# Casinos anything but rigged

April 19, 2016 3:00 AM

by
Elliot Frome

A couple of weeks ago when I discussed the notion that skill-based gaming has existed in casinos for many years, I received numerous comments from readers. One I found to be particularly interesting because it seemingly relegated video poker into the same category as slot machines. Maybe, even worse. He basically said video poker “gave the casinos a license to steal and plain irons people out.” I wrote back to the writer explaining why I disagreed strongly, but I never got a reply.

Outside of the poker room, where players are mostly playing against other players, the best chances a player has is probably blackjack and video poker. Both can easily afford the player a 99%-plus payback. Throw in the points, comps, free play, etc., and you can easily play for very close to 100% (perhaps over it from time to time). Granted, it has become much harder to find full-pay machines, even at the local casinos. But, just because they are harder to find doesn’t mean they don’t exist. The key is to not give in to the casinos and play whatever they offer. If everyone on the Strip stopped playing 6 to 5 blackjack, you’d see the return of 3 to 2 pretty quickly.

Since the writer never replied, I don’t know what he was thinking. Does he think video poker is rigged, essentially like a slot machine? When I say “rigged,” I don’t mean there is anything wrong going on. Slot machines can legally be designed to create near misses and so winning combinations occur on whatever frequency the slot-machine company designs. Video poker does not have this luxury. There are 2,598,960 ways to deal a 5-card hand from a 52-card deck. EVERY one of these almost 2.6 million hands must occur with the exact same probability. This is as completely random as if you took a freshly shuffled deck at home and dealt yourself five cards.

It is because of this feature video poker is NOT a slot machine. Because the deal is as random as dealing from a real deck, we can calculate with absolute precision the probability of every possible deal. We know exactly how many times you’ll be dealt a Four of a Kind (on the deal). We also know exactly how many times you’ll be dealt a 3-Card Straight Flush with one High Card.

But, it gets better. We also know EVERY possible outcome of EVERY possible way you can play the hand. There are 32 ways you can play a 5-card deal in video poker. These range from holding all five to discarding all five and everything in between. If you discard only one card, there are 47 possible outcomes (the remaining 47 cards in the deck, one at a time). Using a computer, we can play each of these 47 possible outcomes and determine the average amount the player can expect to win. This is called the expected value. So, if the player is dealt: 4, 5, 6, 7, J, and chooses to hold the 4-Card Straight, we know there are eight cards that will complete the Straight and every other card creates a losing hand. Thus, the total amount that might be won is 8 times 4 (payout of a straight), which equals 32. We divide this by 47 and get our expected value – 0.68. The same process is used for the other 31 ways the player can play the hand. If he discards two cards, there are 1,081 possible draws. The process becomes a bit longer, but the same principle applies. We look at every possible draw and the final hand that it creates. We sum up the payouts of all these hands and divide by the number of possible draws.

When this is complete for each of the 32 different ways the hand can be played, we compare the 32 different expected values. Whichever of the 32 has the highest expected value is the proper way to play the hand. So, in case you thought about holding that single Jack, the expected value of that would only be about 0.47, which is well below the expected value of our 4-Card Straight. But, if that 4-Card Straight were an INSIDE Straight (make the 5 into a 3), THEN the expected value of the 4-Card INSIDE Straight would only be about 0.34 and we would play the Jack High. And, if that Jack were a 10 instead, we would find the way with the highest expected value is to discard all five cards. This is what is called a RAZGU and is the worst possible hand we “play.”

However, this should not be confused with the worst POSSIBLE way you CAN play a hand. As I just described, if the player were to choose to play the 4-Card Inside Straight, he’d be playing a hand with an expected value of 0.34. The Razgu would have an expected value of 0.36. It’s not MUCH better, but it is still better and thus is the correct way to play the hand.

What I’ve described here is the essence of the strategy for video poker. It applies to EVERY version of video poker. But since it relies on the payouts of hands, this means each paytable combination may have its own strategy. If our Straight paid 5 instead of 4, then a 4-Card Inside Straight would be the playable hand over the Razgu.

So, perhaps my reader just didn’t understand that video poker has a complex strategy that must be learned in order to take advantage of the paybacks it offers. But, then again, this is why I put it in the category of a game that involves skill, not just luck.

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*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**. Email: **ElliotFrome@GamingToday.com**.*