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The GameMaster's Secrets:
Coin Flips and Video Poker

A Note from the GameMaster 10-25-05

It's my sad duty to report that the Double Bonus Video Poker game I wrote about here is no longer available at Intercasino. It might still be found at other Internet casinos that use Cryptologic software, but I haven't had the time to check so I really don't know. Anyway, just two days after we posted this article, an email was sent out from Intercasino advising everyone that the game had been "upgraded." What they've done is taken my beloved "Fortified Jacks", which returned 99.94% and changed it to regular 9/7/5 Double Bonus that returns only 99.10%.

I won't take the credit nor the blame for that happening, but I will say that this game had been around for a long, long time, so the fact that it's being changed now is quite a coincidence. As I've written before, some of my "Secrets" aren't really all that secret, but those that truly are never see print until I have another situation to replace it. That said, it's not like players couldn't figure out what I wrote about here; all of the information was available to anyone who thought about it for more than ten minutes. I wrote about it because those who had been involved with making some serious $$$ had turned their attention to other situations, so I'm now free to tell you an interesting story. This is what I heard:

Several people began playing this game with considerable success in late September; I mean, hitting Royals like crazy (try 3 in a day for one player) and racking up the $$$. The players weren't doing anything other than enjoying a nice swing to the upside, which can obviously happen in a break-even game. Nobody was cheating and I doubt very seriously that the machines were malfunctioning. After all, it's the casino's machine and who could know better if they were working properly or not? No, everything was on the up and up and these players just kept on winning. It got to the point where the machines became unavailable for nearly two days in the early part of October. My guess is that the casino shut them down to see if they were malfunctioning or if some players had found a hidden flaw in the software or were otherwise cheating. But they evidently didn't find anything amiss (and if they had, they'd certainly never admit it), because the games came back on.

And the players started winning again. The only way you can stop Standard Deviation is to let it run out. Be it a downswing or an upswing like the players were enjoying, only an increase in the sample size (number of hands played) will bring good old SD back to "normal". I would assume that the nice folks at Intercasino (and they are nice folks) realized that, so they turned on the games again. But, the players also knew that this was just a huge swing in variance (as most people call it, "luck"), so the party was destined to end soon, anyway. Of course, the players didn't want to just bail out at an arbitrary point so they used the trailing stop-loss that I talk about in the article. Nobody quit at the high point of their winnings, but they were close or so they tell me. I am happy to report that Intercasino lived up to its fine reputation and everyone got paid. There was no hesitation on that, which doesn't surprise me at all, but I'm not sure every casino out there would have handled it in such a classy manner. Of course, Intercasino is a big operation, so an amount of $$$ that might look big to you and me is probably a drop in the bucket to them. Most of the players involved moved their $$$ out in order to take advantage of what will someday be a new "GameMaster's Secret". There are two situations being worked right now that are very lucrative and are, quite frankly, sitting out in the open just as this one was. But that's another story for another time.

With the change in the pay schedule of the Intercasino Double Bonus Video Poker game, the party is officially over, It's no longer a "coin flip", but remember, what I wrote about would still apply to a similar situation. We all need to bear in mind that Intercasino is a business established to make a profit and they have obviously come to the conclusion that the old Double Bonus game is no longer profitable (sigh). However, the new game is worth checking out, because even 9/7/5 Double Bonus is a lot of fun to play, so if you ever get the feeling that you're going to see four Aces, they now pay 800 for 5, as they do in the brick-and-mortar casinos. And it's a fact: If you win at Intercasino, you will get paid.

Sadly, though, it's "goodbye" to my friend, the Video Poker machine.

The Original Article: Coin Flips and Video Poker

Let's say you and a friend decide to engage in a little game of flip the coin. First of all, you both probably already know that neither of you can gain a long-term edge, assuming the coin is "honest"; that is, there's an equal chance heads or tails will show on any given flip. Play long enough and the number of heads will approach 50% of the tosses and the number of tails will do the same. But, an interesting facet of this type of trial is that the percentage will always get closer and closer to 50% on each side, however the actual difference from a numbers point of view will actually increase. For example, in a trial of 100 flips, you could easily end with 47 heads and 53 tails (about 70% of one Standard Deviation), which is a 47-53 percent ratio and a difference of 6 between the actual number of heads and tails. In a trial of 1000 flips, you could just as easily end with 490 heads and 510 tails (the same 70% of one Standard Deviation), which is now a 49-51 percent ratio, but you can see that the actual difference between the number of heads and tails is 20, quite a bit larger than the difference of 6 that we saw in the 100 flips. Bear that fact in mind as we play our little game.

Now, your friend is very nice and s/he agrees to accept any bet (within certain predetermined limits) and will play as long as you want to play. Let's say you both agree that you may bet one, four, eight or twenty units on each flip of the coin. In other words, you're using the coin only to determine the outcome of each "hand" and each bet won will pay even money or one-to-one. If you bet 4 units on heads and it comes up heads, you win 4 units; if it comes up tails on that flip, you lose 4 units. Obviously, there's nothing to be gained by you betting anything other than heads on each flip, because either result - heads or tails - has an exactly 50% probability of occurring. Oh, you might want to swap your bets back and forth between heads and tails just to break up the boredom or to follow some sort of mystical "trend-following" bet scheme or do it because there's a full moon or for any other reason, but the fact remains: In the long run, there will be 50% heads and 50% tails or at least a number very close to that.

As for betting different amounts, there's really no long-term advantage in betting more than one unit. In fact, if you alter your bet size, you could easily lose a lot of big bets and win only the little bets, which will put you at a temporary loss. But, regardless of how you bet, if you play long enough, you'll eventually end up even with your friend. The key word here is "eventually". As I showed in the 100-flip trial and the 1000-flip trial, there can exist quite a difference between the actual number of heads versus tails seen, yet all the while the percentages are drawing closer and closer. In other words, if you were to bet only on "heads", you might start off with a small lead over your friend and could hold that lead even if you were to flip the coin a thousand times. Am I leading up to something here? You bet.

Do you think you can get a lead over your friend from a $$$ point of view? Remember now, your friend agrees to accept any bet within the prescribed limits at any time for as long as you wish to play. So let's say you start by betting just one unit on "heads" for the first 100 flips and your result is a net loss of six units. On flip number 101, you bet eight units and win; you're now two units ahead. Lucky, for sure, but well within the realm of possibilities. Or, let's say you start by betting just one unit on "heads" for the first 100 flips and your result is a net gain of six units. On flip number 101, you bet four units, get lucky and win, so you now have a 10 unit profit. Because your friend will do as you please, you could stop now and walk away with a profit. You just made a profit on a 50-50 proposition, but your friend may feel a bit hurt that you've chosen to end the game so soon. Of course, you could continue to play and you might not ever give up your lead, so your friend may be getting off cheap, at least for the (relatively) near-term. Sure, if you play forever you'll both end up even, but what is "forever"? Is it 1000 flips, 10,000 flips, 10 million flips? I honestly don't know. As the number of trails gets into the thousands, there will undoubtedly be times when your friend recaptures the lead, but time is on your side because you are the one who determines the stopping point and you're not likely to stop when you're at a loss, unless you're totally out of $$$ or have just become so bored you can't take it any more.

What does all of this have to do with Video Poker? Well, let me tell you about my "friend", the Video Poker machine. If a game of VP returns 100% in the long run, it's a coin flip; you'll eventually win as much as you lose. Or lose as much as you win, it's all a matter of time. The tough time will be when you start with a loss, because we already know that our "friend" might keep the lead over us for quite a while, which could cause us to stop playing due to a lack of $$$. But - and it's an important "but" - if we can get a lead, we could conceivably hold on to that for many thousands of hands. And the nice thing about VP is that most hands we win actually pay a bonus; that is, they return more than just even-money. As an extreme example, we might hit a Royal Flush on our first hand. As you know, a Royal pays much more than one for one, thus we could leap out to a big advantage that we might not give up for a long, long time. Of course, we most likely will not hit a Royal in our first hand, nor the 100th hand, nor the 10,000th hand, but if we play long enough, we'll eventually hit one, for sure.

A Video Poker game that returns 100% is, in the long run, a coin flip but in the short term, it carries a certain "variance", which basically means your pool of $$$ (or bankroll as we call it) will vary widely - both up and down - as you play the game. The long run will find you even, but the short term can find you way up or way down; obviously, we want the "up" part to happen to us. Can I guarantee we'll be up at some point? In a word: No. Can I say with some certainty that we can get ourselves up at one point or another? Probably. Sorry, but that's the best I can do. If 1000 of you try what I'm going to propose here, a relative handful will experience disastrous results; a few will see a profit right away and most will lose a little bit in the beginning and their results will hover around break-even for most of the time. I can, and will, show you how to minimize your risk, but my plan calls for you playing a lot of hands and it's just a fact of life that playing more hands - while it increases your probability of breaking even - causes bigger swings in your bankroll. Okay, enough of the risk disclaimer; here's what you can do to make some serious $$$ from a "coin flip" situation.

The Plan

My friend, the Video Poker machine, is the Double Bonus Poker game at Intercasino. If you play this game perfectly, it returns 99.94% of all the $$$ you run through it. A lot of people are rightly skeptical about an online casino that offers such a good game, but you need to remember several things: first, very few people actually play such a game perfectly so each player mistake adds to the casino's edge, plus they have long used this game as a loss leader to attract players that might participate in other games where the casino has a bigger edge. I will say this without any hesitation; the game is honest and the casino will pay you if you win. For me, the appeal of this game has several facets. First, the casino offers a matching bonus of up to $90 (as this was being written in October, 2005) for the first deposit you make each month. That's for every player, every month that makes a deposit of funds, not just new players. It carries play-through requirements that are easily met by Video Poker players, so it's not $$$ you can withdraw right away, but a good deal, nonetheless. Secondly, the Intercasino version of Double Bonus Poker (DB) is really more closely akin to Jacks or Better, rather than the "real" game of DB; so much so, that I called it "Fortified Jacks or Better" in an article I did some years ago. You can find that in the archives of the Video Poker page here, which is accessed via the drop-down menu under the Strategy and Technique header on the front page.

Anyway, this resemblance to a Jacks game means the variance that I spoke about earlier is lower than regular DB because the game pays 2 for 1 on two-pair, whereas regular DB pays 1 for 1 on that hand. In return for that, Trips pays only 2 for 1 (as opposed to 3 for 1 in DB) and other hands have reduced payouts, but the Intercasino DB is still a fun and exciting game to play. Like most Bonus games, it's the Quads or Four-of-a-Kind hands that can make you or break you. Hit four Aces (which pays 750 for 5) and it's going to be a good session; miss the Quad-anything and it's tough to win. But another thing that makes this game so ideally suited for our purposes here is that it's available in $.25, $1, $2 and $5 denominations, which you can switch back and forth to with just a mouse click. Now you can see why I made the bet limits in the imaginary coin flip game 1, 4, 8 and 20 units; the 1 is $.25, the 4 is $1, the 8 is $2 and the 20 is $5. From a practical point of view, one should always bet five coins, because the payout for a Royal Flush is at its maximum (4200 coins, by the way) only when you bet five coins. From that point of view, our bet sizes are $1.25, $5.00, $10.00 or $25.00, which is still a 1,4,8,20 ratio.

With that as background, let me tell you my own approach to winning at this game. I typically deposit about $300, usually at the beginning of the month so that I get my $90 bonus that's immediately added to my account. I begin by playing quarters, which is $1.25 per hand. Sometimes I lose that $390, so I'll deposit another $300 or so. In any event, I'll usually find myself ahead at some point - let's just say I get up by $200 after I deposited the second $300 - so I'm net down $100 ($390 lost, which actually cost me $300, plus a $200 profit) and have $500 in credits on the machine. Now it's time to gamble. We don't do a lot of gambling here, but in this case, it's a reasonable wager. What I'll do is cash out my credits, then redeposit $200 and switch to the $1 mode of the machine. That will give me 200 credits, which is enough for 40 hands of play at this level. If I lose that $200, I switch back to the quarter mode, redeposit my remaining $300, play and pray (although I have to admit that prayer doesn't work very well at VP). Should I win at the $1 level, I'll stay with that mode until I have $600, at which time I'll cash out part of it, assuming I've met the betting requirements for the bonus. Depending upon how lucky I feel (we "experts" don't actually believe in luck, but you get the idea), I might cash out $300 and continue playing at the $1 level or cash out $300 and drop down to the $.25 mode or just cash out the entire $600 and call it even for the month.

Most often, I'll cash out $300 and go back to the $.25 mode so that my entire risk is now the $300 with which I began this month's play. Many times I'll lose that $300, which is really too small a bankroll for such a game, but this does take time and for all of us, time is money and VP is only one way I can earn $$$ on the 'Net, so I only devote a few hours to the game each month. However, if I make another $200 profit at the quarter game, I cash it all out, switch to the $1 mode, redeposit $200 and play on. Should I lose that, I might quit and cash out the remaining $300, which leaves me even for the month or go back to playing quarters. It just all depends upon how I feel, how much time I have and how the cards have been running.

The Chicken Soup Factor

That's something you'll rarely see me say here: "how the cards are running". Regardless of what has happened in the last 10, 20 or 30 hands, the very next hand may change whatever "trend" or "streak" I perceive. To be sure, streaks do exist but they can only be recognized after they're over. No one - and I mean no one - can accurately predict how well they'll do in the next 10 or 20 hands of play. Any actual resemblance to the prediction is pure coincidence, I assure you. But that's the beauty of this approach to the game; so long as you can afford the loss of whatever amount of $$$, relying upon a rabbit's foot or any other scheme to win is like taking chicken soup for a cold: It may not help, but it can't hurt (usually pronounced "hoit", if you're a Jewish mama from New Jersey). Play long enough and you'll eventually get even, especially if you take advantage of the monthly bonuses, not to mention the player "comp" points, which adds about another 0.1% to your return. But self-discipline is the key here. If you were to deposit $300 and play the $1 game, you would probably lose 95% of all your sessions, simply because it's too few bets for a game with the variance of this one, in spite of it being comparatively low. Yes, even if you do that and lose most of your sessions, in the long run you'll eventually break even. However, you're going to find yourself wasting a lot of time by making a lot of deposits and at some point, it may all become very frustrating - and you just know that'll happen when you're on a big losing streak, which might cause you to give up the game entirely, thus assuring a long-term loss.

My approach is to build upon success - sort of the old gambling maxim, "playing on the house's $$$", which is ridiculous of course, because when it crosses the table, it's now your $$$ - but it does have some validity as a concept. Risking a profit in order to make an even larger profit makes sense, especially if you've recaptured your initial investment. Gambling with a certain amount of $$$ that will not change my life in any way whatsoever should I lose it, is the smart way to gamble. It's basically stress-free, so you can at least get some entertainment value from playing the game. As I've often said, when I go out to dinner, I know I'll be trading $$$ for what will hopefully be a good time, but I also know I cannot make a profit on whatever $$$ I spend. That's not the case when I gamble (as opposed to playing games where I have an edge, which is investing, not gambling), because there's always the possibility that I can make a profit on my $$$. Like anyone else who gambles, I lose most of the time, but every now and then I hit for something big; I've hit a lot of Royals at Intercasino and at $300 or $600 a pop, it's going to take a long time for me to drop back to break-even.

If I'm lucky enough to get a nice winning streak, I use what I call a "trailing stop-loss" as my credits increase. For example, if I have moved up to, say, $750 in dollar play, I'll continue to play dollars until the credits drop to a predetermined amount, which might be $500. At that point, I'll usually drop to quarters or just cash out. However, if the $750 were to become $1000, then $700 or so will become my "action" point. In other words, I'm not limiting my upside potential by proclaiming a double or any other random increase of my bankroll as being "enough". I already know I can't predict a streak, but I do know they still exist and this method of play gives me a pretty good chance of taking advantage of them. Sure, there are times when my stop point is hit and I drop back to a lower level of play that immediately begins with a set of Quads, but what I always remember is that I should be so lucky as to have that happen all the time. The tough part here is to lose at the dollar level, then have to make it back at the quarter level, because the tendency is to lose your patience, switch back to dollars and play your bankroll into oblivion. Like I said earlier, self-discipline is a big factor in this approach to Video Poker.

When I'm playing at the dollar level and get ahead by $300 or so, I usually cash out, switch to the $2 mode, deposit $300, which is 150 credits and go for it. Video Poker is a very streaky game, so even though you've been winning, it doesn't automatically mean you'll start losing just because you've decided to bet more per hand. While I'll admit I'm somewhat reluctant to move up after hitting a set of Quads (because of the idea I'm probably not going to hit Quads back-to-back), the concept is nothing more than superstition; there is no mathematical reason why it cannot happen. Sure, it's a long shot, but it can still happen and I've done it. Like I said earlier, though, you can let all of your fears and superstitions run amok with this method of play, so long as you use the proper playing strategy for each and every hand. That really is crucial, so let me talk about it a bit. But before I do that, you might be wondering when and if I ever play at the $5 level, which is $25 per hand. While it's very tempting (a Full House is worth $200!), I seldom get to that point. But I recall with great pleasure the time I decided to risk $500 (100 credits) at that level and on my very first hand was dealt four Aces, which paid $3750! Dealt, not drawn. That was a good day.

>The Proper Playing Strategy

The only way you can make this game a "coin flip" is by using the proper strategy to play each and every hand. Remember, each mistake you make adds to the casino's edge and over thousands of hands of play, those mistakes really add up. Let me give you an example. How would you play this hand: As, Qh, 10h, 5d, 6s. If you said hold the A,Q only, you'd be correct. Now look at this hand: As, Qh, 10h, 5d, 6c. If you said hold the A,Q only, you'd be wrong. The correct play is to hold the Ace alone. In case you wondering why, the answer lies with penalty cards. In the first hand, you'll be discarding the 6 of spades, which can be used with the Ace of spades to make a Flush, if you were to hold the Ace only. For the second example I changed the 6s to the 6c, thus removing that penalty, so holding the Ace alone becomes the better play. By the way, if you thought holding the Qh, 10h was the better play in both hands, you're wrong both times. Admittedly, the differences aren't large, but you really do have to approach perfection in your play for this to work. Fortunately, that's very easy to do. Because you're playing on your computer, you can use any method you wish, short of kicking the machine, to help you. Specifically, you first need to have a highly detailed strategy matrix for the game. That can be produced by a great program called "Video Poker Strategy Master", which is available at www.zamzone.com/. You should also have a copy of "Bob Dancer presents Win Poker", which is available at the same site. This program allows you to check the proper play for any hand on the fly, so to speak. Whenever I'm in doubt, I plug the hand into BDPWP before I play it. Sometimes the difference is in the fourth decimal point, but that's the accuracy you need to achieve. Remember, you may take as long as you like to play a hand on-line, so until you get really good with your accuracy, take it slow and get it right.

Final Comments

So, that's basically my approach to making a profit from coin flips. My "friend" is willing to accept any bet I wish to make, within the predetermined limits; s/he (it) is ready to play whenever I wish and will play as long as I wish, plus my friend is never offended or hurt if I choose to walk away with a profit. Beyond that, my friend gives me a bonus every month and a 0.1% cash back bonus. I have a lot of fun playing this way because I can let what little superstition I have in me come out. If I feel that hitting quad 7s is a good omen, I can switch to a higher mode and let it fly or if I feel that not hitting any hand for a payoff in the last ten hands is not good, I can switch to a lower bet and "ride it out." Either way, I know that in the long run, I'll break even and maybe make a small profit based upon the bonuses and the cash-back feature.

Yes, I'm recommending a casino that has advertised here for a long time and, if you open an account there by clicking on one of their ads on this site we'll benefit, but everything I've told you has actually happened in my own play. I'm well ahead at this game and, while you might be one of the few who will not have a good result, it really is possible to make a profit and have fun at the same time. How much better can it get?

I'll see you here next time.