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Every single casino game (except the poker room) is built solely on math. You are either playing against a paytable (Let It Ride, Mississippi Stud, Video Poker) or against the Dealer (Blackjack, Ultimate Texas Hold’em).

In the case of the latter, the dealer never makes any real decisions. All the rules about how he plays his hand is completely laid out for him. In a game like UTH, he simply plays the highest ranking 5-card hand from his seven cards. In Blackjack he sticks on 17s (except potentially a soft 17). The dealer doesn’t get to decide when he hits or sticks the way a player does.

This is supremely important to understanding that there is no bluffing in the casino, no psyching out your opponent. There have been a few efforts to pit one player against another, but these efforts have all failed. I’ve also heard of some attempts to have the dealer make an actual decision on the casino floor. I would’ve loved to have been in the room when this idea was pitched to a table games manager. The laughing could probably be heard for miles.

When dealing with a deck of cards, you are working with essentially random numbers. The deck is shuffled. You are dealt some cards as is the dealer. Assuming everything has been done properly, your odds of getting any one of the 52 cards is identical.

Knowing this, allows us to calculate with 100% precision the probability of getting every possible hand. This can be done using combinatorial math or through a computer program. The results will be 100% identical. For example, I can tell you the probability of being dealt a 5-card Straight when you are dealt 5 cards from a 52-card deck is 0.39246% or roughly 1 in 250.

What good does this do anybody? Well, it means if you are playing Let It Ride, you will get a Straight dealt about every 250 hands. By itself this isn’t too exciting. But using the same process, I can know that if the first 3 cards in Let It Ride are 2, 8, Q you have absolutely no chance of getting a Straight. So, when making the decision whether or not to pull down your “1” wager, this piece of information needs to be factored in. At the same time, if you are dealt a 5, 6, 7 you are more likely to be dealt a straight in the end than if you are dealt 5, 7, 9.

It is these frequencies that tell us if you should pull back that wager or not. We do not base this on hunches or what happened in the last hand. Even though I just told you a Straight will occur about every 250 hands, even if the last hand was a Straight and you are now dealt a 5-6-7, this does not mean you are any less likely to be dealt a Straight on this hand.

What happened in the last hand (or all those before) is completely immaterial to what is about to happen. There is just math to tell us the probability of each possible outcome.

For example, if dealt a 5-6-7 (unsuited) on the first 3 cards, I know there are 1,176 possible outcomes. Of those, 48 will result in a Straight, 9 with a Three of a Kind, 27 with a Two Pair, 30 with a Pair of 10’s or Better.

This means from this starting hand, only 114 of 1,176 (roughly 10%) will wind up as winners. Of course, we don’t decide whether or not to play or take the bet down based on hit frequency. We make the decision based on whether or not by leaving that wager up, the player is likely to win more (or lose less) than by taking it down.

We add the payouts of all the winning outcomes together (465) and compare this to the total amount of wagers (1,176). Since 465 is less than 1,176, we pull the wager down. Had this been a suited 5-6-7, the total amount we expect to win is greater than 1,176. We’d have 3 chances at a Straight Flush, which pays 200-to-1, and the additional opportunities to get Flushes. Since the number of units returned is greater than 1,176, we would leave the wager in play. Widgets

Now, you could be dealt this hand (or something like it) five times while sitting there for an hour or two and you may hit nothing all five times. Or maybe you’ll get lucky and win all five times. The math is geared over the long run. This doesn’t mean thousands of years, but it probably means a few hundred hours of playing at least.

In the end, playing the right strategy will result in the best chance for you to win the most (or lose the least) over the long run. The casinos didn’t put games on the floor that you might be able to outwit. Every game underwent a complete mathematical analysis by someone like me.

The most critical number to the casino is the payback that can be achieved by playing the best possible strategy. This tells the casino the worst case scenario from their perspective as this results in the smallest house advantage.

Every time you deviate from this strategy, they smile all the more because they know the house advantage can only go up when you do this.

Buy his book now!

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 Contact Elliot at [email protected].

About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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