Discount Gambling

I wanted to know what my session outcome probabilities were for the +EV Mississippi Stud game @Barona, where all the 6 player’s card are exposed. I calculated the distribution below, assuming a 200 Ante bankroll, and playing for exactly 100 minimum bet hands with the collusion strategy. If you use a different strategy, or hit-and-run, then your probabilities will differ.

I revisited the collusion strategy for full-table (6 players), all cards exposed Mississippi Stud, as dealt at my nearby Barona Casino. I fixed a few small decision points, and calculated the EVs of the threshold points, so you can see the value of marginal calls and folds. When I play again, I’ll probably bring this chart to the table. Notice any return less than -1.0 on 3rd street is a fold (folding costs you your ante, but calling would cost more). Similarly, any return less than -2.0 on 4th street is a fold. And any return less than -3.0 on the river is a fold. For example, calling 1x on 5th street with only 2 high outs and 4 mid outs is going to cost you (-3.16)($5) = $15.80, whereas folding would limit your loss to $15. On average, this “chase” is going to cost you $0.80 more than folding. As another example, calling unsuited cards with only 2 high outs and 1 mid out on 3rd street is going to cost you (0.07)($5) = $0.35 more than folding, on average.

There are a lot of players that play way too many hands, as they don’t want to miss a payout. You can see that even the most marginal of folds is around (0.1)($5) = $0.50 for each bad decision. This can add up over each hand, and each bad decision (sometimes multiple bad decisions per hand). Often, people make multiple bad decisions per hand, making worse than -0.10 mistakes (literally, off the below chart), and betting more than $5 Antes.

I’ve been playing +EV Mississippi Stud lately at my local Barona Casino, where all player hands are shown. I’ve found the key to playing the +EV strategy quickly is knowing the folding points, and looking ahead a street or two. I remember the folding points by street and high outs, which is pretty easy. I still play with the strategy table in my hand. The stronger your starting hand, the least amount of help (outs) you’ll need from the community cards. This means that you’ll never fold the strongest hands (5 high outs or better), and strong hands (3 or 4 high outs) will typically go to 4th street before you need to make a decision. I’ve made a flow diagram showing this folding decision. It highlights the key folding decision points, arranged by street and high outs.

Folding strategy for Mississippi Stud, all 6 player hands known.

Don’t use this chart at the tables. Just use it to understand the folding points better, and to learn to play faster. Understand that you’ll never fold a hand with 5 high outs. And with 3 high and 2 mid outs, you won’t have to think until 4th Street. Furthermore, you’ll never fold a hand with 3 high and 4 mid outs. However, if your starting hand has less than 3 high and 2 mid outs, you’ll need immediate help on 3th Street. Chances are, you’ll need more help on 4th Street. And you’ll probably need at least 3 high and 4 mid outs to see 5th Street. It’s uncommon when you end up calling with 2 high and 6 mid outs on 5th Street, and very rare to call then with 1 high and 8 mid outs.

I finally got around to making a nice, colourful strategy card for Mississippi Stud, as it’s played at Barona Casino near San Diego (i.e., where you get to see all the players hands). I’ve been playing with an awful print out of my strategy table, and it would sometimes slow the game down. We won again last night, thanks to a full house on the last hand!

Mississippi Stud strategy table when all 6 hands seen.

My nearby Barona Casino has been spreading the ShuffleMaster game Mississippi Stud face up for some time now. I finally looked at the game, as it’s played there. Here’s a strategy yielding a 1.5% player edge for a full game (6 seated players). Do not use this strategy unless playing at a full table. Otherwise, play basic strategy (4.91% house edge).

“high outs” means the number of cards in the deck that will give you a high pair (Js thru As)
“mid outs” are the number of cards in the deck that will give you a mid pair (6s thru Ts)
“low outs” are the number of cards in the deck that will give you a low pair (2s thru 5s)

2nd Street:

• 3x raise a high or mid pair
• 3x raise with 6 high outs, or with 5 high outs and suited
• 3x raise a small pair with both trips outs still in the deck
• 1x call with 3 or more high outs
• 1x call with 2 high outs if suited, OR at least 2 mid outs, OR at all 3 low outs
• 1x call with 1 high out if suited AND at least 2 mid outs
• 1x call with at least 5 mid outs, OR suited and 4 mid outs
• 1x call with all 3 mid outs and all 3 low outs
• else fold

3rd Street:

• 3x raise any made hand
• 3x raise a low pair if no outs seen (no cards of your hand are out)
• 3x raise if suited and 8 or more high outs
• 3x raise if suited and 7 or more high outs AND 7 suit outs
• 3x raise if suited and 6 or more high outs AND 8 suit outs
• 1x call if suited
• 1x call if low pair and 2 trip outs
• 1x call if low pair and 1 trip out and at least 2 other pair outs
• 1x call if no-gap straight draw > 456
• 1x call if 1-gap straight draw and at least 5 mid outs
• 1x call if 2-gap straight draw and at least 6 mid outs
• 1x call if at least 4 high outs
• 1x call if 3 high outs AND (at least 2 mid outs, OR 1 mid out and all 3 low outs, OR all 6 low outs, OR wheel draw and 3 low outs)
• 1x call if 2 high outs AND (at least 4 mid outs, OR all 3 mid outs and 2 low outs)
• 1x call if 1 high out AND 5 mid outs
• 1x call if 7 mid outs, OR all 6 mid outs and all 3 low outs
• else fold

4th Street:

• 3x raise any made hand
• 3x raise any flush draw
• 3x raise 8 straight outs
• 3x raise 7 straight outs AND (at least 3 high outs, or at least 4 mid outs)
• 3x raise 6 straight outs AND (at least 4 high outs, or at least 9 mid outs)
• 3x raise 5 straight outs AND (at least 6 high outs, or at least 12 mid outs)
• 3x raise 4 straight outs AND at least 8 high outs
• 3x raise 3 straight outs AND at least 10 high outs
• 1x call all other straight draws
• 1x call any low pair
• 1x call 5 or more high outs
• 1x call 4 high outs AND at least 2 mid outs
• 1x call 3 high outs AND at least 4 mid outs
• 1x call 2 high outs AND at least 6 mid outs
• 1x call 1 high outs AND at least 9 mid outs
• 1x call with all 12 mid outs, or at least 6 mid outs and a previous 3x raise
• else fold