Odds Of Winning Poker At A Casino

Remember: in blackjack, your chances of winning or busting will change each time a card is removed from the deck. In Example 1, the probability of the dealer going bust on their next card is. Mobile Casinos Enjoy a favorite casino game on the go with a cutting edge mobile casino. Free Casino Games Play over 225 different games of blackjack, slots, roulette, and video poker for fun. Casino Game Rules Learn basic gameplay for baccarat, craps, blackjack, poker, roulette, and more. Online Casino Payouts View a monthly.

Introduction

The house edge is defined as the ratio of the average loss to the initial bet. In some games the beginning wager is not necessarily the ending wager. For example in blackjack, let it ride, and Caribbean stud poker, the player may increase their bet when the odds favor doing so. In these cases the additional money wagered is not figured into the denominator for the purpose of determining the house edge, thus increasing the measure of risk. For games like Ultimate Texas Hold 'Em and Crazy 4 Poker, where there are two required initial wagers, the house edge is based on one of them only. House edge figures are based on optimal or near-optimal player strategy.

The table below shows the house edge of most popular casino games and bets.

Casino Game House Edge

Notes

Guide to House Edge

The reason that the house edge is relative to the original wager, not the average wager, is that it makes it easier for the player to estimate how much they will lose. For example if a player knows the house edge in blackjack is 0.6% he can assume that for every $10 wager original wager he makes he will lose 6 cents on the average. Most players are not going to know how much their average wager will be in games like blackjack relative to the original wager, thus any statistic based on the average wager would be difficult to apply to real life questions.

The conventional definition can be helpful for players determine how much it will cost them to play, given the information they already know. However the statistic is very biased as a measure of risk. In Caribbean stud poker, for example, the house edge is 5.22%, which is close to that of double zero roulette at 5.26%. However the ratio of average money lost to average money wagered in Caribbean stud is only 2.56%. The player only looking at the house edge may be indifferent between roulette and Caribbean stud poker, based only the house edge. If one wants to compare one game against another I believe it is better to look at the ratio of money lost to money wagered, which would show Caribbean stud poker to be a much better gamble than roulette.

Many other sources do not count ties in the house edge calculation, especially for the Don’t Pass bet in craps and the banker and player bets in baccarat. The rationale is that if a bet isn’t resolved then it should be ignored. I personally opt to include ties although I respect the other definition.

Element of Risk

For purposes of comparing one game to another I would like to propose a different measurement of risk, which I call the 'element of risk.' This measurement is defined as the average loss divided by total money bet. For bets in which the initial bet is always the final bet there would be no difference between this statistic and the house edge. Bets in which there is a difference are listed below.

Element of Risk

Standard Deviation

The standard deviation is a measure of how volatile your bankroll will be playing a given game. This statistic is commonly used to calculate the probability that the end result of a session of a defined number of bets will be within certain bounds.

The standard deviation of the final result over n bets is the product of the standard deviation for one bet (see table) and the square root of the number of initial bets made in the session. This assumes that all bets made are of equal size. The probability that the session outcome will be within one standard deviation is 68.26%. The probability that the session outcome will be within two standard deviations is 95.46%. The probability that the session outcome will be within three standard deviations is 99.74%. The following table shows the probability that a session outcome will come within various numbers of standard deviations.

I realize that this explanation may not make much sense to someone who is not well versed in the basics of statistics. If this is the case I would recommend enriching yourself with a good introductory statistics book.

Standard Deviation

Hold

Although I do not mention hold percentages on my site the term is worth defining because it comes up a lot. The hold percentage is the ratio of chips the casino keeps to the total chips sold. This is generally measured over an entire shift. For example if blackjack table x takes in $1000 in the drop box and of the $1000 in chips sold the table keeps $300 of them (players walked away with the other $700) then the game's hold is 30%. If every player loses their entire purchase of chips then the hold will be 100%. It is possible for the hold to exceed 100% if players carry to the table chips purchased at another table. A mathematician alone can not determine the hold because it depends on how long the player will sit at the table and the same money circulates back and forth. There is a lot of confusion between the house edge and hold, especially among casino personnel.

Hands per Hour, House Edge for Comp Purposes

The following table shows the average hands per hour and the house edge for comp purposes various games. The house edge figures are higher than those above, because the above figures assume optimal strategy, and those below reflect player errors and average type of bet made. This table was given to me anonymously by an executive with a major Strip casino and is used for rating players.

Hands per Hour and Average House Edge

Footnotes

* — House edge based on Ante bet only as opposed to all mandatory wagers (for example the Blind in Ultimate Texas Hold 'Em and the Super Bonus in Crazy 4 Poker.

Translation

A Spanish translation of this page is available at www.eldropbox.com.

I never play slot machines. If I want to play at a gambling machine, I usually stick with real money video poker.

I have various reasons for this, but one of the most important reasons is because the odds of winning at video poker are far better than the odds of winning at a slot machine game.

How do you know what the odds of winning on a video poker machine are? I can offer some guidance in this post. To learn more, keep reading below.

Probability and Video Poker

Before you can calculate the probability of winning at video poker, you need to understand some of the basics of probability math.

The first and most important thing to understand is that an event’s probability is just a number between 0 and 1. The closer that number gets to 1, the likelier it is to happen.

By definition, something with a probability of 0 will never happen. Also by definition, something with a probability of 1 will always happen.

Odds For Casino Games

And if you add the probability of something happening with the probability of it not happening, you’ll also always get a total of 1.

That probability can be expressed in multiple formats, but the most useful formats are odds and percentages.

Everyone knows what a percentage is. It’s just a measure of how many times out of 100 you expect something to happen. If something happens 20% of the time, that means it happens 20 times out of every 100.

Odds, on the other hand, can measure probability. But they also measure the amount a bet pays out. Something with a 20% probability of happening has odds of 4 to 1. You have four ways it can happen and one way that it can’t.

Like other fractions, odds can be reduced. To get to that 4 to 1, we just converted 20% into 20/100, which reduces down to 1/5. That means it happens 1 out of 5 times.

Gambling Machines Measure Their Odds in Terms of Payback Percentage

When you’re dealing with a slot machine, you have a variety of symbols on each reel, each of which comes up a certain percentage of the time. You don’t have any way of estimating how often that symbol will show up, but the slot machine manufacturer knows.

When they take all the possible combinations and their percentages of coming up, they balance that against the payout for each of those combinations to create a profitable game for themselves.

Let’s say you have a really simple slot machine game with four potential winning combinations:

1. You’ll get three bars 25% of the time and win even money.
2. You’ll get three cherries 10% of the time and win 2 for 1.
3. You’ll get three plums 5% of the time and win 3 for 1.
4. You’ll get three pumpkins 1% of the time and win 5 for 1.

It’s easy to calculate the expected return (another phrase for “payback percentage”) for a game like this.

You start by calculating the expected value for each of the possible prizes. You just multiply the probability of winning by the amount you’ll win.

1. 25% x 1 unit = 25%
2. 10% x 2 units = 20%
3. 5% x 3 units = 15%
4. 1% x 5 units = 5%

Add those up, and you have the payback percentage for the game:

Over time, on average, you’ll get back 65 cents for every dollar you bet on that slot machine game.

In the short run, over an hour or so, you might win some money or lose more than that. But over time, your average should get close to this.

The Advantage of Video Poker Over Slot Machines

My problem with slot machines is that they’re the only game in the casino where you don’t know what the odds of winning are.

When I’m rolling a pair of dice, I can calculate the probability of winning. When I’m playing blackjack, I can estimate the odds of winning, because I know what the odds of getting specific cards are. When I’m playing roulette, I know how many red and black outcomes are on the wheel.

But since slot machines are run by a random number generator, I have no way of knowing what the probability of getting three cherries in a row is. It could be 8 to 1, 16 to 1, or 1000 to 1.

All I know for sure is that the odds of getting each payout are lower than the payout odds for that combination.

Video poker, on the other hand, is based on a deck of 52 cards. I know how many of each card is in the deck, so I can estimate the odds of getting specific combinations.

When you combine that knowledge of probability with knowledge of the payouts for those combinations, you wind up with the payback percentage of the game.

Jacks or Better Is the Original Video Poker Game

For the most part, all video poker games are just variations of Jacks or Better. It’s a simple enough game. You bet between 1 and 5 coins and get dealt a virtual five-card poker hand. You then decide which of those five cards you want to discard and which you want to keep. The machine deals you replacement cards and pays off your bet based on the poker hand you wind up with.

The best possible hand is a royal flush, which pays off at 800 for 1 odds if you bet five coins. If you’ve bet fewer coins than that, it only pays off at 200 for 1 or 250 for 1, depending on the machine.

So, you should always bet the full five coins to take advantage of that higher payout. If you play with something approaching optimal strategy, you should get a winning hand about 45% of the time on a Jacks or Better video poker game.

That’s the short answer to “what are the odds of winning on a video poker machine,” by the way. It’s roughly 45%. But that’s not going deep enough. You should know more about it than that.

Since we know the probability of winding up with various combinations of cards, we can calculate the overall payback percentage for such a game. You just do the same calculations we did for the simple slot machine above.

You multiply the probability of winning each prize by the amount of that prize and add them all together to get your payback percentage.

Odds Of Winning At Casino

1. A pair of jacks or better comes up about 21% of the time and pays off at 1 for 1.
2. Two pair comes up about 13% of the time and pays off at 2 for 1.
3. Three of a kind comes up about 7%of the time and pays off at 3 for 1.
4. A straight comes up about 1% of the time and pays off at 4 for 1.
5. A flush comes up about 1% of the time and pays off at 6 for 1.
6. A full house comes up about 1% of the time and pays off at 9 for 1.
7. A four of a kind comes up about 0.2% of the time and pays off at 25 for 1.
8. A straight flush comes up about 0.01% of the time and pays off at 50 for 1.
9. A royal flush comes up about 0.002% of the time and pays off at 800 for 1.

Chances Of Winning At Casino

Multiply those and add them all up, and you have a game with a payback percentage of about 99.5%.

But Not All Video Poker Games Are the Same

Of course, Jacks or Better is just one variation of video poker. You can find dozens of different video poker variations on the market. All of them are based on Jacks or Better, though.

With some of these variations, the big difference is the inclusion of wild cards. In Joker Poker, the game uses a 53-card deck with a joker that acts as a wild card. In Deuces Wild, the deck has the same 52 cards in it, but the twos are wild cards.

With games like these, the payouts for the various hands change based on how much more likely the higher hands are to appear.

But that’s not the only way casinos and game manufacturers vary their video poker games. They also change the payouts on various hands.

If they change those payouts enough, you get a different game. Bonus Poker, Double Bonus Poker, and Bonus Bonus Poker are basically variations of Jacks or Better that provide higher payouts for four of a kind hands of a certain ranking.

Best Odds At Casino

But even within a single narrow band of a game, like Jacks or Better, you can find multiple pay tables available. The differences in these pay tables change the payback percentage for the game.

With Jacks or Better, the pay table I used as an example is the best possible example. When manufacturers want to create a Jacks or Better game with better odds for the house, they have smaller payouts for the full house and the flush. Changing those payouts from 9 and 6 to 8 and 5 reduces the payback percentage from 99.5% to 97%.

Your Decisions Matter

One of the other fun things I like about video poker is that your decisions have an effect on the outcome. These payback percentages that I mention assume that you’re playing your cards optimally. In other words, you’re making the right decisions about which cards to keep and which ones to throw away.

Best Odds Of Winning Slots

Imagine what your payout would be if you broke a pair every time you got one. Can you see why that would hurt your results in the long run?

Conclusion

What are the odds of winning at video poker? On a single hand, on most games, it’s about 45%. But that only tells a small part of the story.

Video poker offers a nearly endless amount of complexity when it comes to payback percentages and correct strategy. It’s a game worth learning to play.