## Wednesday, August 29, 2012

For those of you who read my column regularly, you are probably now well aware that a full-pay jacks or better video poker machine pays 99.5%.  Many people are still confused, however as to what this means.  It does NOT mean that if I start with \$100 I will walk away with 99.5% or \$99.50.  It means that in the long run, you could take the total amount you wager (NOT your bankroll) and multiply it by 0.5% (the 'loss' rate or 100% minus the payback) and this should be the amount you have lost over time.  So, if you play 10,000 hands over the course of a year (or a month or a decade) and you play max-coin \$1 machines, you would have wagered \$50,000 and can expect to lose about \$250.

In video poker, however, 10,000 hands isn't really the long run.  Don't get me wrong, it is certainly approaching the long run.  But, given that a Royal Flush should occur about every 40,000+ hands, it would be hard to declare 10,000 hands to be the long run.  If you've hit at least one Royal, you would be ahead of the game.  If you haven't, it would be totally fair to say you are behind because you still have 30,000+ hands to go.  Royal Flushes account for about 2% of our payback.  So, if you were to NEVER hit one, you'd theoretically be playing only a 97.5% game.

With a hand frequency of 1 in 40,000+, Royals sort of march to their own drummer.  You might hit 2 or 3 in 40,000 hands or you might go 100,000 hands without hitting one.  When you hit one, you're going to have a very good month and when you don't, well, it will be harder to even break even.

Four of a Kinds, on the other hand, should occur about 1 in about 420 hands.  With the average Player playing hundreds of hands per hour and perhaps thousands in a session, this hand becomes critical to our chances of success over a session or two.  It accounts for 6% of our overall payback.  Relative to the other hands, this is not necessarily large, but it is a hand that is frequent enough that you expect to hit it over a session, but not frequent enough to be sure you'll hit your fair share over a few nights.   If you were to play 10,000 hands, you'd probably find that the frequency of High Pairs and Trips and Straights are very close to what they should be.  Royals will by very definition have to be either more frequent or less frequent than expected, but Quads can be just about anywhere over that period of time.

In theory, you should hit about 24 of them over that time.  The math says you very likely could hit only 12 or as many as 36.  If you hit 12, you're about 3% short in payback.  Assuming you haven't hit a Royal and you're now 5% short.  The odds of coming up a winner over that span is very unlikely as you'll be playing at 94.5% and hoping the other hands come up big - which simply isn't very likely.

Conversely, if you've hit36 of them, you'll be at 100.5% EVEN if you haven't hit a Royal.  A winning session is not guaranteed but certainly more likely.  Over time, the frequency of the Quads will slowly head towards that 24 per 10,000 hands, but your results in the short or medium run is heavily dependent on hitting your four of a kinds.

As with anything video poker, the number of Four of a Kinds you get is at least partially attributed to luck.  We've all played for hours and been dealt dozens of Three of a Kinds to watch NONE of them turn into Quads.  We've also all sat there and drawn 3 Kings to a single King.  Nothing that happens is truly out of the ordinary.  However, you can increase your chances by playing the right strategy.  If you hold a 4-Card Straight OVER a Low Pair, you are going to greatly reduce your chances of Quads.  If you hold 3 High Cards instead of just the 2 that are suited, you will lower your chances for getting Quads.  The reason why we hold only the 2 suited cards is both to give us a chance to hit the Royal AND to increase the chances of Quads.  Both of these hands are reduced to ZERO CHANCE if you hold 3 off-suit High Cards!

Of course, if you choose to hold a Low Pair OVER a 4-Card Flush you may increase the frequencies of Four of a Kinds, but you'll do so at your own peril.  Quads are important, but not so important that you should be throwing the proper strategy out the window.

## Wednesday, August 8, 2012

### Playing with House Money

Over the years, there have been numerous successful sidebets to blackjack.  Many people have wondered why blackjack Players would bother with a sidebet.  A good blackjack Player can play the game at 99.5%, so why would they want to play a sidebet that might pay anywhere from 75%-90%.  That would seem to defeat the purpose of playing a game with such a narrow house edge.

I think the success of blackjack sidebets lie in the volatility of them.  Blackjack is essentially a game of coin tosses.  You win one, you lose one.  You win two, you lose three, you win two more.   It is hard to make a real killing (or get killed) on anyone hand unless you have one of those cases where you split 8's, draw another 8 and then a bunch of 2's and 3's for Double Down situation.   The average wager at a blackjack table is a mere 1.15 (roughly) units.

The sidebet on the other hand will frequently afford the Player the opportunity to win big on a single hand.  The more frequent payoffs might pay 4 to 1 or even 10 to 1.  The more rare winning hands might pay 100 to 1 or 1000 to 1.  A \$5 wager can quickly (so to speak) become \$500 or \$5000.    The tradeoff for this opportunity is generally the lower paybacks associated with no strategy sidebets.  The casinos can't offer 97-98% paybacks for games with no strategy because they can't rely on human error to help drive the casino edge.

A couple of months ago, Roger Snow, Chief Product Officer at Shuffle Master brought a game idea to me to analyze.  As is frequently the case when we work together, the game went through multiple iterations before we arrived at the final product.  After we 'ran the numbers', I think Roger liked it but didn't love it.  I, on the other hand, told him I thought we had just come up with a nearly perfect sidebet for blackjack.  It was given the name House Money for reasons which will soon become clear.

As far as I know, it is the first and only blackjack sidebet that has strategy, yet somehow does not affect base blackjack strategy at all.  As a result, if a Player chooses not to play the sidebet, he gives up nothing to the house by sitting at a table that offers it. Also, the casinos are able to offer a sidebet with a payback in the 95+% range because there is the possibility of human error in the strategy.  With all this, the concept of the sidebet is quite simple.

The Player makes a wager before being dealt his blackjack hand.  The Dealer deals the cards as per normal blackjack rules.  If the Player is dealt a Pair, a Straight or a Straight Flush, he wins.  As always, there may be multiple paytables over time, but for now, this is the most common one for a 2, 6 or 8-deck game:

 Hand Pays (TO 1)* Suited A-K 9 2-Card Straight Flush 4 Pair 3 2-Card Straight 1
Those payouts may not look all that spectacular.  In all honesty, they are not.  If the game ended right here, the payback would only be about 75% and this would just be another 'nothing special' blackjack sidebet.  But, the game does not end here.  The Player now has two options:

·         Take his winnings and play out his blackjack end per usual
·         Add any/all of his winnings to his base blackjack wager and then play out his hand per usual

There are NO restrictions on these rules.  If the Player is dealt a Suited A-K, he will be paid 9 to 1 for his sidebet and then can add the entire 10 units to his base Blackjack wager which has ZERO chance of losing.  And YES, the casino will pay 3 to 2 for this additional wagered amount if the Dealer does not also have a Blackjack.

If the Player is dealt a Pair of Jacks, he will be paid 3 to 1 for the sidebet.  If the Dealer has a 6 up, he can add all 4 units to the blackjack wager.  If the Dealer has a 10 up, he can choose to do so too, but here's where the strategy part comes in.  Is this the right move?  In reality, it is the correct move.  I should add that if the Dealer has Blackjack, the Player NEVER risks his winnings from the sidebet.

The real fun begins when the Player is dealt a 5-6 (or 5-6 suited) and wins even money (or 4 to 1) and has to decide whether to risk his winnings on his base blackjack wager.  If the Player chooses to do so, it becomes a part of his wager in every sense of the word.  If he decides to double down, he MUST match the ENTIRE wager.  The same applies if he is dealt a Pair and chooses to split.

Imagine starting with a \$5 wager on both the base wager and the sidebet and being dealt a Pair of 8's.  The Dealer pays you 3 to 1 on your sidebet and you now have to decide if you want to add the \$20 to your base blackjack wager, making it a total of \$25.  Assuming you do and you go ahead and follow standard strategy, you will now split those 8's and you'll have to put up an additional \$25 of your own.  Now, you are dealt another 8 and you put up another \$25.  Then you're dealt a '3' and you double down and play ANOTHER \$25.  You started as a \$5 Player and now you have \$100 down on the table on essentially one hand!

For the record, you would only let your sidebet winnings ride if the Dealer has a 2 through 7 as an upcard.  However, whether you cap your bet or take your winnings, you still follow basic blackjack strategy and split those 8's.  You double down on all 11's.

So far, House Money has been very well received by the casinos that it has been demonstrated in.  It is expected to go live in the next couple of weeks in Reno at the Grand Siena Reno.  It should go live in other casinos shortly thereafter as regulatory approvals are granted.  In a few weeks, after the game has gone live, I'll review the complete strategy for the game.