When gambling think loss rate, not payback
August 20, 2013 3:00 AM
by Elliot Frome
How much of a difference is there in terms of payback from one casino game to another?
Most table games have a payback between 97% and 99.5%. Video Poker can range from about 95% to 101%. Slot machines probably range from about 85% up to 95%. Sidebets, quite frankly, are all over the place, ranging from just over the legal limit of 75% and going up to the low-mid 90%.
While there is a lot of overlap, one of the largest determining factors is strategy. More complex strategy means a combination of more human error and/or players not even trying to follow it.
Simple strategy is much easier to learn and follow. Three Card Poker has one simple strategy rule. Follow it and you should approach the theoretical payback of about 98%. Don’t follow it and you can only do worse.
Video Poker has paybacks considerably higher. Not all of the versions, but you can still find plenty of them well above 98%. Video Poker’s strategy, however, is far more complex than Three Card Poker’s strategy. The average Video Poker machine has more than 30 different strategy items that need to be memorized – in the appropriate order so you know how to play the hand.
So, first you need to review the hand and determine the realistic ways the hand can be played and then you have to know which of these ways has the highest expected value, which tells us the way the hand should be played.
In most games, many of the hands are pretty obvious even if you knew little. If you’re dealt a 6-7-8 in Three Card Poker, I don’t think you need to read a book to know what to do. What if you are dealt K-3-2? What about Q-8-2? What about Q-3-2?
For each hand, the player is really asking himself if he is better off Playing or Folding. Those are the only two options in Three Card Poker. The answer is pretty obvious for the Straight and a good deal less obvious for the other three hands.
The strategy is determined by the math behind the question of whether the player is better off folding or playing. By folding, the player forfeits his original wager (one unit). By playing, he wagers an additional unit. If playing can return at least that additional unit (on average), then the hand is worth playing.
The player does not have to perform some complex calculation on each hand. The decision is to play or fold, and the math, works out very neatly. For every hand stronger or equal to Q-6-4 the player is better off playing. For Q-6-3 or less, he is better off folding. You’ve just become an expert at Three Card Poker strategy.
Video Poker is not nearly this simple. First of all, there is no folding and no additional wagers. You make an original wager and your only goal is to maximize the amount of money you get back, on average, for each hand.
If you’re dealt a Straight off the deal, there isn’t much to think about – unless of course it is also a 4-card Straight Flush or a 4-card Royal – then what? What if you’re dealt Three of a Kind and 3-card Royal? How about a Pair and a 4-card Flush? Does it matter if it is a High Pair or a Low Pair? (Yes, it does!)
In Video Poker, the hands are categorized into about 30 to 40 different hand ranks and partial hand ranks. Each of these is assigned an expected value. This expected value is calculated by looking at ALL the possible draws for that hand and tabulating the total units won for each final winning hand.
We then divide this total by the number of possible draws so we can compare apples to apples. So, let’s look at a simple example. Suppose you are dealt the following hand: 4-hearts, 5-hearts, 6-hearts, 7-hearts, 8-diamonds.
The decision here should not be driven by your favorite Clint Eastwood line (“Are you feeling lucky, punk?”). It should be driven by the math. The straight has an expected value (“EV”) of 4.00. There is no draw in this case and the EV is simply the payout of the hand. If you decide to discard the 8, there are 47 possible draws. Two will result in a Straight Flush, five in a Straight (remember you would have discarded a card that could also have made it a Straight) and seven in a Flush. All other cards result in a losing hand.
So, do you throw away the sure four units to go for the Straight Flush? When we add up the payouts of the winning hands, we get 162 units (2 x 50, 5 x 4, 7 x 6). We divide this by 47 (the number of possible draws) and get 3.45. As this is less than the EV of the Straight, we keep the Straight. In the long run, this will be the better move.
While most players would play this correctly (I guess?), the simple reality is, except for those who learn the right strategy, there will be a significant number of players who will NOT play this correctly. Throw in the roughly 25% of hands that require a real decision and the casinos can count on player error to help pad their winnings.
This is why they can offer the 99.5% paybacks on so many full-pay jacks or better Video Poker machines. Someone like myself might sit down and get the 99.5%, but the vast majority of players will play well below this level. They are likely to play in the 97-98% range if they have some idea of what is going on and perhaps as little as 95% if they just “wing it.”
The difference between 99.5% and 96% may not seem like a lot, but I always suggest you turn that around to the loss rate – 0.5% vs. 4%. Now, there is a 700% increase from one to the other. The impact to your bankroll could be staggering.
Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at ElliotFrome@GamingToday.com.