# That's Why They Call It Gambling

I’m in Las Vegas this week, penning this column from my hotel room.  The other night, I was playing video poker at Sam’s Town, next to a guy who was playing single-line Multi-Strike video poker.  I’m familiar with how the game works, but I have to admit, my knowledge of the strategy changes for this intriguing game is extremely limited.  I know that you have to alter your strategy to increase win frequency at the expense of payback when you are on the lower 3 lines without having received a ‘Free Ride’.

For those unfamiliar with the game, allow me to try and explain the game.  There are four ‘levels’ in Multi-Strike.  To move up to the next level, you have to get a winning hand on the prior level.  Each of the levels pay progressively more than the previous one.  Thus hands on Level 1 pay 1 times the paytable.  Level 2 hands pay 2 times the paytable.  Level 3 hands pay 4 times the paytable and Level 4 hands pay 8 times the paytable.  To play the game you have to wager at least 1 unit on EACH level.  Thus to play ‘max-coin’ you have to wager 20 units – 5 coins times 4 levels.  This means you are paying for a level that you may never reach for each hand.  On each level, you play a brand new hand of video poker.

Roughly speaking, a Player playing proper ‘normal’ video poker strategy will win 45% of his hands.  This can be raised a bit if you tweak the strategy to focus a bit more on winning as opposed to how much you win.  However, at 46-47%, you would get slaughtered playing Multi-Strike because the odds of winning the 3 hands at Levels 1 through 3 would not be enough to be worth putting up the extra coin each time.  Thus, the game also incorporates what is called a ‘Free Ride’.  This is randomly generated by the machine to give the Player an automatic trip to the next level.  The Player continues to play the level that gives him the Free Ride, but even if he loses the hand, he still proceeds to the next highest level.  The impact of this feature is to bring the win frequency very close to 50%.

I’ve never analyzed Multi-Strike, so I can’t provide you with a payback of the game.  Also, there are numerous versions of the game to correspond to regular games (i.e. Jacks or Better, Bonus, Double Double, etc…).  Additionally, the game does not clearly provide the frequency of the Free Ride feature at each level which is required to calculation an accurate payback.  I have seen published numbers from IGT (maker of the game), but there is no way to know for sure if there aren’t different variations and which games are programmed for what frequency.

Then again, the point of this particular column was not necessarily an analysis of Multi-Strike.  The Player I mentioned earlier came across an interesting hand.  He was dealt an Ace High Straight that was also a 4-Card Royal on Level 3.  The Straight paid 4 units times 4 (for Level 3) for a total of 16 units (I didn’t notice what denomination the guy was playing).  He now faced the choice of sticking with that win and guaranteeing a shot at Level 4, OR going for the Royal Flush which would pay 1000 units (250 times 4).  By going for the Royal, he would also risk not winning at all and thus, not being given an opportunity to play the Level 4 hand.

First, I’d like to look at this as if it didn’t happen in Multi-Strike.  So, the question is, when dealt a Straight that is also a 4-Card Royal, what is the right play?  Keep in mind, in this particular case, the Player was NOT playing max-coin, so the payout for the Royal was ‘only’ 250.   To fully analyze this situation, we need to look at every possible outcome of going for the Royal.  However, even at a quick glance, we get our answer.  The Player is essentially risking 16 units to win 1000, which is more than a 60-fold increase.  With 47 cards remaining in the deck, he has a 1 in 47 chance of hitting the Royal, which means his potential winnings are greater than the risk.  This tells us that he should go for the Royal.  When we realize that he will also have an additional chance to get a Straight Flush, 7 more ways to get a Flush, 5 more ways to get a Straight and 9 ways to get a High Pair, the decision to go for the Royal becomes an easy one.   The expected value of going for the Royal is about 8.19, while holding the Straight was only 4.

Of course, in the specific case I’ve spelled out, the decision was a bit tougher.  By going for the Royal, he still has 23 out of 47 chances to wind up a winner and get to Play Level 4.  But, by holding the Straight, he has a 100% chance of playing Level 4.  We cannot dismiss this from the equation.  The expected value for Level 4 is about 7.84 (assuming a 98% payback multiplied by 8).  However, this assumes that we definitely get to play it.  In the case of going for the Royal, we need to multiply this by 23 and divide by 47 to account for the probability of getting to Level 4.  This is only 3.84.

So, we need to add these amounts to the respective EVs stated earlier.  While the decision gets quite a bit closer, going for the Royal still edges out the Straight by about 0.19.  I have to admit that I didn’t exactly do this calculation in my head when the guy looked my way (not knowing who I was) and I said “I’d go for it.”  Good thing for me and for the guy playing that he hit the Royal!  Yes, folks – that’s why they call it gambling!