Advanced Video Poker By Bob Dancer

How Much Do You Really Need? An easy-to-understand discussion of advanced bankroll concepts

Inquiring minds want to know: How much money do you need to play video poker? This question is very important. Over-betting your bankroll can have very real and serious consequences.

Various authors, including me, have tried to approach this subject in a variety of ways. I have stated that a bankroll of three to five royal flushes should be sufficient, as long as you're playing a game where you are unquestionably the favorite. This has the advantage of being simple, but it has the disadvantage of not going through all of the underlying assumptions. This article discusses some of those points, primarily in a non-mathematical way.

Other authors have come up with more mathematical approaches, using numbers to estimate such things as the expected value of the game, the volatility of the game and your willingness to tolerate risk. Let me briefly define these terms with examples. I'll give you two games with an expected value of 100.5%, which is another way of saying you have a half of a percent advantage.

Game A: You flip a fair coin. If it comes up heads, you win $10.10. If it's tails, you lose $10.00. This is gambling. You have an advantage. A relatively modest bankroll would suffice. And the game would be pretty boring.

Game B: You have a fair random number generator. One time in 2,000,000, you win $2,009,999 and the other 1,999,999 times, you lose $1. This, too, has the same expected value. In both games, for every $2,000,000 you put in action, you expect to win $10,000. But the chance to win over $2 million while investing $1 and having a half- percent advantage at the same time would be extremely. In actual fact, most of the time, it would feel like you were throwing everything down the drain. And an enormous bankroll (in the millions) would be required to ensure that you didn't lose everything while playing this game.

Volatility has to do with streakiness. Game A isn't streaky at all. Every value (both plus and minus) is exactly $10.05 higher or lower than the mean. You are the favorite and not much bankroll is required. But the game is very boring. There is no chance at all for a big hit. The only way to win any large sum is to grind it out. Game B, on the other hand, is extremely streaky. Most times your loss is $1.005 greater than the mean win. But once in 2,000,000 trials, your win is over $2 million greater than the mean. The bankroll required for this game is enormous. You have an expectation (i.e. average result over a large number of trials) of being up $10,000 over the next two years, but you have a 37% chance of being down $2 million.

Your willingness to tolerate risk is the opposite of saying how willing are you to go bankrupt. If you are playing a game where you are the favorite and can handle a 10% chance of going broke, then you need exactly half the bankroll as you would if you were only willing to accept a 1% chance of going broke.

Let's list some principles about bankroll, some of which haven't been published before. These aren't in any particular order, and the principles are subjective, but most experienced players will find they agree with many of them. They are stated in general terms rather than with mathematical precision. One of the reasons that they have not been discussed frequently in the past is that it is extremely difficult to formalize these rules mathematically for each person.

o No amount of bankroll can 100% guarantee you will never go broke.

An extended losing streak has a one in a mega-zillion chance of cleaning Bill Gates out. However, you can get the risk down to one part in a single zillion, which, for all practical purposes, is the same as having a 100% guarantee.

Here's a simple but little known truism that was pointed out to me by Liam W. Daily: When you double your bankroll, you decrease your risk by an exponential factor of 2. For example, if a given game required a $7,500 bankroll (assuming a 10% risk of going broke), to reduce that risk to 10% of 10%-which is 1%- you'd need a bankroll of $15,000. Carrying on, to reduce your risk to .01% (1% of 1%), you'd need to double this again to $30,000. Doubling the bankroll again to $60,000 would reduce your risk to .01% of .01%, which is .000001%. While it's true that this is "essentially zero," getting the risk all the way to zero cannot be done, unless of course, you do not gamble at all. We each need to come to grips with how much risk we are comfortable with.

Accepting the inevitability of risk is not as difficult as it seems. We can never completely eliminate the risk, for example, that an airplane will fall out of the sky onto our head. But very few of us stay up nights worrying about this risk. We go out in public knowing that some mass murderer may show up anywhere, any time. We get married. We eat in restaurants not knowing exactly how safe all of the food handling has been. There is risk everywhere and anybody who would want to eliminate risk totally cannot succeed as long as they are still alive.

o Bankroll numbers assume you are using that money strictly for bankroll purposes-not for living expenses.

If you calculated your bankroll requirements for a game as being $5,000, then you'll need $5,000 plus living expenses. If you're spending part of your bankroll for things like rent or food, then you need a lot more bankroll. People with outside jobs require a much smaller bankroll to play than do those who are spending part of their bankroll on living expenses.

No amount of bankroll is sufficient in the long run for people who spend their actual or expected winnings. When considering becoming a full time professional gambler, you need to be able to find games that you can play well enough so that the expected return minus your living expenses is significantly positive-say, 1/2 %. This is very hard to do. Also, you must avoid using your royal flush proceeds to upgrade your car.

o Young people need smaller bankrolls than older people do.

Let's say you're 23 and have a bankroll of $5,000. If you lose it, you'll have plenty of good earning years to replenish it. If, however, you are 63, relevant job opportunities may be scarce. So losing your entire bankroll when you're 63 is a much more serious problem than losing it at 23.

o As your stakes increase, you need to increase your bankroll more than proportionately.

Let's say you've calculated that the bankroll required for a particular $1 game is $15,000. For a $10 game, you need substantially more than $150,000 (or 10 times $15,000). Why? Simply because starting over from $15,000 is manageable, but starting over from $150,000 is a lot tougher. You might be willing to accept a 10% risk of losing the $15,000 bankroll, but only a 1% risk of losing the $150,000 bankroll. By the principle listed above, this would make the required bankroll for this $10 game $300,000 rather than the "obvious" $150,000.

o People with spouses and/or other dependents need more than their unattached counterparts.

The reason is simple. If you end up living on food stamps because of a bad streak of luck, that's one thing. Forcing a wife, four kids, a dog and a cat to do the same thing because of your "hobby" is another thing altogether.

o Home equity may or may not make up part of your bankroll.

Are you willing to take out a second (or third) mortgage on the house to meet gambling shortfalls? If not, then none of your home equity should be counted as bankroll. But there are people who have a lot of cash tied up in their home. They owe, say, $50,000 on a house that is currently worth $200,000. That is a big reservoir and it can be tapped -IF you and your spouse agree up front that that's a realistic thing to do.

o Bankroll is not the same as cash on hand.

Some of your assets are reserved, or should be, for junior's education or for your retirement or as a contingency fund for various things that life throws at you. The more of a "life away from gambling" that you have, the more contingency funds you will need.

o There is a difference between wealth and income.

Economists know that wealth is a stock value (think of the volume of water in a lake) and income is a flow value (think of a river feeding the lake.) To convert income to wealth, economists use something called a "present value" calculation. Without giving the exact formula, consider the following two people: The first man has $50,000 in cash but no money coming in; the second man has no cash on hand but an annual income of $10,000 more than his living expenses. Which one has greater wealth actually depends upon the interest rate, but it is easy to see that they are interrelated. Bankroll is generally considered a stock value. My point here is that the flow of income is important and is usually neglected in the discussion.

o Most gamblers end up broke.

Taking a 10% chance of going belly up one time is risky enough. But taking the same 10% chance again and again and again means that, in most cases, the 10% chance becomes 100%. Over-betting your bankroll is like this. Usually you survive and come out ahead. But when you crash, you crash big time.

On a related matter, just because you get lucky a few times is no guarantee at all that you will get lucky again on a more-than-usual basis. People tend to think of themselves as lucky or unlucky. Usually that's just not true, although convincing people of this is difficult. Frequently, there are reasons-such as a lot of hard work-behind getting lucky or taking a lot of shortcuts behind getting unlucky. Or it just may be that some people tend to emphasize the positive side of life (and hence their luckiness), while others tend to emphasize the negative side of life.

o Loss limits make sense.

Let's say you have somehow managed to accumulate $100,000 in cash and really want to play a $5 10/7 Double Bonus game with a very small slot club. You have the advantage, but a small one. Your bankroll is probably sufficient-maybe. (Liam W. Daily and I plan to publish in the near future more exact bankroll figures for a variety of games at a number of risk levels.) It makes a lot of sense to set a loss limit of, say, $40,000. That means that if you lose $40,000, you'll stop playing the $5 machine. Not stop for this trip. Stop forever, until you replenish your bankroll. If you are willing to do this and have the discipline to stick to your guns, then you'll never go broke.

Remember, if $100,000 was barely enough, and you lose $20,000, you no longer have enough bankroll. Do you stop now or keep going? The $100,000 calculation assumed you'd keep going. But that might be foolhardy considering that you live in the real world and once you lose everything, nobody is going to allow you to have an instant replay and start over again.

o Does today's score matter?

Probably the only thing I've said more than "Today's score doesn't matter" is "Go out and hit a royal flush!" But when I say this, I am assuming that you still have plenty of bankroll. And that is true for most players, most of the time. However, some players, some of the time, will lose half of their bankroll in one day. For them, today's score matters a whole lot!

When I say not to worry about today's score, I am encouraging you to come to grips with the fact that when you gamble, you'll have a lot of good days and bad days, and today is just another one of them. I find it a very good rule of thumb to live by. But it certainly isn't meant to encourage you to keep going until you go bankrupt. If you have lost a significant portion of your bankroll, it's high time to step back and ask yourself what you are doing. Are you sure that you have the advantage? Are you sure you are playing correctly? Are you sure that losing more won't seriously jeopardize things you hold dear, such as your home, your marriage or your psychological well being? While I still think "Today's score doesn't matter" is relevant most of the time, I do admit that it can lead to the wrong conclusion if you have had a large loss relative to the size of your bankroll.

o If you are gambling at a game where the house has the advantage, and you do not have a loss limit, no bankroll is safe.

Fortunately for the player, video poker is a game where those returning over 100% are widely available. Fortunately for the casino, relatively few players go through the necessary effort to be able to learn how to take advantage of this. All of this discussion assumes that you are smart enough to limit yourself to games where you have the advantage. If you do not do this (perhaps because you enjoy games like craps or slots), then I hope you have a loss limit and stick to it. When the house has the advantage, there is a very high probability that you will end up a loser in the long run. This might be fine with you. Gambling might be a pleasant hobby that you are willing to pay for. But if you are serious about winning, find a game where you have the advantage and learn that game well. And never play a game ever where you do not have the advantage.

o Being a pro has its advantages.

Most people talented enough to succeed at video poker could make more money doing something else. However, winning at gambling provides certain psychological benefits. Imagining yourself leading the James Bond sort of lifestyle is fun. Sitting back and daydreaming about what you are going to do with the money when you hit three royals in the same day is quite diverting. Also, working for yourself can be rewarding, if you have the personality for it.

If you are gambling strictly for the money, you are probably making a second-best financial choice. However, if you get real value out of the excitement and amenities that come along with gambling, then perhaps gambling for money plus the things that go along with it makes a lot of sense.

A related point is that most people with enough bankroll to play high stakes video poker could make more money using their bankroll in some other form of business or passive investment. It is possible, however, to do both. Shirley and I have most of our bankroll in mutual funds. The mutual funds may be sold if needed to pay off a marker and until then, it works to increase the value of the bankroll. (It's not too far wrong to consider the stock market to be a casino. Betting that mutual funds or any other group of stocks will increase in value may be a smart bet, most of the time, but it's a bet nonetheless that could backfire. )

o Most people get a significant proportion of their bankroll all at once.

It might have come from a jackpot of some kind, an inheritance, a legal settlement, retirement bonus, or perhaps a valuable asset was sold. Some people manage to accumulate their bankroll $100 at a time, but it's difficult. It's easier to do this if you are single or have the very rare marriage where you are in 100% agreement on the necessity of obtaining a bankroll.

To understand this, picture the following:

"Let me see if I have this, honey. You want to play $5 video poker and we 'only' have $50,000 in cash on hand, which you say isn't enough, even though it is more than anybody else we know has. And because it isn't enough, you say we cannot afford to let Missy spend a week at summer camp this year. Nor can we afford to replace our seven-year-old car. Is that correct? You know I believe in you completely but would you mind helping me explain this to my friends and family? They are all convinced that you have lost it. They think perhaps you need some more bran in your diet!"

To be sure, many of the points is this article provide more food for thought than definitive answers. This is appropriate because how much money you need is different for everybody. Going into it blindly is asking for trouble. If you get away with this gamble, you are a little better off. If you lose this gamble, you are devastatingly bankrupt. With the odds stacked this way, I think you'll want to be extra cautious before you jump in.

That's it for this month. Until next time, go out and hit a royal flush.