Discount Gambling

I’ve been playing more full-exposure Mississippi Stud at my nearby Barona Casino, since it’s the closest casino to me, and the game is nice and full most every night. The game is a lot more fun now, since I’ve learned all the decision points of the +EV strategy. Most every hand is a “no-brainer” now, and I only have to look at my chart for some copied, suited hands.

I’ve fine-tuned the strategy a bit, it now simulates at a +1.85% player’s edge for a full table. I’ll publish the full strategy when I’ve finished optimizing it. I’ve computed the “element-of-risk” (return per average bet risked), and it’s an amazing +0.78%. This results from the ability to 3x bet multiple streets at no risk (i.e., the hand either pushes or wins). The “element-of-risk” figure is the more accurate indicator for games requiring post-Ante bets. This means that after your Ante, you only risk another 1.35 units per hand. That’s pretty low, considering there are 3 streets to bet.

Strategy Details

The discussion below elaborates on the +EV strategy card shown in the original +EV Mississippi Stud @ Barona post. This post clarifies a few of the decision points, and shows you how to use additional information, like high cards seen, and flush cards seen.

3rd Street

Raising Hands

There are a few hands you should 3x raise on 3rd Street, that on average will pay off better than just 1x calling. Notice that the expectation value (EV) is positive and higher for 3x raising vs. 1x calling for the following hands:

Those are the only raising hands. Bet other hands 1x at most. I often see people raising 5 offsuit high outs. That’s a losing move, as a 1x bet has a +0.63 return, while raising the bet to 3x decreases the return to +0.43. So you’re risking more and winning less. You win more by betting less. Don’t raise any hands except the ones in the above table!

Piggyback Bets

Often, people don’t 3x bet their hands on 3rd Street in the above table. Barona etiquette allows other players at the table to piggyback on the betting spot, if it’s not maxed out (3x). I take as many of these bets as I can, because they’re +EV. First, I tell the owner of the hand to max out their own bet, that it’s in their favour to do so. Only if they won’t make the bet themselves, do I ask to ride along a 2x bet. Usually, I talk people into taking their own EV. But, if they’re too scared, I’ll take the bet myself. From the above table, we see that the return for a 2x piggyback bet is the Improvement value. E.g., if someone doesn’t raise their uncopied small pair, a 2x piggyback bet returns +2.6 Ante average win, or a (2.6-2)/2 = +30% average profit. The returns are smaller for other hands, but is pretty good for 6 high suited outs (+11.5% for a 2x piggyback).

Calling Hands

Notes:
* EV varies +/- 0.20 depending on if the hand “reaches” (can make straight), and if less than 4 high cards are seen, and if suited, whether 3 or more flush cards are seen.

** You should call 54s if you can make a straight flush, and you’re not copied, and at most one flush card is seen.

So, you should use the above table as a guideline for calling or folding. Marginal hand (*) decisions depend on whether it “reaches”, the number of flush cards seen (< 3), the number of high cards seen (<= 4), and whether a straight flush is possible. For simplicity, treat each factor equally in making your decision. (A hand is more valuable when less than 4 high cards are seen, because it increases the probability of making a high pair on board).

4th Street

Raising Hands

Calling Hands

The 4th Street calling points are pretty simple, and basically boil down to the following minimum hands:

• 3 high (“pay”) outs
• 2 high (“pay”) outs, and 3 mid (“push”) outs
• 1 high (“pay”) outs, and 5 mid (“push”) outs
• 6 mid (“push”) outs

You should also call a straight draw if just below these minimum requirements.

5th Street

The 5th decision is very easy to compute, since you’re betting on one card, and you know all your outs. Refer to the strategy card for the decision points, but your basic “calling hands” are

• 5 (or more) “pay” outs
• 4 “pay” and 2 “push” outs
• 3 “pay” and 4 “push” outs
• 2 “pay” and 6 “push” outs
• 1 “pay” and 8 “push” outs

These minimum calling hands are pretty easy to remember. I know that once I have 5 high (“pay”) outs, I’m never folding. Or, once I have 4 high (“pay”) outs, I only need to pick up 2 mid (“push”) outs to not fold. And, when I only have 3 high (“pay”) outs, I know I need at least 4 mid (“push”) outs to see 5th street. If my hand is worse than these minimums, on average, I’m better off folding the hand, and losing 3 units, than playing and losing more than 3 units.

You’re getting a lot of odds for the 5th Street bet, so if you feel like it, you can call with a slightly subpar hand (like short one mid out), since it only costs you 5% of an Ante on average. At a $5 Ante, that’s $0.25, so it won’t kill you to play an occasional underdog. Usually, I make the fold, but offer my hand to anyone at the table. Usually, someone wants it, because they’re getting odds for a cheap price ($0.25).

You should 3x raise any flush. It is extremely rare that any flush draw is -EV, so raise them all.

You should refer to the strategy card to know when to raise a straight draw. If all 8 straight outs are available, 3x raise the draw. Else, check the strategy card, which shows you the minimum requirements in order to raise a draw. E.g., you can raise a gutshot (4 straight outs) when you also have 8 high (“pay”) outs and 3 mid (“push”) outs.

Improved Table Rules

If you didn’t think it could get any better, Barona now lets you bet on multiple hands simultaneously. I guess this is part of their Social Wagering concept. Also, the table limits are $5-$100, with no limit on aggregate payout. So that means you can bet $100 Antes on 6 spots, with an EV of (6)($100)(1.8%) = $10.8/hand. If you get a fast table, you could play 40 hands/hr, for an average profit of $432/hr.