Internet Advantage Play: Video Poker

The GameMaster's Secrets:
Internet Advantage Play: Video Poker - Part 2

(A note from the GameMaster: This article and the worksheet that goes with it was revised on 18 August 2006 due to an error in my basic formula. Thanks to our faithful reader, "CMEPTb" for pointing this out. As I often say, I don't really know everything; I just act that way.)

Although this article uses examples of Video Poker games that can often be found mainly at Internet casinos, it will also apply to games that can be found at brick and mortar casinos, particularly those that offer a return of over 100%, very few of which (if any) are available online. A good subtitle for this discussion would be "Excel for the Video Poker Player" because I'm going to show you how to program MS Excel to automatically calculate the answer to a very important question most VP players have: How much can I lose?

We prefer to concentrate on winning here, rather than losing but losses are a part of any game, so by quantifying our potential losses we can make sound decisions on which game to play and how many $$$ we'll need to allow us a fair shot at making a profit at that game. Because Video Poker can be played very quickly - 500 hands an hour is typical - the player will give the casino a lot of "action", which is their term for the total value of all of your bets. For example, if you're playing a dollar machine that has a maximum bet of $5, then you'd bet betting about $2500 per hour, which is basically the equivalent of betting $50 per hand in a Blackjack game where you're being dealt 50 hands an hour, something that you might expect when playing at a full table. These numbers are so big because you are betting your $$$ over and over again and do not imply that you need to have $2500 in cash on you to play for an hour at either game; that would be necessary only if you were to lose every hand, which isn't going to happen.

One big difference between Video Poker and Blackjack from a money-management point of view is what we call "variance" and it directly affects how many $$$ you should bring with you for a playing session of, say, 4 hours. When you play Blackjack, most of the time you'll win or lose 1 bet; now and then you'll win 1.5 bets (when you get a 'natural') and sometimes you'll win or lose 2 bets - if you double and/or split pairs - and very rarely you'll win or lose 3 or more bets because you either resplit a hand or doubled after splitting a pair. As I discussed in my article, "Excel for the Blackjack Player - Part 2", the rules of a particular BJ game are what determines its variance and, although we usually use Standard Deviation - the square root of variance - to describe it, a good average variance for any Blackjack game is 1.35. If 1 is "normal", then you can see that Blackjack is not a game of big variance, especially when you consider that a relatively low variance Video Poker game like 9/6 Jacks or Better has a variance of 19.51.

Okay, before your eyes start glazing over from all of these numbers, I'll explain them as simply as I know how. A variance of 1.35 at Blackjack is a mathematical average that results from measuring how many times in a set number of hands (say 100 million or so) you bet 1 or more units and the number of times you win or lose more than 1 unit. Of course you're never going to bet less than 1 unit so the variance must be at least 1 and, because of the factors I mentioned earlier, it works out to about 1.35 units per hand. That's the measurement for Blackjack - units per hand played. In Video Poker, we can never lose more than our original bet because we cannot split pairs, etc., (although we can double on some machines, but only after playing the original hand and that's not part of this discussion), however in VP we can very definitely win more than 1 bet, like when we hit a Flush or Full House and so forth. Hands like that increase the variance but it's mostly in a good way because you still can't lose more than 1 bet at the game. So, while the variance of Video Poker appears to be huge when compared to Blackjack, it's primarily because of those wonderfully big payoffs. While it's true that a high percentage of the hands you get at VP will return nothing (about 55%), that's also true of BJ, where you'll lose about 44% of all the hands you play. Anyway, when we calculate the variance of a VP game, when can arrive at a variance per coin bet, which is then modified, as you'll see, by the fact that we typically bet 5 coins at each hand of Video Poker.

Enter that wonderful program, MSExcel. Just as I did for Blackjack, if we know the expectation, the variance per hand and the number of hands we expect to play, we can easily project a range of results from that session. In other words, if you expect to play a $1 game of 9/6 Jacks for four hours, you can determine how many $$$ you'll need to have so that you don't run out before the session is over. Rather than just stuffing your pockets with cash, you can fairly accurately calculate the size of the "session" bankroll you'll need to cover all but the worst possible results. A side benefit is that you can use these figures to determine whether or not your losses were due to just bad "luck" or because the casino is cheating you and that applies to both online and brick-and-mortar casinos. Now understand that I don't think brick-and-mortar casinos in the major markets like Nevada, New Jersey, Mississippi and so forth cheat at VP; not for a minute. But I do know that some VP games in non-regulated markets, such as Indian casinos and foreign countries might cheat and I know for a fact that some online casinos have offered "rigged" VP games in the past, so recognizing what's a reasonable loss and what's a loss from being cheated is important.

As a general rule, if my playing session has a result outside the 3rd Standard Deviation, I'm going to be suspicious that something's wrong. That being the case, what I'll show you here is how to set up Excel to produce the parameters for 1, 2 and 3 Standard Deviations. Hopefully you already know that 1 SD covers what will happen about 68% of the time; 2 SD covers what will happen 95% of the time and 3 SD will cover what happens 99.7% of the time. Does that mean you were cheated if you have a result in the 3.5 SD range? No, but it does mean something unusual has happened, which warrants examination. My "kneejerk" reaction is that you do not know the proper playing strategy for the game, so your poor results are simply due to playing mistakes. Yes, the bankroll swings in VP are sometimes wild, but they'll only be wilder if you're not playing properly. We all make errors, but so long as they're random errors and not systemic errors, the long-term effect is negligible. Regardless of where you play VP, in "real" or "virtual" casinos, there is no excuse for not playing each and every hand correctly. We all have the software needed to play perfectly available to us at very low cost and, especially if you play online, it's easy to use, so why settle for anything less?

Okay, back to programming Excel. What you'll need for each Video Poker game you'll be playing is its total return, expressed as a percentage and the variance for that game. Both of these numbers are calculated by an amazing program that I have often recommended every serious VP player should own, "Bob Dancer presents WinPoker" (BDPWP), which is available at www.zamzone.com and other online retailers. In the sample Excel worksheet that I've presented here, you'll see those numbers already filled in for some of the games I personally play, plus a few of the more popular games out there that I don't play, like 9/6 Double Double Bonus and 9/7/5 Double Bonus. Once you have those numbers, the programming is a snap. I'll walk you through the first one so you have the formulas that will work for every other game you might wish to play. Print out a copy of this file and let's talk about it.

The first game is what I call "Queen DB" because it's a variation of Double Bonus that is available on the Casino Queen, which is a brick-and-mortar operation located just across the mighty Mississippi River from my home. Because Illinois state law does not permit the casinos to offer games with a return of over 100% (a dumb rule that fortunately doesn't apply to progressives), the Casino Queen's Double Bonus game pays only 239 for 5 coins on a Straight Flush and 239 for 5 on four-of-a-kind, 5s-Ks. These changes produce a version of DB that returns 99.78% for perfect play with a variance of 27.9 per coin bet. Because it's available only in $1 denomination games, the bet size is always $5. The # of hands column is the number of hands I expect to play, which I estimate by multiplying the time spent by 500 hands per hour. In 4 hours of play, I expect to get about 2000 hands, so that's the number I entered. Of course 2000 hands of play at $5 per hand means I'll bet a total of $10,000 so with a 99.78% return, my Expected Value (E.V.) is to lose $22.00. In the cell under E.V. is the formula: =B3*(D3*E3)-(D3*E3). If this is all Greek (or "Geek") to you, see my article "Excel for the Blackjack Player - Part 1", which is on the Blackjack page here. It covers some of the basics of programming Excel. Or, just copy and paste it into the appropriate cell on your own worksheet - that should work just fine. You can easily see that if you change the number of hands, the E.V. will change proportionately. Play less, lose less - play more, lose more.

To calculate a 1 SD "event" for playing 2000 hands of this game, we multiply the variance by the number of hands, which is 2000 and calculate the square root of the result, multiply that by the bet size and then add or subtract the E.V., as appropriate. A 1 SD loss is figured by one not-so-simple formula, which is: =-((D3*(C3*E3)^0.5)-F3). The symbol "^" means "to the power of" and ^0.5 is square root. You'll see a minus sign before the entire formula because we're figuring a loss, which is a minus number, of course. Because our expected value is a loss also, we must mark that with a minus sign too, so that we can "add" it to a minus figure. Yep, a little confusing, but that's how it works in algebra. The result is a loss of $1203.10, which means very little until we figure what kind of win we might see in this situation. The formula for a win is almost the same: =((D3*(C3*E3)^0.5)+F3. I say "almost" because the win formula is a positive number it does not have a minus sign in front and we must put a + sign in front of the E.V., which allows us to subtract a minus number from a plus number. Weird, eh? No wonder I hate algebra and love Excel. Anyway, you can see that a 1 SD win would be $1159.10, so we can conclude that whenever we play 2000 hands of Queen DB Video Poker at $5 per hand, 68% of those sessions will end with a result somewhere between a loss of $1203 and a win of $1159.

Naturally, wins are never a problem when it comes to figuring how many $$$ to bring with us for a playing session. But as we already know, at least 32% of the time our result will be outside the range of -$1203 and +$1159. If we want to cover what will happen 95% of the time, we need to calculate a 2 SD event. That's easy. If we multiply the 1 SD result by 2, then add or subtract the E.V. as appropriate, we'll know the parameters of a 2 SD result. Now don't get confused here. In this case we're still playing 2000 hands and are still betting $5 per hand so our E.V. will remain a loss of $22.00. That's what the math tells us will happen in the long run. But in the short run our result will vary widely, which is why we call this stuff "variance." The formula for a 2 SD loss is =-(2*(D3*(C3*E3)^0.5)-F3), which is hopefully self-explanatory. A 2 SD win is calculated by this formula: =(2*(D3*(C3*E3)^0.5))+F3. As you can see, the range of probable results has expanded. What this means is that 95% of the times we play 2000 hands of this game, our result will be somewhere between a loss of $2384 and a win of $2340. From that you can interpolate that only 5% of our 2000-hand sessions of this game will ever produce a loss of more than $2400 or so. That tells me I'll be in good shape a vast majority of the time if I carry $2500 with me as my session bankroll - assuming a session is 2000 hands of play.

I included a column for a 3 SD event in order to give you a tool to help you check the honesty of a game. Because 3 Standard Deviations cover what will happen 99.7% of the time, any result outside those parameters have got to make you suspicious. Either the game is rigged, you're playing incorrectly or the VP gods are really pissed at you. Were I to play the Queen DB game for 4 hours and lose more than $3500 while doing so, I'd be convinced the VP gods hate me because I do play the game "perfectly" and I know it's not rigged. All kidding aside, it can happen just through bad "luck" alone, but it won't happen often - hopefully never in my lifetime.

Let's get back to the Excel worksheet. As you can see, I put 9/6 Jacks or Better on the line below the Queen DB. I then entered the return and variance for the game, as calculated by BDPWP, entered the bet size and number of hands, but that's all of the entries I need to make manually. To calculate the E.V. I just need to "pull down" the formula from the line above and Excel will do the rest. It'll automatically change the formula to be =B4*(D4*E4)-(D4*E4) and if you do the same for all of the other calculations, it'll do them automatically, too. Great, isn't it? Once you have the first line set up and all of the columns in the right place all you need to do in order to check various probabilities is just enter the number of hands you expect to play at whichever game and you'll get all of the answers by hitting "Enter." So, if I plan to play 5000 hands of Bodog Casino's full-pay Pick 'Em game, I just type 5000 in the # of hands column, hit enter and the SD parameters are automatically calculated.

You'll notice one other column at the end, which is a slot club cash back computation. At the Casino Queen, they rebate 0.25% of all the $$$ you run through a machine in cash (or you can use them for comps, but it's at the same rate as the cash). If I play 2000 hands, that's $10,000 in total bets so 0.25% is worth $25 in rebates. The formula for that is =D3*E3*0.0025, which then allows Excel to calculate the cashback for any number of hands I might play. If you were wondering why I would play a game where the casino has an edge, now you know. Add in the cash back percentage and this game has a total return of 100.03% at any time - on Tuesdays the points are tripled until 7 p.m. so that gives me a total return of 99.78 + .75 = 100.53%. Thus, at least on Tuesdays, my expected value per hour is $2500 x 0.53% or $13.25 an hour. Sure, I can do a lot better by staying home and playing poker, but I really do enjoy $1 Video Poker and it gets me out of the house. The fact that I hit a Royal on this game recently doesn't hurt, either. Just a few more comments and I'll let you go.

Look at the figures for the Pick 'Em poker game at Bodog Casino. For my $$$, this is the best Video Poker deal available on the Internet at this time (June, 2006). Not only is the casino edge downright tiny, but the variance is the lowest of any VP game I know of. I wrote about this game in my Internet Advantage Play: Video Poker (Part 1) article, so I won't go into all of their great bonuses and cash rebates in this article, but you really should check it out. If you'll click on the link above or one of their ads here, it'll help keep this site free for your use and we'll appreciate it. Now look at the All American game in the last row. It's not available online, to the best of my knowledge, but it is available (again, as this is being written) at the President Casino on the Admiral, which is right here in good ol' St. Louis. Offered only in quarter denomination, it's definitely a good deal for VP players on a budget. I'm not sure what kind of cash back they offer there, so I left that part blank, but you've got to believe it's at least 0.10%, so have at it!

If there's a game you play for which you don't know the variance, send me the pay schedule and I'll calculate it for you, if at all possible. I can be reached at Aceten1@mindspring.com

I'll see you here next time.

The GameMaster's Secrets:
Internet Advantage Play: Video Poker - Part 2

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The GameMaster's Secrets: Internet Advantage Play: Video Poker - Part 2