Discount Gambling

Lately, I’ve been playing more full exposure Mississippi Stud at my local Barona Casino. I’ve called it “the least enjoyable +EV game” around, because of it’s high variance. Generally, it’s an “expensive game”, played by an older crowd that can afford it. Even though the full exposure game is +EV (around +1.5% of the Ante) using a simple strategy, the game is only full (exploitable) on weekends. The way I think, people should be all over this game, keeping it full, betting $25 Antes, and grinding out $0.37/hand. But the game is usually empty for good reasons: it would take months of full-time grinding and a huge bankroll to take advantage of it. And you’d need a full team of 6 players.

Even when the game is full, the house’s hold (EV) is huge. Because there is no way on earth that people are going to play correctly, no matter what. I play with my cheat sheet, which tells me the approximate return of hands on 3rd and 4th street, and their exact returns on 5th street. Other players wouldn’t be caught dead following this advice, because it tells them to fold more than they like to (and occasionally, it tells them to raise more than they like to). Most players don’t like folding their hands, especially at 2nd street (first two cards), and at the river. They acknowledge that they shouldn’t “chase”, but they don’t know how bad (-EV) it is, and they get caught up in it.

The cheat sheet points out the cost of each mistake, and even the smallest mistake is usually in double digit territory. For example, if you’re on 2nd street, and you have only 1 high out and 2 mid outs, you’re giving up about a 31% house edge (of the Ante) to 1x call and see 3rd street. The return of this call is -1.31 Antes. Folding would be a better choice, costing only 1 Ante (-1.0 return). Calling will return -1.31 on average, or an additional 0.31 Ante loss to see a card. At a $5 Ante, this is an additional $1.55 cost over folding.

When you “chase” a hand, you often pick up just enough outs to “force” you to call again. In our 1/2/0 (high/mid/low outs) example, we called to see 3rd street, making our hand worth -1.31. If we pick up 2 more high outs on 3rd street, we now have a 3/2/0 hand, and we should 1x call again to see 4th street, since folding has a value of -2.0, while calling has a value of -1.75. Notice that we now have a hand that is 0.75 Antes worse than folding on 2nd street (-1.0 Antes), and we’re forced into investing 3 Antes. Chasing could get worse. If we pick up another 2 mid outs on 4th street, we’re again forced into another 1x call, to “protect” our 3/4/0 hand and 3 Ante investment to extract out its -2.94 Ante value (would be -3.0 to fold on 5th street). So that’s how a 31% mistake escalates to a -300% cost. Of course, if we paired up our hand, we could win big. That’s why it’s only a 31% mistake on average.

“Chasing” is horrible, because you should just fold and wait for the next hand, instead of forking out -EV to the house. If you don’t hit, EV just gets worse. Often at the table I hear, “I always see the first card”, meaning they’ll play any two cards to 3rd street. I simulated this “call anything” 3rd street strategy combined with perfect strategy on 4th and 5th street, and the result was a 13.5% house edge. Notice that’s worse than having no other information and playing basic strategy (4.91% house edge). It’s no wonder that most people lose a tremendous amount of money at the game. It’s hard to say, but I’d guess the average player is giving up about a 20% (of an Ante) edge to the house. At a $5 Ante, that’s $1 a hand.

Of course, that $1/hand cost might be the marginal utility of “not folding” + “getting lucky” + “playing hunches” – “bleeding off” to that player. I’m kind of the exception. To me, giving up a 5% edge to the house on a mistaken call feels a lot worse than its $0.25 average cost 🙂