One of my local, friendly casinos pays 7x slot club points on Mondays and, since their cash rebate works out to about 1.5%, you'll find me there, bright-eyed and bushy-tailed when they open. This casino doesn't have a great inventory of Video Poker games, but with an additional 1.5% added, there are some choices available to me and all are profitable, at least from an "expectation" point of view.

You probably know that we "experts" measure almost everything by expectation, which is simply another way of saying "long-term return". If a game returns 99.5% in the long run, then an additional 1.5% cash back yields an expectation of 101%. But that expectation may not be realized in a short period of play or it may even be exceeded, due to what we call "variance" and others call "luck". If you've played any VP at all, you know that you might win or lose a bunch of $$$ in a two or three-hour playing session and your result will appear to have nothing whatsoever to do with the expectation.

But does that mean we can ignore expectation? It does not, although there are those who would like you to think so. Yes, anything can happen in a short period of time, but that doesn't mean your results are random. What many people don't understand about VP is that what you're seeing in any given session is just a few "clips" from a movie. Sure, you might hit 2 Royals the first time you sit down at a game, but you'll eventually pay the price for them, unless you end your playing career at that point. If you were to record every hand of play for the rest of your life, you'd discover that you got a Royal roughly every 40,000 hands (depending upon your chosen game and strategy) and nothing is going to change that. Maybe you'll never play the four million or so hands that it takes for the stats to "even out", but I guarantee that your experience will be pretty much as we expect.

My point here is that we have to plan our short-term playing sessions with the long-term in mind or pay the price later. I've won plenty of $$$ at machines with lousy pay schedules, and it has always cost me at some point. To think that your next playing session is unrelated to your last session is a mistake, because those machines don't know if you left town, but the odds know you played "X" hands last time and now you're playing "Y" hands and the odds will have their way, whether you want them to or not.

But look at it this way: If I always play machines with returns of over 100%, at some point I must realize a return of over 100% of all the $$$ I run through the machines, plain and simple. Much like in Blackjack, the profits you make at Video Poker come in "chunks" and, at VP it's even more magnified because of the "jackpot" nature of the game. But the profits will come and, if you're not playing games with a 100+% return, the losses will eventually come, instead.

I usually play quarter All American with a bankroll of $4000, so I need to use that as a basis for comparison (sadly, the casino running the promotion doesn't have All American poker). In other words, I could just forego the bonus and play my AllAm and expect to make my usual profit. But 1.5% cash back is too big a "gift" to ignore; consequently, I'm not going to ignore it.

Okay, let's analyze the games I'm considering for this once-a-week promotion:

This is the most obvious choice, because it closely resembles the $.25 All American game that I usually play, but the long-term return for proper play is only 99.1%. But with the cash back bonus of about 1.5%, that goes up to 100.6%, so there is a profit to be made here. I can play this game accurately at a rate of approximately 600 hands per hour, so in a 7 hour promotion, it's probably fair to say that I'll get in about 4000 hands of play (if my kidneys hold out).

Here's how the statistics stack up:

Total bets in 4000 hands of play: $5000
Cash back value (at 1.5%): $75
Expected loss from play alone (0.9%): $45
Net expected gain: $30

Of course, $30 isn't much compensation for 7 hours of play, but that's the "expectation" and I would be shocked if my results were a win of exactly $30. I might win a lot more or I could lose a lot more; something I'll discuss in the Risk section below, but all-in-all, it doesn't compare all that favorably to what I could accomplish by playing 7 hours of All American, which has a return of 100.7%, plus a 0.25% slot club cash rebate.

Because this is the "full-pay" version of the game, the long-term return is 100.17% for proper play, so with a 1.5% cash back bonus added, the total expectation is 101.67%. I won't lie to you and say that I play this game perfectly, so a more reasonable return would be about 101.6%. Also, a lot of the "bonus" hands (quad Aces, etc.) are hand-paid and that takes some time, so my rate of play on this will be more like 500 hands per hour and that cuts into the expectation for 7 hours of play.

Here's a look at the stats using those numbers:

Total bets in 3500 hands of play: $17,500
Cash back value (at 1.5%): $262.50
Expected gain from play alone (0.10%): $17.50
Net expected gain: $280.00

Now we're getting somewhere! An expectation of $280 in 7 hours of play is obviously worth $40 an hour and that's a nice number. But risk is a big factor here, so we'll just have to wait and analyze that in the section below.

Yes, I am actually giving some thought to playing their $5 machine during this promotion. With 5 coins in, that's a total bet of $25 per hand and it generates some very impressive statistics. I can play this game very quickly and very accurately, but it does get slowed down when hands like Four-of-a-Kind or higher are hit, because they are hand-paid by the slot attendants. Also, a Straight Flush generates a form W2-G and that takes time to fill out, sign and so forth. Sadly, the long-term return for proper play of this game is only 99.54%, but I figure I can play it at a rate of about 500 hands per hour. It would be madness to play this game without a big slot club cash rebate.

Here are the statistics on it:

Total bets in 3500 hands of play: $87,500
Cash back value (1.5%): $1312.50
Expected loss from play alone (0.44%): $385
Net expected gain: $927.50

An expectation of $132.50 per hour is just awesome, isn't it? I (and a lot of other people, I'm sure) would do it weekly if it weren't for the risk. Naturally, if there were no risk, there wouldn't be any casinos, so it's a moot point. You may not believe this, but I am not one of the world's richest people, so clear, succinct analysis will be required before I sit down at this game.

If you play just one hand of Video Poker with a $5 bet (five $1 coins), the most you can lose is $5. But, depending upon the game, the most you can win might be $4000 or more. Or, you might hit some payoff in between, but most likely you'll hit nothing. This is what makes the risk analysis of Video Poker rather complicated but I'll try and present it in a way that we'll both find helpful for looking at situations like I'm presenting here. I must use some technical terms in this, but don't let the jargon scare you away. When we're done, you'll have a good answer to that age-old question: "How much can I lose?"

Calculating how much you can lose in "X" hands of play is very simple if you have the software, "Bob Dancer presents WinPoker" (BDWP), which I am constantly recommending to our readers. That program automatically calculates what's known as the "variance" for almost any game and that's a key component to calculating risk. But rather than explain it all with complicated formulas and so forth, just follow my explanation for each of the three games I'm considering and you'll get the idea.

Total bet on one hand: $1.25
Variance from BDWP: 28.55
Number of hands planned: 4000

To calculate one Standard Deviation (SD), I square the bet ($1.25 x 1.25) = $1.5625, then multiply that by the variance and then by the number of hands. So, we have arrived at this: $1.5625 x 28.55 = $44.609375 x 4000 = $178,437.5. Don't worry, I'm not going to lose $178,437.50. But the square root of that number is what we're after and it's $422.42.

This is 1 SD for 4000 hands of play at a 9/7 Double Bonus Poker game with an average bet of $1.25 per hand. Okay, so what does that mean? Simply this: If I were to play 4000 hands for 100 weeks in a row, when all was said and done, I'd find that about 68% of my results were between a profit of $377.42 ($422.42 minus the expected loss of $45 from play alone) and a loss of $467.42 ($422.42 plus the expected loss of $45.00 from play alone). Ninety-five percent of my sessions would fall within a range of a profit of $799.84 ($377.42 plus another $422.42) and a loss of $889.84 ($467.42 plus another $422.24) and 99.7% of all my sessions would fall within 3 SD (just add another $422.42 to the preceding numbers).

Realistically speaking, I have found that my very worst Video Poker playing sessions have been in the neighborhood of a 2.6 SD loss, so I'm comfortable with using that in calculating my risk for this venture. So, by playing the $.25 9/7 Double Bonus Poker, I'll need to take about 2.6 times $422.00 or $1100 with me.

While it's certainly possible for me to lose that $1100, I want to point out that the calculation doesn't include the cash rebate and, assuming the casino continues to offer this promotion, I have a good chance of making back any losses because the total long-term return is over 100% and my VP bankroll can support several $1100 "hits". But the profit potential is quite small, even with a $1000 "kicker" from a Royal. Let's move on.

Total bet on one hand: $5.00
Variance from BDWP: 28.25
Number of hands planned: 3500

So, let's square the bet, then multiply that by the variance and then multiply that by the number of hands, determine the square root of the result and we'll have 1 SD for 3500 hands of play: $25 x 28.25 = $706.25 x 3500 = $2,471,875. The square root is $1572.22; so 2.6 SD is equal to about $4100. Ouch!

That means I'll need to take with me (and risk) $4100 in an effort to earn $280 in 7 hours of play at a dollar full-pay Double Bonus game. How many people do you know that will risk $4100 while making $17,500 in bets to keep rice on their table? But that's what I do and I want to again emphasize that this game offers a 100+% long-term return, so I can eventually make back any losses. In spite of the risk, the $40 "pay" per hour makes this very attractive. But if I get a bad start, my VP bankroll could suffer for a long, long time.

Total bet on one hand: $25
Variance from BDWP: 19.51
Total number of hands planned: 3500

I'll spare you the walk-through on the math and just tell you that 1 Standard Deviation is $6532, so I'd need to carry about 2.6 times that or nearly $17,000. That ain't gonna happen, folks.

A more realistic approach here is to do some "educated" gambling (if such a thing exists). For example, I might be willing to risk $2000 or so and take a shot at this, because the cash back is attractive at $.375 per hand and I could hit the "kicker": a $20,000 Royal Flush. I'll be the first to admit it's not very likely, but it sure would be a lot of fun to do!

However, with a bankroll of only $2000, I cannot expect to play for the full 7 hours, unless I get really lucky, really early. So, how long is it likely to last? Fortunately, there was an article in the March, 2000 issue of "Video Poker Player" (go to www.vpplayer.com for subscription info) that addressed situations like this. Called "DON Analysis", this article took the premise that most VP players don't have unlimited time nor unlimited $$$ to devote to this business, so the author, Tim Sefton, came up with some very helpful numbers.

Total bets in 1521 hands of play: $38,025
Cash back value (1.5%): $570.38
Expected loss from play alone (0.44%): $167
Net expected gain: $403.07

To sum it up, I'd stand a pretty good chance of losing $2000 to make $403.07, but I could hit a $20,000 Royal. Of course, I could also lose $2000 at the $1 DB game, but at least I could fight back from that with my current bankroll. The 9/6 Jacks game is a loser without the slot club bonus, so its long-term appeal isn't that great, should the casino drop this promotion, plus I don't have a bankroll big enough to continue playing it, anyway.

I guess you can tell that I don't know exactly what I'm going to do at this point, but I promise to add an update after I go play on Monday, December 3, 2001.

The End

©copyright, 2001 The GameMaster Online, Inc.