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Let me present to you two different betting scenarios. They are similar, yet different. Tell me what you'd do:
Case 1: I show you a fair coin, meaning that heads and tails both come up equally. You'veBob Dancer is one of the world's foremost video poker experts. He is a regular columnist for Casino Player, Strictly Slots, and the Las Vegas Review-Journa land has written an autobiography and a novel about gambling. He provides advice for tens of thousands of casino enthusiasts looking to play video poker. Bob's website is www.bobdancer.com watched me flip it and you know that tails has come up 19 times in a row.
I tell you that betting on the next outcome will cost you $2.20, where winning gets you your money back plus $2 and when you lose you get nothing back.
Which side do you bet on?
Case 2: You're playing a dollar Double Double Bonus video poker machine in Las Vegas. You are dealt Ah As Ac 6d 6s. You know the "proper" play is to just hold the aces and that you're supposed to get 4-of-a-kinds once every 23.5 times starting from this position.
But you've been counting, and the last 50 times you held trip aces on this machine, not once did the fourth ace pop up. So how do you play this hand?
In Case 1, I think the smart bet is on tails. Although I told you the coin was fair, the chances against a fair coin coming up tails the next 19 times is more than a half-million to 1. I would therefore conclude that the coin WAS NOT fair. For some reason tails come up more often on this coin, and if you're going to bet, that's the intelligent way to go.
If you decide that I might be a hustler of some sort and therefore determine you should stay away from the bet altogether, that's a smart way to go as well. Obviously there's something fishy with me telling you a coin is fair and the evidence says it most likely isn't.
Even if you decided that it's a 50-50 bet (which is being a sucker on your part), if you stayed away from the bet because I'm asking for a 10% vig on the bet, that's smart as well. Every intelligent gambler knows that he needs to have an edge before he bets. Since he believes he doesn't, he shouldn't bet.
But with all this, I still believe you should bet on tails.
In Case 2, I think the smart bet is to hold the aces only. Striking out 50 times in a row from this position happens about 11% of the time, or one time in 9, assuming the game is fair. You'd rather be on the plus side of receiving the aces, because it's $800 or $2,000 for every set of aces as opposed to $15 for the trips, but sometimes you on the down side.
Even though you're supposed to get the quad aces once every 23.5 times, not getting them 50 times in a row should NOT be enough to get you to change your basic strategy.
So, what's the difference between these two cases? In Case 1 I went against the stated odds just because of 19 consecutive trials and in Case 2 I stayed with the odds even though there were 50 consecutive trials against me. Assuming I'm a knowledgeable guy, why would I let practical (as opposed to theoretical) evidence affect by bet in the first case but not the second?
Let me take the second case first. I 99.99% believe that video poker machines are 100% fair in Nevada. It's going to take A LOT more than a 50 trials to shake me from this belief.
Can I be shaken from this belief? Yeah, I suppose, but I'm not sure what it will take. I bet more than 1,000,000 video poker hands a year assuming they are fair, and every year since I started in 1994 I've come out ahead. That's a pretty major winning streak.
Whatever skills I have at identifying the good opportunities and playing them accurately ASSUME the games are fair. And since I continue to win, that validates this assumption in my opinion.
Now let's go to Case 1. Here we are told the coin is fair, but we really don't have any way of knowing whether or not it is true. Even if we give the coin the benefit of the doubt for a few flips, 19 hands in a row is more than enough to make me seriously doubt the coin's fairness.
Beyond that, instead of doubting the coin's fairness, I now believe that the coin is definitely weighted so that tails comes up more often. And I believe that the 10% vig you have to pay to make the bet is small enough so that you'd still have a significant advantage betting on tails.
In next week's column we're going to revisit these two cases. Even if we leave aside the "can you trust the fairness" issue, having 19 trials go one way in the first case was significantly more important than 50 trials going against you in the second. We'll discuss that next week.
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