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  4. How Does Casino Make Money On Texas Holdem

Up until the 2000s, seven card stud was the dominant form of poker throughout many parts of the world. But this changed during the poker boom of the mid 2000s, when Texas holdem became the preferred game for every major tournament.

Thanks to this popularity, millions of people now play Texas holdem on a daily basis. And no matter whether you’re just playing with friends or grinding in online casino cash games, the goal is always to win money.

But how do you win if you’re a beginner and / or not very good at poker?

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Find out in this comprehensive guide, where we take you from the basics to the techniques that’ll help you beat Texas holdem.

The Basics of Winning at Texas Holdem Poker

Texas holdem is often described as taking 5 minutes to learn and a lifetime to master. This is even truer today with strategy being so readily available, giving more players the opportunity to become experts.

Nevertheless, everybody has to start somewhere with the game, and that somewhere should not immediately be real money poker tables.

If you’re new to the game or just looking for a solid strategy base, here are the basic concepts that you should know.

Table Position

One of the most overlooked concepts among poker beginners is table position, meaning you act after opponents.

Position is measured by where you sit in relation to the big blind. The dealer button is the latest position, while the small blind is the earliest.

The reason why position is so important is because it allows you to gain more information based on your opponents’ decisions. Additionally, having position on most or all of your opponents helps you control the pot size and better read your opponents’ hand strength.

On a 9 seat table, here’s how table position looks:

Early Position


Small blind, big blind, seat to the big blind’s left. You generally want to play strong hands from these spots because you don’t have as much information.

Middle Position


The next three seats. Middle position gives you an idea of what a few players are doing. But you still want to be cautious about what hands you play in this area.

Late Position


Dealer button, best, and the two seats to its right. Late position gives you a good opportunity to steal blinds, small pots, and judge opponents’ hand strength on later streets.

While it’s entirely possible to win from any position on the table, the majority of your Texas holdem winnings will come from late position, while most losses will come from early position.

Limit the Number of Hands You Play

The single biggest Texas holdem mistake bar none is playing too many hands.

Many new players think that they can play a wide range of hands on speculation. But the truth is that most of the 169 possible starting hands are complete garbage.

Before we continue, here’s a look at the top 10 starting Texas holdem hands:

These are premium hands that are playable in many situations, regardless of your table position.

As you can see, popular hands like A Q, K J, and 9 9 are not on this list. Yet many players treat these cards like they’re premium hands, playing them in any situation.

The majority of beginners also have trouble understanding how their hand strength relates to position.

If you have QQ through A A, table position won’t be a factor because these are premium hands. But when you play hands like K J, Q J, 8 8, and A T from early position, you can be put into a difficult situation if somebody raises.

Another mistake that players make is overvaluing speculative hands like suited connectors, or consecutive cards of the same suit, i.e. 6d 7d. While there are certainly times where these hands are valuable, you’ll be better off folding these cards the vast majority of the time.

In fact, you should be folding 80 to 85% of your hands until you develop a better understanding of poker. As you gain more experience, you’ll develop a better idea on when to play certain hands based on opponents, table position, and previous bets.

Reading Opponents

Reading Texas holdem opponents is less about identifying a nervous ticks than it is about paying attention.

When you first come onto a table with new opponents, you have no information about what range of hands they like to play or the type of bets they make in specific situations. The best that you can do in these situations is pay attention and take mental notes.

The good news is that if you’re folding 80 to 85% of the time like we suggested before, you’ll have plenty of hands to observe opponents. You can then use this information when you’re faced with difficult decisions against the same opponents whom you’ve been watching.

You’ll find no shortage of things to look for when observing other players. But key factors to look for include what range of hands they play in each position, when they bet, the size of their raises / re raises, and how often they bluff.

As you play more Texas holdem, you’ll eventually begin seeing patterns in less skilled opponents that you can exploit.

Limit Your Bluffing, Look for the Right Opportunities

Aside from playing too many hands, another mistake that new players make is bluffing too often. We can blame Hollywood for this, but the key is that you understand the reality behind bluffing.

Before we continue, the main types of bluff include: small bluffs, semi bluffs, and naked bluffs.

Small Bluff

Small bluffs are bets that are normally made in late position to steal blinds and small pots. The idea is to keep your bet low so that you risk very little to earn a small profit.

Here’s an Example

The flop is Js Jh 4c, and everybody checks to you on the dealer button.

Either somebody has a jack in this situation and they’re slow playing it, or nobody has a jack and they don’t like the board.

Odds are that it’s the latter, and you can steal this pot with a small bet that represents strength.

Semi Bluff

A semi bluff is a bet / raise where you don’t have a made hand, but you could possibly still win the pot later.

Here’s an Example

You raise pre flop with Ac Kc and draw two callers. The flop is dealt 10c 2h 8c.

The first player checks, and the second makes a two thirds, pot sized bet. You make a pot sized raise in late position in hopes of pushing them out of the hand.

Assuming they have any pair, then they currently have you beat. But the fact that you can still win with your over cards or flush draw makes this a semi bluff.

Naked Bluff

The naked bluff, a.k.a. stone cold bluff, is the type that you see in poker movies, where somebody goes all in with 2 7 off suit and forces a fold.

These are the worst possible bluffs because they leave you totally exposed and out your money if the opponent calls.

Here’s an Example

You raise with 8s 7s in late position to steal blinds, but the small blind calls. You then see a flop of Kc 4d 2c.

The opponent makes a two thirds pot sized bet to open, and you come back with a 1.5x pot sized raise.

You have absolutely nothing in this situation because both your flush and straight draws were killed on the flop. Your only hope is that the opponent doesn’t have kings, or another made hand, and folds.

Naked bluffs can be useful in the right situations, for the right player. But you need to have experience and good reads on opponents before you can turn these plays into long term profits.

A good rule of thumb is to completely avoid naked bluffs until you’re adept at small bluffs, semi bluffs, and reading opponents.

Understand Basic Poker Math

Poker is often miscast as a game where you need to make great reads and incredible bluffs to win. While these aspects can help you gain an edge, it’s far more important that you understand the math behind playing certain hands rather than when to bluff with 3 9 off suit.

Below are the most important Texas holdem math concepts in the order that you should learn them.

Counting Outs

The best place to begin is with counting your outs, or the number of cards needed to make your desired hand.

Here’s an Example

You have an open ended straight draw, meaning there are four cards on either end that will complete your straight, giving you 8 total outs.

In order to calculate your outs, you need to know how to read the board, which shouldn’t be hard as long as you understand poker hand rankings.

Also note that you can’t count outs that will give your opponent / s a better hand.

Here’s an Example

You have an open ended straight draw, but two diamonds on the flop. Anybody with two diamonds in their starting hand will form a flush if another one lands on the turn or river.

That said, you can’t count the two diamonds that will complete your straight on either end, thus reducing your outs to 6.

Pot Odds

Pot odds help you decide when to make a tough call based on the amount of money in the pot compared to how much you must contribute to see the next card / showdown.

Here’s an Example

$20 is in the pot and your opponent bets $10, making the total pot $30. You now need to call $10 to play for the $30 pot, making your pot odds 30 to 10 or 3 to 1.

This alone doesn’t tell you anything, which is why you must figure out your chances of getting the card you need to win the hand.

An easy way to do this is by taking your outs, then multiplying this number by 4, which puts your chances of winning the hand into a percentage.

Here’s an Example

You have a flush draw, which gives you 9 outs to make your flush. Multiplying this by 4, you have a 36% chance of making your hand, or a ratio of 64 to 36.

The final step is to compare your ratio of winning the hand 64 to 36 to your 3 to 1 pot odds.

Since it’s hard comparing 64 to 36 to 3 to 1, let’s simplify 64 to 36 by dividing 64 by 36, making the ratio roughly 1.8 to 1.

Now, you can compare your 3 to 1 pot odds to 1.8 to 1 hand odds.

The idea is that you want to call if your pot odds are higher than your hand odds. Since they’re higher, you would make the call in this instance.

Implied Odds

Once you’re adept with pot odds, you can start factoring in implied odds, which take into account whether calls are worth making based on future betting action.

The goal of implied odds is to determine if your opponent will pay you off after your drawing hand is completed. In essence, implied odds can make what appears to be a non-profitable call based on pot odds turn into a profitable call.

The only problem with implied odds is that they don’t have a clean mathematical formula like pot odds. Instead, you’re estimating based on the board and an opponent’s previous betting patterns if they will pay you off.

Here’s an Example

You work your pot odds out to 3 to 1, and your odds of winning a hand to 3 to 2. Based on pot odds alone, you shouldn’t make this call.

But let’s also say that you hold 8s 9c on a board of Jh 10h 3s, and your opponent bets into the pot. Based on their previous betting patterns, you feel that the opponent will pay you off if you make the straight.

Based on the slim ratio that you’re already facing with 3 to 1 pot odds versus 3 to 2 hand odds, any future raise from the opponent will make this play worth calling.

Reverse Implied Odds

Continuing on the example above, you also have to consider that your opponent could have a flush draw based on the board. And if they hit this flush, you’ll lose regardless of whether you complete the straight.

This is where you should consider reverse implied odds, or the amount of money that you stand to lose based on an opponent making their hand.

Just like implied odds, this concept doesn’t have a clean mathematical formula that you can base your decision on.

But the basic idea is that you don’t want to call without pot odds if an opponent / s can form a better hand than you based on the board.

Essentially, reverse implied odds call on your to forget implied odd when opponents are drawing for a better hand.

Texas Holdem Tournaments vs Cash Games

In order to win in both Texas holdem cash games and tournaments, you need to understand that there are crucial strategy differences between the two. Here’s a closer look at the strategy nuances that you’ll see when moving from cash games to tournaments.

Texas Holdem Cash Game Strategy

One notable aspect about cash games is that you theoretically have unlimited chances to win. If you go all in and bust out, you can buy back in and continue playing.

This allows you to be more aggressive with your chips and play the odds to a T. Furthermore, you’ll find that it’s always correct to chase draws when you estimate good pot odds and implied odds.

How Does The Casino Make Money On Texas Holdem

Even if you fail to make your hand, which happens the majority of the time, you’re still making smart positive expected value +EV plays.

Another notable factor about tourneys is that you should always be playing with a full stack size. This allows you to get maximum benefit out of any +EV situations where you need to make large raises / re raises or go all in.

Any time that your chip stack is less than the max buy in, you should get more chips to build it to the max.

Texas Holdem Tournament Strategy

Chips gain more value in poker tournaments because, outside of rebuy events, you can’t replace them. This means that you need to be more conservative with your chips in certain spots.

Here’s an Example

You’re getting 4.2 to 1 pot odds and have a 4 to 1 chance to hit your drawing hand. In a cash game, the correct decision would be to call; in a tournament, this thin value isn’t worth the risk to your stack size.

Aside from representing your tournament life, your chip stack size also plays a role in the overall strength of your bets, raises, and bluffs. The larger your stack, the better you can intimidate smaller stacks that are fighting for their tournament lives.

On the reverse side, having a smaller stack forces you to be more aggressive in situations that you might not otherwise be.

Specifically, when your chip stack falls below 10 big blinds, you need to look for any chance you can to steal blinds and / or double up. Oftentimes, these won’t be your favorite time to go all in, but you can’t afford to let the blinds wither your chip stack to nothing.

Quality of Tournament Players vs. Cash Players

One more thing worth noting is that you’ll generally face weaker players in Texas holdem tournaments.

For starters, Texas Holdem is one of the simplest poker variations to learn, making it popular among beginners and recreational players.

Another element is that players can only lose as much as their tournament buy in. This is more comforting than cash games, where there’s no limit on the amount of money that you can lose.

Online Texas Holdem vs Live Texas Holdem

Another big division in Texas holdem strategy comes between the live and online format. That being said, let’s look at what you need to be aware of when transitioning between the two.

Hands Per Hour

The rate of hands that you play in online poker versus live poker isn’t even close.

At a standard online Texas holdem table, you’ll play anywhere from 60 80 hands per hour HPH on average. If you multi table, you could easily play hundreds of HPH.

Contrast this to live poker, where, even with an experienced dealer, you’ll only play 20 to 30 HPH.

This is both good and bad as far as online poker goes. On one side, you gain more experience through internet poker since you’ll see more hands. On the other hand, you stand to lose more money if you’re not very good.

Assuming you do become great at poker, the online version will provide you with a better hourly rate. You can also get over downswings quicker since you’ll be playing more HPH.

Online Poker Forces You into Quick Decisions

Internet poker sites feature timers that force you into quick decisions.

This is good from the perspective that other players can’t stall when thinking about decisions. But it’s also bad when you’re trying to improve and can’t make snap decisions.

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If you start playing bad due to the faster pace, this can lead to tilt, or the mental state where you make bad decisions because you’re no longer in the optimal poker mind state.

This makes being aware of yourself and your mind state one of the most important factors in online poker success.

Live Texas Holdem Offers Physical Tells

The number of tells that you can gather from nervous facial expressions is overrated in live poker. But the fact is that you can gain physical information from live poker players through their facial expressions, hand movements, posture, and talkativeness.

When playing internet poker, the only tell that you have is your opponents’ betting patterns and range of playable hands.

This is still enough to gain crucial information that can help you win. But it also cuts out one weapon since you can’t physically observe how your opponents react in certain situations.

Texas Holdem Bankroll Management

Far too many beginning poker players jump into tournaments or cash games with only a few buy ins to their name.

We get it: the prospect of winning money through poker is exciting when you set your mind to it. But due to the variance / downswings of poker, you won’t last very long without a sizable number of buy ins.

Below, you can see what to plan for in terms of bankroll management.

What Stakes Should You Play?

The first step to poker bankroll management is figuring out how much money you can afford to play with. Look at your finances and bills, then come to a determination on a comfortable amount that you can put towards poker.

The next step is figuring out what stakes you should be playing based on this amount.

A good guideline for cash games is to never play stakes where you have to risk more than 5% of your bankroll at once. If you have $500 set aside, then you should never play a cash game where the max buy in is over $25.

Tournaments are different because there’s more variance involved due to only 10 15% of the field making money. This is why it’s good to play stakes where you can cover at least 100 buy ins.

If you want to play tourneys with $10 + $1 buy ins, you should have a bankroll of $1,100 or more.

Deal with Variance

Expanding on the previous topic, having a solid bankroll helps you survive downswings and variance that might otherwise wipe out your funds.

Given that poker has elements of chance, you’ll go through periods where nothing seems to go right no matter how well you’re playing. Bad beats, poor card runs, and tilt will all wreak havoc on your bankroll at some point.

Pulling out of these downswings not only requires patience and skill, but also enough money to cover the losses.

Focus on More Than Money

The primary reason why people play Texas holdem is to make profits. But if you’re only focusing on how much you win and lose each session, then you’ll do far more of the latter.

Instead, you should focus on goals that will improve your long term skills so that you can make money.

Examples of non monetary goals include:

  • Playing x number of hands per month
  • Studying poker strategy for x number of hours each week
  • Playing sessions for x number of hours
  • Spending x number of hours analyzing your own play

Drop Down in Stakes

What should you do when you can’t pull out of a rut and are questioning your poker skills?

The best answer is to drop down in stakes for two reasons: 1) you’ll facer weaker competition, and 2) you’ll be risking less money per buy in.

Nobody wants to work their way up to a certain level, only to have to drop down because they’re not playing well. But sometimes this is the best remedy when nothing else is going right.

Poker Tools to Help You Beat Texas Holdem

What we’ve covered so far only scratches the surface of how you can become a better Texas holdem player.

Next to the lines you can adjust the amount of bet per one line. Each line win adds to your total win for the single spin. At least 3 symbols count! Winnings of oz free slots. Note that it multiplies by the number of lines you are betting on with each spin.By clicking the Info button, you can access the paytable which shows the probability of winnings on each line.

The best tip we can give you is to never stop in your quest to keep improving because there’s always something to learn. Here’s a closer look at some tools that’ll boost your poker skills.

Texas Holdem Articles

Since the mid 2000s, thousands of poker articles have sprang up on the internet covering every Texas holdem topic imaginable.

You can either visit major poker sites and browse through their strategy section or just perform simple Google searches to find the exact topics that you’re looking for.

Texas Holdem Books

Books were once the dominant way to learn poker strategy. After all, the internet didn’t exist and players had no way to quickly access Texas holdem information.

Poker books aren’t as popular as they once were, but you can still find a great deal of information through both ebooks and hardcover works.

One of the best things about Texas holdem books is that they allow you to dive deep into the mindset of pros and how they play their hands.

Coaching

You can hire professionals to teach you poker either in person or online. Regarding the latter, coaches can use screen sharing software to see how you play internet poker and offer suggestions over the course of your play.

This is perhaps the quickest way to improve if you find a good coach. But the downside is that you have to pay a high hourly rate to hire the best coaches.

Forums

Since the Poker Boom, forums have become populated with both Texas holdem tips and discussion groups.

This has archived a great deal of poker strategy information that you can use to improve your play. You can even pose your own questions, although forums are becoming a less popular today thanks to the spread of social media.

Poker Software

Third party companies sell software that you can use at poker sites to gain advanced statistics on opponents.

The most popular type of software is a Heads Up Display HUD, which offers numbers and percentages on players’ tendencies.

Some HUDs can even offer you statistics on players whom you’ve never even seen. For this reason, many online poker sites have banned HUDs to give recreational players who don’t use software a fighting chance.

Training Videos

For Texas holdem players on a budget, the best value in poker strategy is training videos.

These videos feature mostly skilled pros explaining different strategy concepts while playing online poker.

This not only gives you more insight into how pros think, but it’s also cheaper than coaching. Many sites allow you to access thousands of training videos for a $30 monthly subscription fee.

Conclusion

One final thought on becoming a better poker pro is to constantly think about and analyze your play.

This is made easier through the use of online hand histories. But when you don’t have access to these, then at least replay difficult situations in your head and try to come up with solutions on how to work through these problems.

You can also pose specific hand questions / problems on forums or ask coaches.

Additionally, you should spend at least one hour studying strategy for every 3 to 4 hours you spend playing. This might not sound like fun, but the improvement that you see in your play will be well worth it.

And once again, there’s no cap on the amount of time that you can spend improving as a player. If you truly want to become a profitable player, then keep fine tuning your strategy and working your way up the stakes.

Peter Chi

Peter Chi is an Assistant Professor of Statistics at California Polytechnic State University (Cal Poly) in San Luis Obispo, CA. While his professional interests lie mainly in biomedical research and genetics, he is an avid poker player and enjoys looking at applications of statistics to poker and gambling in general. He also enjoys teaching Probability Theory at Cal Poly by using numerous examples from poker and other games of chance.

As the 2014 World Series of Poker winds down with the Main Event right around the corner, it is hard to imagine that the game of poker might not be very profitable to a casino. Players have come from over 70 countries from across the world, to fill the Rio All-Suite Hotel and Casino for more than a month. Surrounding poker rooms have also benefitted from the additional traffic due to the sheer number of poker players currently in Las Vegas.

However, this is not the norm for the entire year. At many Las Vegas casinos, their poker room may not actually be profitable in and of itself, even with the uptick during the WSOP months. Indeed, the fact is that casinos, in Las Vegas or otherwise, tend to make the vast majority of their revenue through their slot machines and table games. These two types of games generally make more money for the casino than everything else combined.

How Do Casinos Make Money On Texas Holdem

So, if poker is unprofitable or not as profitable to a casino as its other games, then this leads us to the following question: does poker drive business to the real money slot machines and table games? This question actually has many possible facets to it, including the effect of the existence of poker in general, online poker in particular, and most specifically, the poker room at an individual casino and how its presence may or may not draw slot machine and table game traffic there. From a business standpoint, casinos certainly may be interested in this question, as the answer can help them decide whether to support online poker legislation, and/or whether to have a poker room in their property.

Anecdotally, many poker players would say that poker definitely does drive traffic to other games: a quick perusal of the online poker forums would reveal a number of posts from poker players stating that they never would have placed a bet on one of these house games if it were not for the fact that they played poker first, or that when they go to a casino primarily to play poker, they might also play some of the other games as well. Speaking for myself, I can say that I certainly have spent way more time at the blackjack and craps tables than I would if I had not first built a gambling bankroll through poker.

But, how about some actual data? Many casinos likely have done at least some sort of analysis on this question internally; however, for the sake of unbiased, scientifically rigorous answers, it would be preferable to turn to peer-reviewed research published in academic journals. A recent study published in the UNLV Gaming Research and Review Journal is actually the first instance of exactly that.

This study specifically examined the question of whether there is an association between an individual casino’s poker room traffic and its slot machine and table game revenue. Currently, a common assumption is that even if a poker room is not very profitable in and of itself, it still may be useful to have as it would in fact attract people to their property, and specifically to their slot machines and table games. However, the conclusions from this study were that there is actually no evidence that such a relationship exists.

Performed by Dr. Anthony Lucas, Professor of Hotel Administration at UNLV, this study examined data obtained from three Las Vegas resorts, which contained daily revenue statistics over the course of almost a year. On these data, Dr. Lucas executed six statistical tests: for each of the three properties, he tested whether its poker room rake was associated with its slot machine revenue, and also with its table game revenue. In only one of these six tests, he found statistically significant evidence in favor of an association. Thus, his overall conclusion was that five out of his six results question the notion that poker rooms drive business to the slot and table games, and that casinos might want to reconsider having a poker room if it is not profitable on its own. For those of us who like to play poker in a casino, this may come as dismal news. However, I would like to offer a different interpretation of these results.

The first reason for this is because of the distinction between statistical significance and meaningful effect sizes. To illustrate this, consider a poker player whose ability we would like to evaluate — perhaps if we are interested in staking him. So, to answer this question, it would be good to collect some data to see if he is truly a winning player in the long run.

To this end, imagine that we follow him for a few sessions, in which he plays for 30 hours and comes back with $3,000 in profit. Thus, with these data, we would have observed some evidence that he is a winning player. But, how strong is it? Those of us who have examined our own win rates rigorously will know that this is not very strong evidence, because of the enormous variance in poker. Indeed, if we were to do a formal statistical test, we would inevitably conclude from these data that we did not have statistically significant evidence in support of the notion that he is a winning player (to have “statistically significant evidence” that he is a winning player essentially means that the result we observed is sufficiently unlikely to have happened if the truth is that he is not a winning player). With only 30 hours of play in our records, it is not too unlikely that he simply went on a small heater to win $3,000 in that time, even if he is actually a losing or breakeven player in reality.

On the other hand, what if you were forced to “guess” his true win rate? You might object and say that we simply do not have enough data to do this, but suppose, hypothetically, that I give you no choice. What would your guess be? Well, a reasonable guess would just be straight from the data that we do have, or $100/hour. Of course, due to the high level of variability, it is more likely that this estimate is wrong than right, or even close. However, if these are the only data that we have, then this is the best that we can do.

Thus, in this example, our estimate of $100/hour is our “effect size,” or how much we would guess that this player wins per hour on average based on the data. Although we would not find statistically significant evidence to suggest that he is a winning player from a formal statistical test, this estimate of $100/hour would still be our best guess at his true win rate given the data that we have.

How Does The Casino Make Money On Texas Hold'em

Now, let us look at the results from Dr. Lucas’ study. Recall that he did not find a statistically significant result in five out of six tests that he performed. However, what were the effect sizes? From his analysis, his model e.g. for Resort 1 shows that a 10 percent increase in poker room traffic is associated with an expected increase in profits from slot machines by approximately $965 in any given day (see addendum for details). While this result was not statistically significant, it seems to be a substantial amount of real dollars. If you are thinking that $965 does not sound like very much money for a casino, notice that this is $965 per day, and resulting from merely a 10 percent increase in poker room traffic.

Also, this figure of $965 accounts for the fact that a casino can only expect to keep approximately 7.5 percent of the money that goes into a slot machine (or “coin-in”), since players sometimes win; the associated increase in the raw coin-in from a 10 percent increase in poker room traffic is thus much greater, at just over $12,800 (or $965 divided by 0.075). Additionally, this particular poker room in Resort 1 only has eight tables, as stated in the original study. Thus, it is clear that a 10 percent increase can actually be no more than eight added people, on average over the course of a day. Considering this, I would say that a $965 increase in slot machine profits resulting from this is rather remarkable (although as a brief aside, this figure does not account for any possible operating expenses associated with running a slot machine).

Just like with our poker player, we may not have obtained a statistically significant result, but I would suggest that we do not ignore the real dollars that have been gained. In other words, if $100/hour is an amount that our poker player considers to be worth playing for, it would make little sense to conclude that he should not be playing, from the data that we have. Clearly, we just need to observe this player for longer, to obtain more data. Likewise, from Resort 1, the important question is this: does the casino consider $965 per day from a 10 percent increase in poker room traffic to be an effect size that would be worth caring about? If so, then we would not want to conclude that our evidence questions whether the casino should have a poker room; we would instead want to collect more data to see if this initial estimate stands or not.

In the addendum, I also examine each of the other five results. In each case, we have varying levels of associations in terms of real dollars, with some being greater than others. However, this leads me to my second reason for interpreting these results much less negatively than the original study does: for every single one of the six statistical tests, the estimated association between poker room rake and the outcome variable (either slot machine or table game revenue) is positive. That is, albeit being statistically significant in only one of the six tests, Dr. Lucas estimates from the data that an increase in poker room rake is associated with an increase in the outcome variable, in all six cases.

This observation is one that should not be ignored. The reason is simple: if there truly is no association between poker room traffic and each outcome variable, then it is equally likely that we should observe a negative association as it is that we should observe a positive association, due to chance and variability in the process. Thus, the chance that we would observe positive associations in all six tests, if the truth is that there really is no association, would be the same as flipping a coin six times and having it land on heads each time. Since this is fairly unlikely, then this provides some evidence that there actually is an association between poker room traffic and revenue from the other games (in statistics, this procedure is known as the “sign test”).

I want to point out that there were, however, many positive aspects to the study. It is an important question to examine through a rigorous, unbiased study that could be published in a peer-reviewed journal, so I was very pleased to see that one had been done. I feel that it was well performed overall, and in particular, the author is careful to note that his findings should not be extrapolated beyond the three resorts that he specifically studied. I also do not mean to suggest that his negative conclusions were necessarily “wrong.” The statistical methodology that he performed was largely correct, and he used standard acceptable criteria to assess statistical significance from his models. I am simply offering a different interpretation of the results obtained in this study. However, I believe that the points I have raised here are important to consider before any managerial decisions would be made by a casino, based on this study or any other like it.

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