Playing according to long term math

[Alan Mendelson]

I had a fascinating discussion with our board member John about the long term math of video poker. John basically said he plays according to long term math and I said the long term math doesn't matter because none of us will ever see the long term.

I also said that yes, I would play video poker games with the best pay tables.

I just looked at the Wizard of Vegas forum and there is a thread there asking what is the long term? And the Wizard said, in part:

" It can be said that the more you play the closer to the "long run" you will get, but you will never fully arrive there."

I agree. None of us will ever see the long term, nor will we ever see a full and equal distribution of results in any game and that includes video poker, craps, roulette or blackjack.

My position is that with each repeat of a combination of cards or a number in craps or roulette the chance that you will ever see the long term and an equal distribution of numbers gets harder to reach.

Using a single six sided die is the easiest way to explain this:

With one die the long term equal distribution would be getting one roll each of 1, 2, 3, 4, 5, 6. But if just one of those digits repeats just once then the long term equal distribution would become:

1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6

And if you get one number to repeat four times, then the long term equal distribution would be:

1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6

Now consider a game like video poker with 52 unique cards and let the distribution of that deck of 52 vary with just one card being dealt twice... and then see how many hands the long term becomes!

[Rob.Singer]

All agreed, and all is exactly right. The trick in vp at least, is in first understanding, then putting that knowledge into practice, and finally -- at least for social purposes -- trying to explain why and how using a short term approach is a far superior method of successful play.

People do have to understand the best explanations of what the long term really is if they ever hope to understand how to play short term strategy successfully. But the interested player MUST FIRST set aside their misguided bias that playing positive machines will yield winning years, and playing negative games will not. Only then will said player be able to enter into a world that will unveil the sensibilities of beating any machine on a regular basis, with adequate bankroll, proper discipline, and a strategy designed to leave the casino after a minimum 5% win. The player will also discover the harsh truth that few ever have the willpower AND the tools to do it. And that's why the casinos, together with their long term math supremacy, will always remain open to all.

[arcimede$]

Alan, we've been over this before. While you never get to the exact long term, you approach it within a range that can be predicted. That's why the amount of edge a person has is important. If the error range is less than the edge you can be highly confident of winning. The question becomes one of probabilities. Do you play when you have a 95% chance of winning or not? Is it worth an effort to give yourself that kind of chance? Or, do you just conclude a 99% chance of losing is the same as a 5% chance of losing and ignore the math?

[Dan Druff]

This willful ignorance of basic mathematics is the reason the casinos are standing and doing brisk business (all mismanagement of resources, aside).

The long run is very important because it indicates the average of what you can expect to lose in a given session.

The higher the average, the more you will lose.

Vegas realized over time that most gamblers don't care about odds or averages, so they are progressively worsening the games year after year, and the public comes back for more.

People don't understand that they will lose 4 times as much at a 96% return than a 99% return machine. All they care is that they see that big hand hit every so often, and they think, "Wow, just a few more of these, and I'll really be kicking ass!"

I just had a similar argument with someone who was insisting that he liked playing 6:5 blackjack, because he has "better luck" at those tables.

[Rob.Singer]

This willful ignorance of basic mathematics is the reason the casinos are standing and doing brisk business (all mismanagement of resources, aside).

The long run is very important because it indicates the average of what you can expect to lose in a given session.

The higher the average, the more you will lose.

Vegas realized over time that most gamblers don't care about odds or averages, so they are progressively worsening the games year after year, and the public comes back for more.

People don't understand that they will lose 4 times as much at a 96% return than a 99% return machine. All they care is that they see that big hand hit every so often, and they think, "Wow, just a few more of these, and I'll really be kicking ass!"

I just had a similar argument with someone who was insisting that he liked playing 6:5 blackjack, because he has "better luck" at those tables.

This post is an excellent example of misguided bias. There is no relationship between the so-called long run and the average expected loss/session. It's nothing but a state of mind from someone who loses because they play bad games at CET casinos that lure him in with a promise of untold freebies that he can value himself in order to create a year-ending "feel good" so all was not lost.

The math favors the casinos. Always has. The success of the player, outside of extreme good luck, rests only in being able to perform exactly the opposite as the casinos want and expect players to perform. The AP concept of playing only +EV games (or more precisely, to concoct positive plays out of the many "reel 'em in" promos casinos continue to offer this group) and that you should approach expectation the more you play, has always been flawed in that, just as there are very, very few of the extremely lucky winners out there because they just happened upon machines at their most giving part of their timeline, it is just as rare for the machines to cooperate for any "grind it out" player that wants to get to any imaginary expectation point somewhere in the future. The idea makes sense in the classroom, but is practically impossible to duplicate in a real setting. Theory regularly gets destroyed by reality.

[Dan Druff]

This post is an excellent example of misguided bias. There is no relationship between the so-called long run and the average expected loss/session. It's nothing but a state of mind from someone who loses because they play bad games at CET casinos that lure him in with a promise of untold freebies that he can value himself in order to create a year-ending "feel good" so all was not lost.

The math favors the casinos. Always has. The success of the player, outside of extreme good luck, rests only in being able to perform exactly the opposite as the casinos want and expect players to perform. The AP concept of playing only +EV games (or more precisely, to concoct positive plays out of the many "reel 'em in" promos casinos continue to offer this group) and that you should approach expectation the more you play, has always been flawed in that, just as there are very, very few of the extremely lucky winners out there because they just happened upon machines at their most giving part of their timeline, it is just as rare for the machines to cooperate for any "grind it out" player that wants to get to any imaginary expectation point somewhere in the future. The idea makes sense in the classroom, but is practically impossible to duplicate in a real setting. Theory regularly gets destroyed by reality.

This is nonsense, and also why most here don't believe you actually win.

You say a player should "perform exactly the opposite as the casinos want and expect players to perform".

What does that even mean? Give a single tangible example of how a player can turn the tables to beat the casino, aside from "advantage play" tactics (which you constantly deride).

The bottom line is that you will lose more if you play games with a worse pay table. Period. Forget the long term. Even in the medium and short-medium turn, a larger casino edge will take its toll.

There is one exception to this. It's when the expected return hinges upon an event that is unlikely to be achieved in the number of hands/spins you can play.

For example, say there were a prize of $100 billion on a $1 bet, but you had a 1-in-25-billion chance to hit it.

Let's say that the returns on this machine are otherwise very bad, but the machine is overwise +EV because of the $100 billion return on a 1-in-25-billion chance.

It still wouldn't be worth it, because a human being could never play 25 billion hands to where you would ever expect it to hit.

Of course, this is an extreme example, but it illustrates my points. A lesser example of this is why a player might prefer to play a 99.26% Aces and Faces machine over the 99.40% ACE$ machine, since ACE$ itself will only hit about once every 300,000 hands.

But barring payouts that are very unlikely to ever hit for an individual player, Rob's logic is garbage.

[Rob.Singer]

This is nonsense, and also why most here don't believe you actually win.

You say a player should "perform exactly the opposite as the casinos want and expect players to perform".

What does that even mean? Give a single tangible example of how a player can turn the tables to beat the casino, aside from "advantage play" tactics (which you constantly deride).

The bottom line is that you will lose more if you play games with a worse pay table. Period. Forget the long term. Even in the medium and short-medium turn, a larger casino edge will take its toll.

There is one exception to this. It's when the expected return hinges upon an event that is unlikely to be achieved in the number of hands/spins you can play.

For example, say there were a prize of $100 billion on a $1 bet, but you had a 1-in-25-billion chance to hit it.

Let's say that the returns on this machine are otherwise very bad, but the machine is overwise +EV because of the $100 billion return on a 1-in-25-billion chance.

It still wouldn't be worth it, because a human being could never play 25 billion hands to where you would ever expect it to hit.

Of course, this is an extreme example, but it illustrates my points. A lesser example of this is why a player might prefer to play a 99.26% Aces and Faces machine over the 99.40% ACE$ machine, since ACE$ itself will only hit about once every 300,000 hands.

But barring payouts that are very unlikely to ever hit for an individual player, Rob's logic is garbage.

Unlike you and your thin-skinned approach to virtually any discussion Dan, it only matters that I win to myself and my family. It's certainly no secret why a loser such as yourself moans & groans about slot club "freebie cutbacks" non-stop, why you can't get away from the CET "grip of humiliation", and most of all, why you can't stand to see pictures of my big winners that you'll obviously never be able to experience yourself. Losers absolutely HATE winners....even the mere mention of it, and they will never, ever listen to them because they can't. But, I will answer your question in a "teachable moment" type of gesture.

Try to think in terms of Business 101 instead of as a trampled-on gambler. A casino is an entity designed to profit by taking as much of its customers' money as possible, and by any conceivable means possible under the law. They try to get gamblers to open casino credit accounts. Why? For two reasons: first, to be able to look into a player's finances to see if they're worth "stretching" them to the limit; then, to get the customer to tap into their credit line when their pocket cash is gone. Casinos also use this process to dole out more and better of those sacred comps you losers go so goo-goo over. DO THE EXACT OPPOSITE OF THIS AND NEVER FOOLISHLY SIGN UP FOR THIS CASINO TOOL.

Next, always ignore those ATM and cash advance machines so cunninglty scattered around the casino floors. As a loser, you know why. Nuff said.

Some people hit jackpots at their comfortable playing denominations. But what do the majority of players do after hitting them? (And you can ask Alan about this one). Correct--with a fistload of unexpected cash and RIGHT ON CASINO CUE, they waltz right on into those beautiful, alluring high limit rooms, complete with a gutload of confidence and high from the big win. And what overwhelmingly happens (Jason can attest to this in spades). You know the drill. Just as the casino wanted and expected the player to do, all was lost, and more, and the only thing the sucker has to show for such a stupid move is a handful of AGI-busting W2G's. NEVER, EVER MOVE UP IN DENOMINATION AFTER WINNING.

Now onto another typical player weakness: tipping on handpays. This is another of the traits casinos want and expect gamblers to do, because it allows them to pay lower wages to the floor people, fully knowing that the intimated handpaid "winners" will gladly make up the difference in tips....of course, given out in the euphoria of the moment. KEEP YOUR MONEY THAT YOU WON GAMBLING, AND LEAVE SALARY ISSUES TO THOSE IN CHARGE OF SALARY ISSUES. AND NEVER , EVER BE SO WEAK AS TO FEEL OBLIGATED TO GIVE YOUR MONEY AWAY TO CASINO EMPLOYEES BECAUSE OF SMILES, CONGRATULATIONS, OR OTHER STUPID SOCIAL MISGUIDEDNESS. PERIOD.

Set win/loss goals for your casino visit, your day, and/or your trip, and then leave immediately when they're attained. No casino wants or expects any player anywhere to do this. THIS IS THE SINGLE, MOST DIFFICULT, MOST UNPOPULAR TASK IN A WINNING PLAYER'S LINEUP. CASINO AMBIENCE, AND THE INSATIABLE NEED FOR GAMBLERS TO KEEP MORE ACTION COMING BECAUSE THEY JUST CAN'T BEAR TO SEE IT END (Alan will attest to this) IS THE NUMBER ONE REASON FOR CUSTOMERS LEAVING WITH THAT GUT-WRENCHING FEELING OF STUPIDITY AND INCOMPETENCE.

You guys all worship those idiotic casino hosts. That's one of the casino's most effective tools they use in systematically taking your money. These people make you feel oh-so-special and pretend to be your trusted friend at your "home away from home". But the ONLY reason they're there is to make you feel just a little bit better about transferring your money from your bank accounts to the casino's...aka, their EMPLOYER'S! Using and having one of those sacred "relationships" with them will also reduce your marketing offers, and they will keep a close eye on your every move while you're inside their casino. Very stupid indeed. NEVER USE THESE PEOPLE FOR ANYTHING. WINNERS DO NOT EVER WANT TO BE ON ANY EMPLOYEE'S RADAR; LOSERS WANT TO BECAUSE THEY FEEL THE "COMPS" HELP MAKE UP FOR SOME OF THE LOSSES WHILE HELPING JUSTIFY THE TRIP, AND WHEN THEY RETURN HOME A LOSER THEY CAN SOOTHE IT ALL OVER BY THINKING THEY HAVE A TRUE FRIEND, INDEED, AT THE CASINOS THAT JUST SURGICALLY SCRUBBED THEM .

Finally--and you fight this losing battle all the time here....I'm sure it keeps you up endless hours of your looong "what-if" laced nights: you and your fellow gamblers are almost all completely controlled by the slot clubs, their mesmerizing offers, all that "free stuff", and you constantly find yourselves roped in by juicy sounding promos, specials, giveaways, point bonanzas, etc. etc. etc. NEVER, EVER BE CONTROLLED BY THIS NONSENSE. IT IS IN PLACE FOR ONE SINGLE REASON: TO KEEP GETTING PLAYERS COMING BACK WITH amazingly high anticipation and WITH FRESH LOADS OF CASH FROM ANY MEANS POSSIBLE, WHILE MAKING THEM FEEL GOOD ABOUT LOSING ALL OF IT BY DAY'S END.

As a bonus helping hand, get rid of that dumb belief that playing positive games means you'll win, and playing negative games means you'll lose. I've disproved that nonsense for 15 years. Play each session like you do each hand--like it is independent of every one that's come before and every one that's yet to come. And shake that BS about 99.1% vs. 101.6% vs. 94.7%. That stuff doesn't matter one way or the other in any given session. You either play with a strategy meant to take complete advantage of the big & other winners that come along, or you don't. And, you either hit them or you don't. And get rid of your silly advantage play belief if you ever expect to be a winner. They only win if they get consistently lucky, just like anybody. Only they don't win much. They want you to believe they win because that's what the math books say will happen in a perfectly controlled environment. And some can't take it when this theory doesn't pan out for real, so they lie about it in order to keep their sanity.

In short, here's your chance: wise up.

[Alan Mendelson]

Alan, we've been over this before. While you never get to the exact long term, you approach it within a range that can be predicted. That's why the amount of edge a person has is important. If the error range is less than the edge you can be highly confident of winning. The question becomes one of probabilities. Do you play when you have a 95% chance of winning or not? Is it worth an effort to give yourself that kind of chance? Or, do you just conclude a 99% chance of losing is the same as a 5% chance of losing and ignore the math?

I agree. This is why I said above in a comment to Dan: play the best games and make the best bets. You just cannot bank on the "long term." In other words, if a machine returns 99.98 over the long term you will never be at that machine for the long term to be guaranteed 99.98%. But in your "short term" you might hit 99.98% or do better or worse.

Arc, where have you been? Missed you here.

[arcimede$]

I agree. This is why I said above in a comment to Dan: play the best games and make the best bets. You just cannot bank on the "long term." In other words, if a machine returns 99.98 over the long term you will never be at that machine for the long term to be guaranteed 99.98%. But in your "short term" you might hit 99.98% or do better or worse.

Arc, where have you been? Missed you here.

Alan, you can't "count on" living another day. Does that man you should just sit around all day eating bonbons? Everything we do has some risk. I managed to "bank-on" the long term probabilities each and every year for over a decade. I found it a decidedly better way to approach gambling.

PS. I have checked in occasionally but none of the topics interested me.

[slingshot]

Alan, you can't "count on" living another day. Does that man you should just sit around all day eating bonbons? Everything we do has some risk. I managed to "bank-on" the long term probabilities each and every year for over a decade. I found it a decidedly better way to approach gambling.

PS. I have checked in occasionally but none of the topics interested me.

Correct. So we just live for the moment-the short term.

[arcimede$]

Correct. So we just live for the moment-the short term.

No, you develop a plan based on the best statistical approach and follow it. Sure, it takes a little work but it is well worth it. Do you use short term thinking for everything you do? I developed a plan for my retirement when I was young. I saved and lived within my means. I was able to retire at age 52 and live comfortably. Long term thinking paid off handsomely.

[Alan Mendelson]

Dan I agree that players have to be aware of odds and payback, but I think the point is this: there is no such thing as the long term.

Better if you just said -- play the best games, and make the best bets.

[slingshot]

All that being said, I see that Rob's advice to try to just win $5 on bp will probably be necessary with the worsening casino holds.

[a2a3dseddie]

Using a single six sided die is the easiest way to explain this:

With one die the long term equal distribution would be getting one roll each of 1, 2, 3, 4, 5, 6. But if just one of those digits repeats just once then the long term equal distribution would become:

1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6

And if you get one number to repeat four times, then the long term equal distribution would be:

1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6

Now consider a game like video poker with 52 unique cards and let the distribution of that deck of 52 vary with just one card being dealt twice... and then see how many hands the long term becomes!

Alan, what are you trying to say here? If the number 1 was rolled 4 times in a row, the subsequent rolls do not need to be 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6 for the results to be considered an equal distribution. The sample size here is much too small. That pattern looks like anything but random.

If that die was rolled six billion times, (the die and roll was fair) wouldn't you approach results that showed approximately one billion "1's", one billion "2's" etc? The actual order of the numbers rolled cannot be predicted, but the final results can be pretty well approximated.

[Alan Mendelson]

Alan, what are you trying to say here? If the number 1 was rolled 4 times in a row, the subsequent rolls do not need to be 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6 for the results to be considered an equal distribution. The sample size here is much too small. That pattern looks like anything but random.

If that die was rolled six billion times, (the die and roll was fair) wouldn't you approach results that showed approximately one billion "1's", one billion "2's" etc? The actual order of the numbers rolled cannot be predicted, but the final results can be pretty well approximated.

My point is that there really is no "long term" because the long term is not "fixed" and the long term changes with each subsequent play.
The return that is posted on a machine is not a long term result, it is the expected return based on one play given the pay table that is available.

There is no "long term return." Every time you play one hand the long term return will change.

[Dan Druff]

My point is that there really is no "long term" because the long term is not "fixed" and the long term changes with each subsequent play.
The return that is posted on a machine is not a long term result, it is the expected return based on one play given the pay table that is available.

There is no "long term return." Every time you play one hand the long term return will change.

Alan, that is partially true, but the long term indicates what your odds are for winning for each hand played. And that's what's important. Sometimes you'll beat the odds, sometimes you will fall behind the odds, but as you play more, you will get closer and closer to the expected return.

You can't ignore the per-hand odds and say, "Well, I'll never reach the true long term, so who cares?"

That's like saying mountain climbing and spending the day at the library don't have a considerable difference in danger, as a few people have died in library fires over the years, and most people survive mountain climbing, so each instance of library visitation and mountain climbing each carry their own chance of death, and you shouldn't worry about the long-term odds of dying in either of them.

[Alan Mendelson]

but the long term indicates what your odds are for winning for each hand played.

Read what you wrote because that is the essence of the confusion.

You wrote "the long term indicates what your odds are for winning for each hand played." That is not correct.
The long term has nothing to do with the odds for winning each hand played. The odds of winning each hand played is only the odds for that hand.

The "long term" payback is actually nothing more than an extrapolation of the overall payback on each hand based on the pays. And it is not correct to make that extrapolation. Let me explain:

Let's take a 9/6 Jacks game with a "theoretical return" of 99.6%. On each and every hand the theoretical return is 99.6% but that doesn't mean over the long term I will have a return of 99.6% does it?

In fact, if I had a million dollar bankroll and kept playing a 99.6% return game I would be left with ZERO money. This is because if you keep losing 0.4% hand after hand eventually your money will all be gone.

So, to say that the long term of a 9/6 Jacks game is 99.6% is absolutely wrong. In fact, the "long term" of playing a 9/6 Jacks Game is zero.

[quahaug]

Read what you wrote because that is the essence of the confusion.

You wrote "the long term indicates what your odds are for winning for each hand played." That is not correct.
The long term has nothing to do with the odds for winning each hand played. The odds of winning each hand played is only the odds for that hand.

The "long term" payback is actually nothing more than an extrapolation of the overall payback on each hand based on the pays. And it is not correct to make that extrapolation. Let me explain:

Let's take a 9/6 Jacks game with a "theoretical return" of 99.6%. On each and every hand the theoretical return is 99.6% but that doesn't mean over the long term I will have a return of 99.6% does it?

In fact, if I had a million dollar bankroll and kept playing a 99.6% return game I would be left with ZERO money. This is because if you keep losing 0.4% hand after hand eventually your money will all be gone.

So, to say that the long term of a 9/6 Jacks game is 99.6% is absolutely wrong. In fact, the "long term" of playing a 9/6 Jacks Game is zero.

The expectation isn't to win $0, it's to LOSE everything. Big difference.

[arcimede$]

The "long term" payback is actually nothing more than an extrapolation of the overall payback on each hand based on the pays. And it is not correct to make that extrapolation. Let me explain:

Let's take a 9/6 Jacks game with a "theoretical return" of 99.6%. On each and every hand the theoretical return is 99.6% but that doesn't mean over the long term I will have a return of 99.6% does it?

In fact, if I had a million dollar bankroll and kept playing a 99.6% return game I would be left with ZERO money. This is because if you keep losing 0.4% hand after hand eventually your money will all be gone.

So, to say that the long term of a 9/6 Jacks game is 99.6% is absolutely wrong. In fact, the "long term" of playing a 9/6 Jacks Game is zero.

You are misusing or confusing terms. A return of 99.6% means the game will return .996 dollars for every dollar bet. To lose a million dollars also means you would have winning hands totaling 249 million dollars. So, both claims are true. You will receive 99.6% of bets and you could lose a million dollars if you gamble a large amount of money. Once again you are confusing bankroll with amount gambled.

PS. In some venues that amount of play could produce more than a million dollars worth of comps/cashback/etc.

[arcimede$]

My point is that there really is no "long term" because the long term is not "fixed" and the long term changes with each subsequent play.
The return that is posted on a machine is not a long term result, it is the expected return based on one play given the pay table that is available.

There is no "long term return." Every time you play one hand the long term return will change.

Not relevant. All that matters is your probable return. While the pay table provides information about the long term, it also provides information about your most probable future results no matter how much you play. If you don't like the words "long term" then don't use them. The fact remains the same. The pay table provides the best information to determine your future results.