Crazy 4 Poker (C4P) is one of the more popular poker variants. As I discussed in this post, it is extraordinarily tough for a hole-card player to get an edge. That doesn't mean an edge is impossible. In a recent disaster at the Hollywood Casino in Columbus, Ohio, a whole bunch of APs enjoyed an edge of over 30% for a sustained period of time. And they didn't do a single thing more than play by the rules of the game. Let me explain.

The design of C4P actually consists of two separate wagers that must be made together. There is a standard Ante/Raise part of the game, where the Raise bet can be up to three times the Ante. The player has a huge edge over the house on the Ante/Raise part of the game.  To be precise, the player's edge is 31.3606.

To compensate for this edge, there is a second required wager, which must be made in an amount equal to the Ante wager. This second wager is called by the suggestively generous title "Super Bonus." It is anything but "super" or a "bonus." The house edge on the Super Bonus wager is 34.7795%. Taken together, the house edge on C4P is 31.3606% - 34.7795% = 3.4189%.

I personally don't like games that have combinations of two or more forced wagers like C4P. The player will naturally enjoy the wager they are crushing, in this case the Ante/Raise. However, only the most unobservant player will fail to realize that the other required wager (the Super Bonus) is a gimmick to win back the money lost on the first wager. Most players will see right through this set-up and balk at the combination. Win here, lose there, and so it goes.

But what if the casino didn't require the players to make the Super Bonus wager at all? What if the players could play the Ante/Raise alone?

This headline says it all. Click on the image to read the story on the associated website at CardPlayer.

C4P Card Player


Here is a full article on this debacle, from the Columbus Dispatch.

To quantify this snafu , assume the table had six spots and that the maximum wager allows was $100. Then the casino will lose 6x($100)x(0.313606) = $188.16 per round. At 40 rounds per hour, the table gave up over $7,500 in profits to the players per hour. If the game was full round-the-clock (I am sure it was), then the casino lost slightly more than $180,000 per day on this table. If the table maximum was higher, or the game pace was faster, then the losses would have been even more dramatic.

APs will find any legal way they can to get an edge over proprietary games. But sometimes, the edge comes to them.

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received his Ph.D. in Mathematics from the University of Arizona in 1983. Eliot has been a Professor of both Mathematics and Computer Science. Eliot retired from academia in 2009. Eliot Jacobson