Cutting Losses

31 December 2020

By John Grochowski

QUESTION: I was faced with a Mississippi Stud hand that I had some doubts about.

My first two cards were 7 and 9 of spades. I made a 1x bet because the strategy says to be equal to your ante if you have at least two points in the first two cards.

The first common card turned up was an 8 of spades. It looked great in my hand, three cards to a straight flush, so I made the 3x bet.

After that was a 4 of hearts. That pretty much shot the hand. Now I couldn't get a straight. I couldn't get a flush. The best I could do was pair up the 7, 8 or 9 for a push.

That left me nine possible ways to get my money back with no winnings (the other three 7s, three 8s and three 9s). The other 39 cards were all losers for me.

So why does the strategy call for me to make another 1x bet on the final card? Isn't that just throwing good money after bad.

ANSWER: It's a matter of mitigating losses. If you fold, you lose your ante, another bet equal to your ante and a third bet of three time your ante -- a total of five times your ante. If you bet another 1x, you'll lose six times your ante on 38 hands per 47, but on the other nine hands you'll get all your investment back.

The net effect is that your average losses will be higher if you fold than if you make that one last bet. That's why basic strategy for Mississippi Stud calls for a 1x raise at the last opportunity provided you have at least three points AND you've made at least one 3x raise.

For the uninitiated, points in Mississippi Stud are a player device for evaluating a hand's possibilities. They help guide us in whether to fold, raise and the in the size of the raise.

Count cards that would bring no return if paired as zero points. Those are 2s, 3s, 4s and 5s. The pay table starts at pushes on pairs of 6s through 10s, and we count each of those cards as one point. Pairs of Jacks or higher bring even-money payoffs, those cards are counted as two points each.

The hand the player described has three points: one each for the 7, 8 and 9. Even though there are no flush, straight or high pair possibilities after four cards, there are three points. So with a 3x bet having been made with three known cards, we cut losses a little by making the 1x bet after four cards.


QUESTION: I've seen there are 2,498,960 possible five-card poker hands. I calculated to satisfy curiosity, and I got a different answer. The first card can be any of 52 in the deck, the second can be any of the other 51, then any of 50, 49 and 48. Multiply 52 x 51 x 50 x 49 x 48 and you get 311,875,200 possible hands.

That seems like it would make a big difference in odds for five-card games. There are more possibilities than players realize in video poker, five-card stud, Caribbean Stud or anything else.

ANSWER: Your answer would be correct if card ordered mattered, but it doesn't. Jack-10-7-5-3 of hearts is the same hand as 5-Jack-3-10-7 of hearts.

To adjust, multiply the five possible card positions -- 5 x 4 x3 x 2 x 1. That's 120. Divide your 311,875,200 hands by 120 and you get 2,598,960 five-card hands in which card order doesn't matter.