# Discount Gambling

## Edge Sorting Groups for Mississippi Stud

Posted in +EV, edge sorting, mississippi stud by stephenhow on June 13, 2013

You probably know that I’m not much into advantage play based on edge-sorting cards. That’s the realm of Phil Ivey and Eliot Jacobson. It’s a pretty cool technique, but it’s way too involved for my attention span, regardless of the payoff. However, I did watch Warren Beatty in Kaleidescope, if that counts for anything.

Anyways, a reader who saw Eliot’s post on Edge Sorting (Jacks in) Mississippi Stud asked me if it’d be worthwhile to also sort the Queens, Kings, and Aces. That’s a pretty interesting question, since I can see how Eliot would start out with just the Jacks, as you’d know when you had a sure winner. But, maybe sorting the other “pay” cards would improve the return. You might not know exactly when you had a winner, but you’d have a good idea, and much more often.

I realised a Monte Carlo analysis would easily yield the ideal return for any selected sorting group. I modified a few lines of code, and violá, I simulated the estimated theoretical max return for the following sorted card groups in Mississippi Stud:

Max Return for Known Card Groups
Sorted Card Group Ideal Return
Jacks +39.7%
Jacks & Queens +48.9%
Jacks, Queens, Kings +59.0%
Jacks, Queens, Kings, Aces +63.4%

(I use the paytable that pays 5:1 for a straight.)

So it’s probably worthwhile to sort all the “pay” cards, unless it really complicates the practical strategy (not too likely).

While it’s easy to get the return for an ideal strategy for any sorting group, it takes time to work out a practical strategy. It’s straightforward, but tedious, so I’m not doing it. (Well, I actually did it for a reader, so it’s his now.)

## Barred From Barona: A Win-Win Outcome

Posted in +EV, mississippi stud by stephenhow on March 14, 2012

Well, I finally got barred from table games at my local Barona Casino. Some of you may have seen this coming, and I probably should have too, especially after the multiple private warnings from their director of table games. When they first came by to talk to me, I didn’t think they’d worry about a \$5 player like me. I mean I don’t even take my \$5 action seriously. So when they talked to me, I thought they were just stopping by to talk shop (they work in a casino, I live in a casino). But I eventually got the vibe that they were kind of watching me. Well, they were certainly reading this blog, and the day I posted the Mississippi Stud calculator (all 6 hands seen), they came by and nicely told me I couldn’t play tables games anymore.

I figured they wouldn’t like that post. The calculator showed all the players hands face-up, like it’s played at Barona, and showed you the exact value of your hand, and the best decision (3x, 1x, or fold). I guess if the regulars saw it, and all started playing optimally, it’d be a problem. But that will never happen; I’ll bet any amount of money on it. People don’t play optimal strategy, that’s not why they’re there. People play the way they want to, and that’s the way it should be. I pretty much just wrote the calculator for myself, and one or two guys who wanted to see it.

At any rate, someone at Barona thought it best to bar me, and I can’t argue with their decision. I doubt I influenced any players about the game, but everyone got the idea that I played tight. (People also thought I played too aggressively at Ultimate Texas Hold’Em.) Worse-case, I took up a weekend seat playing tight \$5 Antes, and locked out a bigger player when the game was full. Best-case, I “prop’ed” up the game on weekday nights, when an additional player helps build up critical mass in the game. (Everyone agrees it’s better to have more players and see more cards per hand.)

Like I said, being barred is a “win-win” situation. They’re happy, and don’t have to worry about me meddling with their Mississippi Stud game. I’m happy, since getting barred was the only way I’d stop playing 60 hrs/week there. So instead of coming back from the casino every night until 3am, I go downstairs and take hour-long walks through Little Italy and Balboa Park. Although it was pointless, it was easy playing a game with a 1.5% tailwind. It’s like being the house, but without all the expenses, and with comp’ed food. But it was just an attractive nuisance, something that draws you in, but ends up harming you.

## Grinding Outcomes for +EV Mississippi Stud

Posted in +EV, mississippi stud by stephenhow on February 16, 2012

In case you’re thinking about grinding out a profit at +EV Mississippi Stud (all 6 hands seen @ Barona), I’ve plotted an outcome distribution curve to show you what to expect. The following curve shows the cumulative outcome distribution of playing 5000 hands of Mississippi Stud at a fixed Ante, with a 1000 Ante bankroll. At a \$5 Ante, this is a bankroll of \$5000, and it would take a month of full-time play to see 5000 hands.

You can see the game is slightly in your favour, because of the asymmetrical bias towards bigger wins than losses. There’s a nice long tail of huge wins (although rare). On average, the expected win is (5000)(+1.25%) = 62.5 Antes. (This used a slightly older strategy; it could be improved.) However, there’s still a 6% chance of busting out, and you still have a 50% chance of losing after 5000 hands!

So, your +EV lies in the asymmetry of the curve, and the long tail of big wins. Not to mention that playing 5000 hands of normal (-EV) Mississippi Stud would cost you (5000)(-4.5%) = 225 Antes, and the outcome distribution curve would look much worse (I don’t have Basic Strategy coded up, but imagine the curve shifted higher and to the left.)

The best way to look at the face-up game is that it’s gambling with a tailwind. Anything can happen, but overall, you’ll feel the help of the tailwind, especially over the long run. Before I was barred, I really enjoyed playing the game hour-after-hour, week-after-week, because it all worked out in the end. It was like playing cards for free.

## Mississippi Stud Calculator (All Hands Seen)

Posted in +EV, mississippi stud by stephenhow on February 2, 2012

At my local Barona Casino, Mississippi Stud is dealt with all player hands face up. I’ve posted many times about the +EV strategy used with this information. No one at the tables plays optimally (i.e., no one listens to me), so the game still retains a huge house edge. In fact, the house edge is probably much higher at Barona, because players tend to play loose on 3rd Street (i.e., “see the first card”, or “always see the first card”) as long as they can see some outs, or some ways to make a hand. These 3rd Street mistakes range from 10% to 50% of the Ante, and are pure house edge. At casinos where players only see their own hand (not allowed to share info), they release losers more quickly, and tend to converge on correct basic strategy.

Of course, the only real advantage to seeing all the players cards is being able to fold early. The other advantage is knowing when to raise draws, but these are fairly rare (e.g., small pairs with all outs remaining on 3rd and 4th Streets, 6 high outs or 5 high suited outs on 3rd Street, certain straight draws on 5th Street). So folding early is the main use of the other player card info.

I wrote a Java calculator for Mississippi Stud when you can see all 6 player hands. It shows you the best decision at each point of the hand. (It’s a huge .jar file and may take some time to load, sorry.) Click on the screenshot below to try it:

The EV numbers tell you the expected value of the hand if you Fold, 1x, or 3x the bet for the next card. The EVs are normalized to the Ante, and a positive EV means an expected profit, and a negative EV means an expected loss. If you’re playing \$5 Antes, then multiply these numbers by \$5 for the value of the Fold, 1x, and 3x decisions.

## Free Rides @ Mississippi Stud (Barona Casino)

Posted in +EV, mississippi stud by stephenhow on September 3, 2011

The Social Wagering at Barona gets better and better. Unlike other casinos, Barona is fine with players passing chips around and betting on each other’s hands, and even promotes it. So, at the Mississippi Stud game, not only do you get to see all the player’s hands face up (player edge > +1.5%), you can take additional +EV bets when the hand owner doesn’t utilize his 3x bet. (E.g., small pairs with 2 trip outs on 3rd St., 6 high outs on 3rd St., flush draws on 5th St., etc.)

Last night I realized there’s an additional way to squeeze out some more EV from the game. Often, there’s players at the table that like to over-bet other people’s hands. They often want to piggy-back another 1x or 2x bet on your hand, when the correct decision is just to 1x bet the street. In this case, let them bet on your hand, but remove your own 1x bet on that street. This way, you see the street “for free” (well, the EV improvement is only around 15%). It also helps you preserve your capital, which is very important while you wait for a winner.

For example, say you have KJo, and someone else has a Jack. You’re offsuit, and have 5 high (winning) outs. You’re only supposed to 1x bet 3rd Street. But depending on the table, someone might want to “bet on your hand”, and piggy-back a 1x or 2x bet on your 3rd St. If they pass you the money, place their bet, and then remove your own. This way, you see 3rd St. “for free” (actually, you only save about 13% of the Ante in this case). While your hand is actually +EV (+.64), it’s not good enough to 3x bet (+.43, for higher risk). If someone else bets your 3rd St. for you, your EV goes up to +.77.

Or, say you have a small pair (e.g., 55). You see one of your trip outs, so you only 1x bet 3rd Street. But someone wants to gamble, and add 1x to your 3rd St. bet. Go ahead and place their bet, but remove your own. In this case, you’ll save about 14% of the Ante. The hand will return +.31 for a 1x bet, but increases to +.45 if someone else bets your 3rd St. for you.

In general, any time you’re only supposed to bet 1x, but someone wants to bet on your hand, book their action but don’t bet your own money. This way, you get to “check” through the street, and only bet when you should. This happens quite often when people are winning and having fun.

I haven’t started doing this, but I suspect people might slow down when they see you’re not willing to bet your own hand. For example, I always offer to give away my hand before I fold it. That means they can take over the hand, if they want it, for “free”. They used to snap up the offer, but lately, they all pass. They’ve either figured out the true EV of a hand, or simply realize that if I don’t want it, they shouldn’t either.

Any way, there’s just more and more +EV opportunities at the already +EV Mississippi Stud game @ Barona. Now if only they brought the Party Pit to pit 3 …

## Mississippi Stud @ Barona Casino (Update)

Posted in +EV, mississippi stud by stephenhow on August 9, 2011

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:

3rd Street Raising Hands
Hand 1x EV 3x EV Improvement
6 high outs (suited) +1.93 +2.16 +0.23
6 high outs (offsuit) +1.48 +1.55 +0.07
6 high outs (QJo) +1.58 +1.71 +0.13
5 high outs (possible straight flush) +1.44 +1.49 +0.05
small pair, no copies +10.7 +13.3 +2.6

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
3rd Street Hands
Outs 1x EV Notes
High Mid Low
3rd Street (Offsuit)
3 0 -0.47 Call
2 2 -0.79 Call
2 1 -1.09 Fold*
2 0 3 -1.05 Fold*
1 3 -0.99 Call*
1 2 -1.31 Fold
0 5 -0.71 Call
0 4 -1.12 Fold*
0 3 3 -0.95 Call
0 0 6 -1.43 Fold
3rd Street (Suited)
2 0 -0.87 Call
1 2 0 -0.96 Call*
0 4 -0.75 Call
0 3 3 -0.71 Call
0 3 2 -0.98 Call*
0 0 6 -1.20 Fold**

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
4th Street Raising Hands
Hand 1x EV 3x EV Improvement
low pair w/ all 5 outs +1.41 +1.67 +0.26
at least 7 or more high outs (suited) +1.06 +1.22 +0.16
at least 3 high outs and possible straight flush +3.05 +3.85 +0.80
##### 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.

5th Street Hands
Outs 1x EV Notes
High Mid Low
5 0 -2.72 Call
4 2 -2.95 Call
4 1 -3.05 Fold
3 4 -2.95 Call
3 3 -3.05 Fold
2 6 -2.95 Call
1 8 -2.95 Call

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.

## Simplified Collusion for Mississippi Stud (4 Players)

Posted in collusion, mississippi stud by stephenhow on May 22, 2011

I know it’s not always feasible to wait for 6 players in a Mississippi Stud game, nor is it easy to get 6 strangers to collude together. So while I was at it, I figured I’d work out a simple collusion strategy for 4 players, and see how well it worked. It helps a lot, improving the game from a -4.91% house edge down to about a manageable -1.4% house edge (or, an element of risk of about -0.4%). Here’s the simplified strategy for 4 colluding players:

• 3rd Street
• small pair: 3x bet if 0 copies, 1x bet if 1 copy, fold if 2 copies
• 3x bet 6 high suited outs
• if suited, 1x bet at least 3 high outs, or 2 high outs and 1 mid out, or 1 high out and 3 mid outs, or 4 mid outs
• if offsuit, 1x bet at least 3 high outs, or 2 high and 2 mid outs, or 5 mid outs
• fold all others
• 4th Street
• 3x bet 7 suited high outs
• 3x bet suited 6 high and 1 mid outs
• 3x bet 0-gap straight flush draw
• 1x bet small pair
• 1x bet suited cards
• 1x bet 3 high and 2 mid outs
• 1x bet 2 high and 4 mid outs
• 1x bet 1 high and 6 mid outs
• 1x bet 7 mid outs
• 1x bet 6 mid outs w/ 2-gap
• 1x bet 5 mid outs w/ 1-gap
• 1x bet 4 mid outs w/ 0-gap
• fold all others
• 5th Street
• 3x bet flush draw, or open-ended straight draw with all outs remaining
• 1x bet low pair, or straight draw
• 1x bet 6 high outs
• 1x bet 5 high and 1 mid outs
• 1x bet 4 high and 3 mid outs
• 1x bet 3 high and 5 mid outs
• 1x bet 2 high and 7 mid outs
• 1x bet 1 high and 9 mid outs
• fold all others

The strategy is very close to the simplified 6 player strategy, where you only play a little tighter — you only need one more mid out on the 4th and 5th Street decisions. So it’s really easy to remember both strategies. It’s also pretty easy to collude with 4 players, since 4 players sitting together can easily see each others cards, unless someone is deliberately hiding their hole cards.

## Simplified Collusion For Mississippi Stud

Posted in +EV, collusion, mississippi stud by stephenhow on May 22, 2011

When I play Mississippi Stud at the casino, I use a simplified collusion strategy that’s easier to remember than my full advanced strategy. The simple strategy only needs knowledge of your high and mid outs. It’s very easy to track them, once you know your starting outs (you have to ask around at the start of the hand). The full strategy uses low outs for the 3rd and 4th Street decisions, and uses detailed tables for 3x betting straight draws on 5th Street. The simplified strategy is very simple to remember, and still returns a positive expectation (+EV) for a full table of 6 players.

### Simplified Collusion Strategy

The following simplified collusion strategy returns about +0.5% for a full table of 6 players. That’s more than a 5% improvement over playing without info (-4.91% house edge).

• 3rd Street
• small pair: 3x bet if 0 copies, 1x bet if 1 copy, fold if 2 copies
• 3x bet 5 high suited outs, or 6 high offsuit outs
• if suited, 1x bet at least 2 high outs, or 4 mid outs
• if offsuit, 1x bet at least 3 high outs, or 2 high and 2 mid outs, or 5 mid outs
• fold all others
• 4th Street
• 1x bet small pair
• 3x bet 8 high suited outs
• 1x bet suited cards
• 1x bet 3 high and 1 mid outs
• 1x bet 2 high and 3 mid outs
• 1x bet 1 high and 5 mid outs
• 6 mid outs
• 5 mid outs, 1-gap
• 4 mid outs, 0-gap
• fold all others
• 5th Street
• 3x bet flush draw, or open-ended straight draw with all outs remaining
• 1x bet low pair, or straight draw
• 1x bet 5 high outs
• 1x bet 4 high and 2 mid outs
• 1x bet 3 high and 4 mid outs
• 1x bet 2 high and 6 mid outs
• 1x bet 1 high and 8 mid outs
• fold all others

### How To Collude

You have to communicate with your fellow players at the start of the hand to learn your initial outs. For example, if you have K5o, you need to know how many Kings are out there. I’ve suggested a few ways for players to collude, and I think the simplest is for everyone to quietly announce their hand, in order. This only takes a few seconds, and everyone figures out their outs. For example, with K5o, all you need to know is if there are any Kings out there. If someone else holds a King, you fold. Otherwise, you 1x bet your hand. Then, as the dealer turns up the community cards, you know how many outs you pick up. Say 3rd Street is a 6. If no one 3x bets this card, this means you now have 3 high and 3 mid outs, enough to 1x bet and see 4th Street. On the other hand, if three people 3x bet this card, it means you only have 3 high outs, and you should fold your hand.

Notice the pattern of the minimum calling hands in the table. You can see that 2 mid outs are equal to 1 high out. This makes it easier to remember the cutoff points.

## Easy Way To Play +EV Mississippi Stud

Posted in +EV, mississippi stud by stephenhow on May 21, 2011

A lot of people love Mississippi Stud, but at a 5% house edge, the game is fairly expensive. On the other hand, if you can count your “outs” during the hand at a full table, you have a 1.5% player advantage over the house! That’s a 6.5% EV swing, and it’s a pretty simply matter to keep track of your outs. I’ll show you how to do this, without getting the floorman or the dealers upset with you.

First, you’ll need to play at a full table of 6 players. You only need to commute with the players at the start of the hand. On 4th and 5th Street, its very simple to track your outs, just by looking at the player bets (3x means they hit the board). So the key is finding out how many outs you have at the start of the hand. There’s a few ways to do this (all verbal).

The best way to share info is for each player to quietly announce their hand, in order. Each player says just what their hand is, e.g., “King Five” or “Ace Deuce” or “Six Trey”. This is a quick process, and takes a few seconds. No one asks anything, and there’s no talking over each other. Just listen, and each player knows exactly how many “outs” he has left.

This method requires cooperation, and can probably only work with friends. If you can’t get the players to follow this scheme, you still might be able to count your outs. You quietly announce your hand, look around (make eye contact with everyone) and hopefully they raise their fingers to tell you if they have your cards.

Ok, so lets say you know how many “outs” you have at the start of the hand. As you know from my collusion analyses, you know what the starting hands are (e.g., 5 mid outs, 3 high outs, 2 high and 2 mid outs, etc.). You make your 3rd Street bet accordingly.

The dealer then turns up 3rd Street on the board. You can tell by the 3x bets, how many “outs” remain for this card. For example, say 3rd Street is a Jack, and 2 people start betting 3x on the Jack. Almost certainly, that means there’s only one Jack left, so you can only add one high “out” to your hand. Or, let’s say that 3rd Street was an Ace, and nobody bets 3x on the card (and no one is screaming “three of a kind!”) Then, you can safely assume 3 more high outs for your hand.

It’s pretty simple to know if you should 1x bet to see 4th Street. You typically need 3 high outs, or 2 high outs and 4 mid outs, or 1 high out and 6 mid outs. See my decision charts for more details (e.g., low outs), but these are basically your thresholds.

The dealer then turns up 4th Street of the community cards, and again, it’s simple to see how many “outs” you’ve picked up. On 4th Street, low outs no longer matter. You typically need 5 high outs, or 4 high and 2 mid outs, or 3 high and 4 mid outs, or 2 high and 6 mid outs, or 1 high and 8 mid outs to 1x bet and see 5th Street. Again, see my decision charts for complete info, and details for raising draws.

That’s it. When you play the game with collusion, you should only be thinking about how many outs you have. Usually, I just care about high and mid outs. I don’t count my low outs, and just assume I have none. I don’t give up much EV with this tighter strategy. If you have a poker mind, this should be an easy way to play the game. Of course, you should practice on my flash game, which includes a 6 player collusion mode with your outs counted and displayed.

## Updated Online Mississippi Stud Practice Game

Posted in mississippi stud by stephenhow on March 1, 2011

I’ve stayed out of the casinos for the last few days, and updated the Mississippi Stud practice game using my new Flash libraries. I’m quick posting the new game now, and will complete all the features soon. The new Flash games play so much better than my old basic Java games, that there’s really just no comparison. I know that most people play their own strategies, and just need a playable tool to practice with. Hope this helps.

Click on the screenshot below to play:

I’ll link the new game into the other pages, and this game will eventually replace the old Java game.