are the version of a particular type of video poker that have the commonly found highest paybacks.  The obvious example of this is what is called the 9-6 full pay jacks or better machine.  We call it 9-6 because this is the payout for the Full House and Flush.  What about the other pays?  Well since the bottom 4 pays are usually 4-3-2-1, we don't see much variation in these payouts.  Lowering any one of them would require an identical payout for two hands of different ranks.  Casinos try to avoid this where possible.


            In a minute, you'll see that there is another reason why these payouts change infrequently (aka never).  Calculating the payback of any paytable game works the same whether we are talking about video poker or a blackjack sidebet.  We multiply the frequency of each winning hand by the payout of that hand and sum up these values.  In a blackjack sidebet, this is all relatively easy as calculating the frequency of a winning hand usually involves either some simple combinatorial math or a quick computer simulation of every possible hand.


            In video poker, calculating the frequency of winning hands is a bit more complex.  As I've covered many other times, the frequency changes as the paytable changes.  Thus, the frequency of a Flush with a payout of 6 may not be the same as the frequency when the payout is 5.  We also need to take into account the payout of all the other hands.  Fortunately, no one needs to this on the fly and we have already developed computer programs that can calculate the frequencies no matter what the specific paytable is.


            Most importantly for the purpose of this topic is that this means that the impact of a reduction (or increase) in the payout of any single hand is roughly the frequency of that hand.  I say roughly because as I just described this frequency changes as the payout changes.  But, for hands like a Flush, it is not going to go from 0.5% to 2.0% frequency.  It might change by a few hundredths of a percent because of a single unit or two. 


            This brings me back to why we don't see the payout on High Pairs, Two Pairs or Three of a Kind change very often.  The frequencies of these hands on a full pay machine are approximately 21%, 13% and 7.5%.  A single unit reduction in these payouts (which is impossible for the High Pair unless we eliminate the payout) would cause a 21%, 13% and 7.5% reduction, respectively in the payout of the video poker machine.  There just isn't that much variation in the paybacks so modifications of these hands for the purposes of adjusting the payback just doesn't happen.


            On the top end of the paytable we have Royal Flushes, which occur about 1 in 40,000 hands.  With an 800 payout these add 2% to our payback (1 / 40,000 x 800).  So, in theory, the casinos could lower these to 400 and shave 1% off the payback.  But it is this 800 payout that makes the Player salivate a little.  It is an attainable significant win.  Cutting it would hurt the allure of video poker, so you're not going to see this.  In fact, once in a while a casino will increase the payout here to make the game even more attractive.  Alternatively, you'll find a Progressive where the payout might get to 1000 units and add 0.5% to the payback.


            Straight Flushes contribute only 0.5% to our payback.  The bottom line is that lowering the payout won't do much to change the payback.  I'm a bit surprised that there aren't a few variations of the game that haven't paid 100 for a Straight Flush to offset some other hand being lowered.  Straight Flushes are the black sheep of video poker hands because of this somewhat low payout for such a rare hand.


            That leaves us Straights, Flushes, Full House and Quads.   No surprise that this is where we see most of the payout variations.  Four of a Kinds are occasionally cut to 20, but this is rare.  Four of a Kinds occur about 1 in 420 hands (0.24%).  The 25 payout contributes 6% to our payback.  Cutting to 20 reduces this by just over 1%.  But, like the Royal, reducing this payout doesn't really please the customer much.  Instead, bonus poker and all its variants were created to create payouts above 25.


            Ironically, despite payouts ranging from 4 to 9, Straights, Flushes and Full Houses all occur at rather similar frequencies of just over 1.1%.  This means that a 1 unit reduction in any of these hands results in a just over 1% reduction in the overall payback.  Unfortunately, most Players don't even pay attention to these middle payouts.  Who cares about a 1 unit reduction of payout for a hand that occurs about 1 in 90?  That won't cost you much, will it?  Well, now you know that it will cost you just over 1%.  The most common paytable where this happens is the 'infamous' 8-5 short pay paytable.  The 1 unit reduction in payout for both the Full House and Flush costs the Player over 2% in payback.  Instead of the 99.5% payback of a full-pay machine, it plays at 97.5%


            What will this cost you?  If you play a quarter machine at max-coin at 600 hands/hour (a good but not top speed), you'll play $750 in an hour.  At 99.5%, this will cost you $3.75.  At 97.5% this will cost you $18.75.  It is a $15/hour difference.  Over a vacation week,  you could easily be looking at dropping an extra couple hundred dollars.   If you're a local who plays more regularly or a $1 player, the cost of playing 8-5 vs. 9-6 could be devastating to your bankroll.