John Grochowski writes about money management.

[Alan Mendelson]

Not me. When I hit a royal I dance on the display tops of the machines and use the row of machines as a stage and sing Hallelujah and sound as loud as the Mormon Tabernacle Choir which is a pretty good trick inside a casino!

[regnis]

We need video proof!!!

[Alan Mendelson]

Next time I hit a royal, you will see it here. I'll put on a show with a dance more fantastic than what Gene Kelly did.



And with that sound more dramatic than the Mormon Tabernacle Choir.

[FrankScoblete]

"Singing in the Rain" is a great, great movie.

[Alan Mendelson]

Not me. When I hit a royal I dance on the display tops of the machines and use the row of machines as a stage and sing Hallelujah and sound as loud as the Mormon Tabernacle Choir which is a pretty good trick inside a casino!

We need video proof!!!

Well, here it is... about as much proof as I could give you without getting cited for disorderly conduct, or just being called "drunk"....

[Alan Mendelson]

John Grochowski has responded to my email, and here it is, complete and unedited:

Hi Alan,

The win goals/loss limits advice applies only to negative expectation games, which means it applies to a vast majority of players. I'd put no such restrictions on players who have an edge on the house, provided bankroll is sufficient.

I'd just add a couple of cautions. Advantage players in blackjack need to be wary of surveillance catching onto their edge. The longer you play, the more likely it is that you're going to be spotted. Counting cards is not illegal, but casinos are private clubs and can bar you from playing. One defense is to play short sessions and to move on after an hour or so, win or lose.

And advantage players at any game need to be wary of fatigue. Regardless of whether you're a blackjack card counter, dice controller at craps or a video poker player who sticks to expert strategy at the best games, if you play when weary you're going to start making mistakes. Get some rest, and come back to the games refreshed.

Good luck,

John Grochowski

I sent a follow-up question to John about recreational players. Specifically I asked this:

Is there any fear that even on a game you have an edge at that you might run into a string of bad luck which could offset your "edge" and take away your profits? Do you not protect any of your profits even if you have an edge at the game?

And this is the response I received:

Hi Alan,

Sorry this took so long.

Yes, I think there's value in a casual player, even one who has an advantage over the casino, in locking up a percentage of profits.

It's a matter of bankroll. A pro who is sufficiently bankrolled, with tens of thousands of dollars in reserve, probably is just going to play on when he draws a $1,000 royal flush. He has an edge, and continuing to play is pursuit of profit.

But if I go into the casino with $500 and win a $1,000 royal, leaving me with a bankroll of $1,500 minus whatever I'd already invested, I have to be aware that a long losing streak --- which happens to everyone --- can wipe me out. In that situation, I'm probably going to lock up my original $500 plus $500 more.

One advantage casinos have even over players who have an edge on the game is that the casino has more money than you do. They can withstand longer losing streaks than you can. So yes, unless players have very deep pockets, locking up some winnings is a smart way to go.

Best,

John

[regnis]

I sent a follow-up question to John about recreational players. Specifically I asked this:

Is there any fear that even on a game you have an edge at that you might run into a string of bad luck which could offset your "edge" and take away your profits? Do you not protect any of your profits even if you have an edge at the game?

And this is the response I received:

Hi Alan,

Sorry this took so long.

Yes, I think there's value in a casual player, even one who has an advantage over the casino, in locking up a percentage of profits.

It's a matter of bankroll. A pro who is sufficiently bankrolled, with tens of thousands of dollars in reserve, probably is just going to play on when he draws a $1,000 royal flush. He has an edge, and continuing to play is pursuit of profit.

But if I go into the casino with $500 and win a $1,000 royal, leaving me with a bankroll of $1,500 minus whatever I'd already invested, I have to be aware that a long losing streak --- which happens to everyone --- can wipe me out. In that situation, I'm probably going to lock up my original $500 plus $500 more.

One advantage casinos have even over players who have an edge on the game is that the casino has more money than you do. They can withstand longer losing streaks than you can. So yes, unless players have very deep pockets, locking up some winnings is a smart way to go.

Best,

John

And before Arci says again that it doesn't change the expected return, no one is saying that it does. What it does is lock in an actual return, which I value much more than a theoretical return.

[Alan Mendelson]

And before Arci says again that it doesn't change the expected return, no one is saying that it does. What it does is lock in an actual return, which I value much more than a theoretical return.

Is there going to be a Super Bowl prop bet in 2014 with the over/under on the number of times Arc will bring up "expected return" when the rest of us are discussing "actual return"??

[arcimede$]

Actual return approaches expected return over time. Sorry that some of you can't understand simple math. The actual return varies each and every session.

BTW, the whole thing about having a sufficient bankroll is to handle losing streaks. John's comment about locking up profits is somewhat mystifying after he already made the point about bankroll. Either you have it or you don't. If you have a sufficient bankroll and are playing with an advantage then worrying about your current sessions result is of little value.

[Alan Mendelson]

Actual return approaches expected return over time. Sorry that some of you can't understand simple math. The actual return varies each and every session.

Okay Arc, I am all ears for this one. Please explain in detail how and why actual return approaches expected return over time. I really want to see this.

[arcimede$]

Alan, it all has to do with randomness. Over time we will all see a random distribution of every card in every position of the dealt/drawn cards. What this means is we will see specific frequencies of one pair, 2-pair, four for a straight, etc. In addition, we will see a certain frequency of hits. That leads to seeing things like RFs every 40,000 (or so) hands, quads every 420 (or so) hands, etc. Finally, the payback on those results determines how well we do relative to amount of money invested.

In order to do better than the expected return one has to get a higher frequency of good paying results (actual return). But there is nothing that makes an RNG produce better than average frequencies of cards. It can do both better or worse than the average frequency over short time spans. This is called variance. However, over time those highs and lows tend to average out and you end up very close to the random values.

There is nothing you can do to make an RNG generate a higher frequency of the card arrangements that produce better results. If there was then the machines would not be random. It's that simple.

And this applies to every game based on randomness. It applies to craps, blackjack, slots, etc. This is the exact math that casinos use to make a profit. Life for a gambler really is one long session.

And don't try to use Singer's silly argument that somehow this all breaks down when playing short sessions. You are just as likely to get results below the expected frequencies in the short term as you are to get better results.

[FrankScoblete]

Are the results of randomness changed based on what cards you hold and/or disgard? If you get three aces, for example, would that change how many aces you can get on the next draw? Obviously yes. So would that change the cards or patterns of the cards over time? I think yes. We are still dealing with randomness in the distribution but on the draw the number of certain types of cards would change, meaning fewer of "this card" and more of "those cards." Just some thoughts off the top of my head.

[redietz]

What people have been telling you ad nauseum, Alan, is that if you are sufficiently bankrolled, as I am for what I play, there is no reason to stop if you have an edge. It isn't brain surgery.

You are so hung up on this, and you have put your nose in the air at using a 200K bankroll to play 25-cent video poker (and other things), that I have to ask the simple question, which I guess hasn't been asked, "What exactly is your 'bankroll' for a video poker session?"

See, if you tell us, then we can evaluate if you are playing beyond your means for that session.

Personally, I think playing any game you know is negative is wrong, but at least your risk of ruin can be calculated for your likely session length.

By the way, pocketing money when you don't have enough to play for any length of time kind of sidesteps the issue. If your risk of ruin is really high for a session, then you're not lugging enough money to the table.

[arcimede$]

Are the results of randomness changed based on what cards you hold and/or disgard? If you get three aces, for example, would that change how many aces you can get on the next draw? Obviously yes. So would that change the cards or patterns of the cards over time? I think yes. We are still dealing with randomness in the distribution but on the draw the number of certain types of cards would change, meaning fewer of "this card" and more of "those cards." Just some thoughts off the top of my head.

Right you are. The distributions of individual cards are always based on the available cards. On the draw the discards are not available which would change the distribution slightly. Of course, each game is different and the changes for games like deuces and bonus games would reflect that difference.

This is all factored into the expected return of the game. For example, if you always pressed draw without holding any cards the actual distribution of every card would be the same. However, the frequency of the various winning results would drop significantly. Same would hold if you held every card in each hand. In this case we know the RF distribution would be ~650K hands. This is why the expected return of those kind of strategies would be horrible.

However, the main point still stands. You can't make a machine give you non-random distributions (of the available cards).

[Alan Mendelson]

Arcimedes, this is what I asked you:

Okay Arc, I am all ears for this one. Please explain in detail how and why actual return approaches expected return over time. I really want to see this.

And you responded with this:

Alan, it all has to do with randomness. Over time we will all see a random distribution of every card in every position of the dealt/drawn cards. What this means is we will see specific frequencies of one pair, 2-pair, four for a straight, etc. In addition, we will see a certain frequency of hits. That leads to seeing things like RFs every 40,000 (or so) hands, quads every 420 (or so) hands, etc. Finally, the payback on those results determines how well we do relative to amount of money invested.

In order to do better than the expected return one has to get a higher frequency of good paying results (actual return). But there is nothing that makes an RNG produce better than average frequencies of cards. It can do both better or worse than the average frequency over short time spans. This is called variance. However, over time those highs and lows tend to average out and you end up very close to the random values.

There is nothing you can do to make an RNG generate a higher frequency of the card arrangements that produce better results. If there was then the machines would not be random. It's that simple.

And this applies to every game based on randomness. It applies to craps, blackjack, slots, etc. This is the exact math that casinos use to make a profit. Life for a gambler really is one long session.

And don't try to use Singer's silly argument that somehow this all breaks down when playing short sessions. You are just as likely to get results below the expected frequencies in the short term as you are to get better results.

You did not (repeat: did not) answer this: Please explain in detail how and why actual return approaches expected return over time.

And to save everyone more of your side-tracking, actual return will approach expected return over time only if a player never makes a conscience decision of when to stop playing. In other words, over the long term your actual return will be the expected return if you sit at a machine and decide never to quit when ahead... or quit when you are way behind.

I think you could not say it because you cannot understand the concept. The math of long term play blinds you to the idea of pocketing wins and leaving.

[Alan Mendelson]

What people have been telling you ad nauseum, Alan, is that if you are sufficiently bankrolled, as I am for what I play, there is no reason to stop if you have an edge. It isn't brain surgery.

If like you, redietz, and there was a positive game at 25-cents I would play it also and my bankroll would allow me to sit and play indefinitely without regard for being bankrupted by a cold cycle. But alas, there is no positive paytable available at a 25-cent game where I play.

I am also a recreational player and my time in a casino is limited, so I go for the fun and the thrill of playing. Sitting at a 25-cent machine to win eight dollars an hour is neither fun nor exciting for me... it's not the way I would spend my two or three or even four hours playing video poker.

You are so hung up on this, and you have put your nose in the air at using a 200K bankroll to play 25-cent video poker (and other things), that I have to ask the simple question, which I guess hasn't been asked, "What exactly is your 'bankroll' for a video poker session?"

See, if you tell us, then we can evaluate if you are playing beyond your means for that session.

Generally, my bankroll is $1500 but it has also been as little as $500 and I start on a $2 game.

Personally, I think playing any game you know is negative is wrong, but at least your risk of ruin can be calculated for your likely session length.

Perhaps for you "professionals" such calculations are necessary. But for a recreational player such as myself the calculation is quite simple. I decide in advance what percentage of my session bankroll (max is $1500) I am willing to lose, and since I use a system of "rising stop losses" I leave when I am happy with the money I've won.

By the way, pocketing money when you don't have enough to play for any length of time kind of sidesteps the issue. If your risk of ruin is really high for a session, then you're not lugging enough money to the table.

Lug enough money to the table? When I go to a casino the idea is to bring as little money as possible and to leave with as much money as possible. Since I have a loss limit I have a "zero risk of ruin" (not your term, but "real people" will understand what I am saying).

[arcimede$]

Arcimedes, this is what I asked you: "Please explain in detail how and why actual return approaches expected return over time."

And that is what you got.

You did not (repeat: did not) answer this: Please explain in detail how and why actual return approaches expected return over time.

Well, you may not have understood what I said, but that is not the same as me not answering. How much effort did you put into understanding what I told you?

And to save everyone more of your side-tracking, actual return will approach expected return over time only if a player never makes a conscience decision of when to stop playing. In other words, over the long term your actual return will be the expected return if you sit at a machine and decide never to quit when ahead... or quit when you are way behind.

Think about what you are saying. You are saying you can fool the machines into giving you a non-random distribution of cards. Really, that is exactly what you just said. I realize you didn't mean to say that, but that is because you don't understand the basics of what randomness means.

I think you could not say it because you cannot understand the concept. The math of long term play blinds you to the idea of pocketing wins and leaving.

The math is the math. It isn't "math of long term play". It is the math of random events. It doesn't change when you leave a casino and return another time. It affects each and every hand which is why your results approach the statistical average over time.

Let's look at some other examples. Say you are driving and encounter 12 traffic lights. Each traffic light holds the same amount in each direction and are not synchronized. When you drive through these lights you would expect to make 6 light and stop for 6 lights. What you are claiming is ... if you made 4 lights out of the first 6 on one trip you could change drivers and somehow you personally will not see an average of making 50% in the future and you can continue to do this forever.

Were you somehow destined to miss 4 of the next 6 lights if you hadn't stopped? How does switching drivers affect your next trip? Couldn't you miss 4 out of the first 6 lights on that trip? Same holds true if you switch drivers after missing 4 lights in a row. How could that affect your next trip? Think about it, Alan.

[Alan Mendelson]

Think about what you are saying. You are saying you can fool the machines into giving you a non-random distribution of cards. Really, that is exactly what you just said. I realize you didn't mean to say that, but that is because you don't understand the basics of what randomness means.

OMG. I'm fooling the machines? Wow.

[arcimede$]

OMG. I'm fooling the machines? Wow.

As I expected. You don't want to understand. Why did you ask for an explanation if you don't want to know the answer?

[Alan Mendelson]

As I expected. You don't want to understand. Why did you ask for an explanation if you don't want to know the answer?

We have a communications problem. You're too smart for me. I have no idea what you are talking about.