Recently, a poster on the videopoker.com forum wrote words to the following effect: “I have no doubt that if I could ever learn to quit while I was ahead, I’d be far ahead at video poker, even though I play games returning only about 99%.”
Let’s look more closely at that statement.
Assume you’re playing Jacks or Better for quarters. On your very first hand you end up with two pair. You are ahead $1.25. Do you quit?
This is probably not what the poster meant by being ahead. He drove 20 miles for 30 minutes to get there and would not consider being ahead $1.25 worth his while. He’s not about to drive home now.
But, for now, let’s assume he did mean his statement literally. If he got ahead, at all, he’d quit. Usually, when he played, he’d end up a small amount ahead. He might hit a flush or a full house, or even, on very rare occasions, a royal flush. Often his score would be more than $1.25, but he’d quit whenever his head was above water at all.
Under these conditions, would he be a net winner over time?
The answer is no. The game returns 99%. Occasionally he loses everything he brings — $20, $200, $2000, whatever. The machine goes ice cold for some period of time and he never gets ahead in the entire session.
Eventually he loses enough and goes home. He then comes back the next day and wins $1.25, and $2.50 the next day, and . . . and sooner or later he’ll run into another cooler session again that will totally wipe him out.
This also works the same if he sets win and/or loss limits. He’ll keep playing until he gets, say, $50 ahead or $25 behind, or any other arbitrarily set amounts. There will be days when he gets $48.75 ahead, and then everything goes south. Over time, assuming he plays well, his scores will average 99% of his coin-in.
What I assume he really meant (and he is welcome to post in the comments that my assumption is incorrect and why) was that if he could quit when he reached the high point of the session (because somehow, he’d magically know that he was at the high point), he’d be ahead. In the case where $48.75 was his high point, in his mind he wants the ability to quit there if it doesn’t go any higher. If it moves up, he’ll take the higher amount. But if it goes down, he wants to lock in the $48.75.
If you can do this, you will definitely end up ahead. The problem is you never have enough information to do this. At any point in your gambling session, you might know where you are at that moment, but you can’t know what the next hands will bring until you play them. And if you play them and they go minus on you, you can’t unplay them and take the amount you had before you played.
So, technically speaking, this poster was correct. If he can do something that is impossible to do, he’ll definitely end up ahead. The problem is, he will never be able to do this. Whenever you quit, you’ll never know when the very next hand would have been a royal flush had you played it. About once every 40,000 sessions, that would be the case. But you’ll never know which one of the 40,000 sessions it was because you stopped just before that royal flush happened.