Last year, I played about 186,000 hands of dollar video poker (at $5 a pop!) without hitting a Royal Flush. Did I lose $$$? You bet! But so far in 1999, I've hit 3 Royals in about 30,000 hands of play. Is there any rhyme or reason to all this? The answer is, not really. All we can say with certainty is that a Royal will happen once every 40,400 hands in the long run. Now, what's the "long run"?

Since I recently upgraded my computer to a 686, 233Mhz processor with 72 megs of RAM, my video poker simulator plays 10,000 hands a second...a second! And that lets me run massive simulations in a short time. (Yes, I'm still fascinated by the power of a computer.) Anyway, I thought I'd try to get to the "long run" and always felt that 4 million hands would do it. Four million hands at 600 hands an hour is about 6500 hours of video poker and that's almost two years of fulltime play. And, while it's close, the hands received in that period of time isn't exactly in line with mathematical expectation. Of course, each simulation would be a bit different, so to really get an exact 'fit', I'd have to run a million sims or so and then average all those.

But playing video poker in a casino has nothing to do with 4 million-hand simulations; it's one at a time and you never know what's going to happen. But, if you are able to play enough, you should see the results. And that's what I'm really after here - proof that no matter how unlucky you may think you are, if you hang in there (and play accurately), your results will be the same as the computer. Yes, that takes time and lots of $$$, but this is as sure a thing as you'll ever see in a casino.

I've said it before and I'll say it again: I don't play video poker, I invest in it. I lose, time after time, but in the "long run", I get the $$$. I just cannot predict when they'll show up and I can't help you, either. But the more you play good games, the more you'll eventually make. Let me give you an example of how I view it. Most of my play is at dollar video poker games with progressive Royals and I have minimum levels at which I'll play. For the two sets of 9/6 Jacks games available to me, I only play if the Royal is $5200 or more, so it stands to reason that I can never hit a Royal under $5200 and, in fact, the ones I have hit actually average closer to $6000. A 9/6 Jacks game with a $5200 Royal has a long tern return of 100.18% and the Royal counts for 2.96% of that return, so until it hits, I'm getting a return of just 97.22%. Just betting the pass line at craps offers a 98.6% return, so you can see why there are so many losing sessions at video poker and craps. But, the return on VP will rise above 100% one fine day. That won't happen at craps.

If my average edge at VP is .2% and my average bet is $5, my 'expectation' is to win $5 X .002 = $.01 or one red cent per hand. Thus, 600 hands an hour is $6.00 an hour in expected income. Now, add to that a .25% slot club, double bonus day and comps, etc. and the number goes up considerably. Plus, we're talking about minimums here; my average edge is more like .7 or .8% because I also play full-pay Double Bonus games on 'triple point day' (1.85% total return) and an excellent Bonus Poker game. But that's how you have to view this, each hand is worth "X" cents, but you can't pick the time when you'll collect. If you're lucky, you might get paid in advance or, if you're like me, you'll have to pay before you collect. But, collect you will.

So, what are the results of a 4 million hand 'play'? If this was done at a dollar machine, it means $20,000,000 was bet. Yes, that's 20 million bucks! In my sim, I had a $5200 Royal, so my playing result was a loss of $19,160, which is significant on its own (I mean, 19 grand is 19 grand, right?), but is just the tiniest fraction of 20 million; about one tenth of one percent (.000958 to be exact). A side note here: In about 2 years' fulltime play, a dollar VP player generates $20,000,000 which is the sales volume of a nice little company. Don't be afraid of asking for comps at any casino where you're generating those kind of $$$.

Okay, some more analysis. If we played 4 million hands at a casino with a .25% cash return slot club, that would total .0025 X $20,000,000 = $50,000. Subtract from that the $19,160 loss and the net profit is $30,840 which isn't very impressive on an hourly basis, since it's under 5 bucks an hour. Even though our expectation was to get back 100.18% (the total return on a 9/6 Jacks game with a $5200 Royal), we actually realized a return from play of only 99.9%. The sim hit 94 Royals or one every 42,553 hands. That's a bit short; 99 Royals were expected. The sim had a few extra straight flushes (437 expected, 440 received) but was way short on quads (9456 expected, 9363 received).

Here are the complete stats on the simulation:

So, do we ever get to the long run where reality equals expectation exactly? Maybe, but it's a very big number. Hell, I ran a 10,000,00 hand sim as I was writing this and, while I 'expected' 248 Royals, I got 269. And so it goes.

See you here next time.

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