# Discount Gambling

## Simple +EV Collusion For Caribbean Stud

Posted in +EV, caribbean stud by stephenhow on November 24, 2010

This is an update to my previous collusion analysis for 6 players. I found that Caribbean Stud games actually seat 7 players, and I constructed a simple collusion strategy that yields a +1.1% player advantage.

If you enjoy playing Caribbean Stud, and have a set of friends that can fill up a table, there’s a simple way to play together to obtain a +1.1% advantage against the house. Here’s what each player (i.e., you and your 6 confederates) need to do:

• For each copy of the dealer up card a teammate holds, he places a \$5 chip (red) in a designated signaling area.
• For each remaining Ace or King a teammate holds, he places a \$1 chip (blue) in the designated signaling area.
• Each player now knows how many total copies of the dealer upcard the confederates hold, as well as additional Aces and Kings.
• Each player adjusts the basic strategy decision according to the table below (i.e., confederates know when to Raise with junk, and fold weak hands).
Caribbean Stud Collusion Strategy for 7 Players
Hand Modified Strategy
Junk Raise if see at least 3 red chips and 4 blue chips.
(3 upcard copies and 4 A/Ks.)
A K J 8 3 Fold unless 3 red chips seen.
(All upcard copies held by friends.)
One Pair 2’s thru 6’s Fold if upcard is higher than pair, unless 2 or more red chips seen.
(2 or more upcard copies.)
One Pair 7’s thru K’s Fold if upcard is higher than pair, unless 1 or more red chips seen.
(1 or more upcard copies.)

While this collusion strategy is non-verbal, and no one will really care if you do it for \$10 bets, the casino would very quickly catch on to a table full of \$100 Ante players all calling with junk at the same time. Otherwise, a table full of players would make on average (7 players)(\$100/player)(1.1%/hand)(40 hands/hr) = \$308/hr. And of course the variance would swamp the average for any reasonable time frame (i.e., shorter than months).

### Examples

Let’s say your hand is a pair of Kings. The dealer upcard is an Ace. Your confederates do not hold any Aces (i.e., they place no red chips in their signaling areas). You should fold the hand.

Say you have junk. The dealer upcard is a Trey. Your confederates indicate they have all the Treys in their hands (they place 3 red chips in the signaling areas). The confederates also place 5 blue chips, signaling they have 5 Aces/Kings between them. Everyone should call (2x) no matter what they hold.

The dealer upcard is a King. The confederates place 3 red chips, indicating they have all the King “outs”. They also place 4 blue chips, indicating they have all 4 Aces between them. Everyone should call, no matter what they have, since there are at least 3 red chips and 4 blue chips seen.

You have a pair of Treys. The dealer upcard is a Ten. The confederates place 2 red chips, indicating they have 2 Tens between them. You should call your hand. Junk hands should fold.

### 15 Responses

1. KB said, on January 5, 2011 at 1:51 pm

Nice analysis!

I don’t understand the left side of the chart above- is “junk” is defined as anything below an AKJ83 (including many AK hands), and “A K J 8 3” is defined as less than a pair, but equal or better than AKJ83?

2. stephenhow said, on January 5, 2011 at 4:32 pm

Yes, the “junk” row means anything less than AKJ83. And yes, the “A K J 8 3” row means anything less than a pair, down to and including AKJ83.

3. Gambler_guy said, on September 17, 2011 at 2:18 pm

That collusion analysis was really cool. I have a question about it:

In my city (Europe) there is an improved version of Caribbean Stud poker called Oasis Poker where the player has an additional possibility to switch one of his initial 5 cards for a cost of one ante. So, for example, if player has a four-to-a-flush, the player could pay one ante and draw a replacement card to make the flush, which then pays 5 to 1 if dealer qualifies. If player misses the draw and has only junk, he can then fold the hand as normal, having paid one extra ante for the shot.

Other rules and payouts of the game are identical to standard Caribbean Stud poker. According to WoO, this lowers the House edge to only 1.04%, if you follow optimal card switch strategy.

Now, based on on your article, significant gains could be made from this game by player collusion, as there is not anymore the 5% initial house edge to overcome but only 1%. But I doubt I could get more than 1 or 2 friends to join me to the table, so could you give me some strategy tips to follow (red chips / blue chips) for only 1 or 2 colluding confederates, and how much 1 or 2 confederates would increase the return?

Of course, the option to replace player’s card makes collusion decisions more complex (for example with a low pair and four-to-flush you should normally break the pair and draw to the flush, but you’d prefer to keep the pair if you peeked at the cards of the player next to you and saw him holding many cards of the suit you want). But I would assume that the highest differences in expected return would still come from the raise/fold decisions like you descibed in the article, and much less from optimizing card switching.

Regards,
Gambler_guy

• stephenhow said, on September 18, 2011 at 8:59 pm

Wow. I’d guess that 6 or 7 player collusion in Oasis Poker would yield a huge player edge, maybe 5% or higher. While it’s hard to get a 6 or 7 member team to play for a long period of time, it’d probably be worth it here. I’ll probably post about collusion for this game in the next post(s). Thanks!

4. Gambler_guy said, on September 19, 2011 at 6:30 am

Yep, I always knew that it was possible to get a very small player edge by imperceptibly peeking at the other player’s cards in this game, but only after I read about your “signalling with chips” -system, I realized the huge potential of this game.

I don’t know how practical it is to play with 6 colluding players because the dealers and background table monitorers would surely catch any signalling quickly? So, maybe 2-3 colluding players max. and the rest of the seats being regular players would probably give much better long-term cover.

I hope you could post about collusion strategy for 1-2-3 colluding players in this game.

Oh and I forgot one more thing. This casino has even one more favourable rule for this game. If the dealer doesn’t qualify, the player always has an option to replace dealer’s highest card for a cost of one ante. So imagine that you have a flush (dealt pat or by switching one card) and the dealer doesn’t qualify. You can then replace dealer’s highest card by paying one ante and have a shot of making dealer qualify to get a 5 to 1 payout. The bad part is that if the dealer still doesn’t qualify after replacing his highest card, you will not be paid the regular one ante payout, so replacing dealer’s card costs you 1 or 2 antes depending on whether he qualifies or not. So I calculated that this option should be only played with player’s straight or better, and even then the correct play depends how many common cards you have with the dealer (ie. how many “outs” dealer has to make a pair by card replacement).

Anyway, I roughly calculated in Excel that the additional rule of replacing dealer’s card decreases the house edge (relative to Ante) by 0.8% so this game in fact delivers around 99.80% return with no knowledge of other player’s cards. I feel like I have a gem in my hands!

• stephenhow said, on September 19, 2011 at 12:59 pm

You definitely have an incredibly beatable game in your city, but the edge with only 3 colluding players might be small. I just simulated the edge for 3 colluding players @ Caribbean Stud (i.e., without the favourable Oasis rules), and I only picked up a 1.1% improvement. With the Oasis rules, you might pick up some additional edge by limiting draws depending on known “outs”, and when the probability of dealer qualifying is high. I’ll look into it in the next few days.

Anyways, with 3 confederates, you should 2x raise junk when there are 3 upcard copies and at least 1 additional Ace or King seen, or 2 upcard copies and at least 2 additional Ace or Kings seen. Also, play AKJ84 with one or more upcard copies. Play AK-anything with 2 or more upcard copies. Fold a pair of deuces when there are no upcard copies. These strategy modifications will improve your return by 1.1%.

5. Gambler_guy said, on September 20, 2011 at 9:21 am

Hi again and thanks for your response. Only 1.1% improvement with three colluding players (me plus two others) is a bit disappointing and it doesn’t sound enough to be worth the effort. And more colluding players than this is not so practical for various reasons.

I speculate that a better approach might be that I just sit in between two regular players whose cards I am able to discreetly peek (it helps if they are drunk so they don’t hide their cards so much). This way I could see Ten extra cards and play according to the fold/raise rules you mentioned in your latest post. So, with 10 extra cards seen I’d never fold a higher pair than deuces right?

The advantage of this approach would be that I can do this solo (no friends needed) and I can also see the ranks and suits of all cards which helps me with card replacement decisions. You mentioned that you could look into this more, I really appreciate any help you can give me.

Oh, and I already developed the close-to-optimal basic strategy for this game taking into account both card switches (both for player and dealer) without any extra card info. I prefer not to post this strategy in public but I could send it to you for review, if that’s okay with you. But I didn’t find any contact info (your e-mail address) from this blog.

Regards,
Gambler_guy

6. Gambler_guy said, on October 4, 2011 at 6:28 am

Stephen, you wrote that:

“With the Oasis rules, you might pick up some additional edge by limiting draws depending on known “outs”, and when the probability of dealer qualifying is high. I’ll look into it in the next few days.”

But you never got back to me with that. So do you still think you would have time to look into this at some point? I understand if you are too busy and that’s completely fine but at least let me know, thanks!

• stephenhow said, on October 4, 2011 at 6:47 am

GG,

Sorry, I got busy on a few other things. I probably won’t follow up on the 3-player collusion optimized strategy, since I’ll be working on the baccarat dragon for a while. Thanks for understanding!

Steve

7. Gambler_guy said, on October 4, 2011 at 6:55 am

Ok, no problem stephen. You already gave me a plenty of useful advice and I believe I can work out the rest on my own from here. The Baccarat dragon is useful info for me too so keep up the good work mate!

8. Discount_Gambling_Is_Sharp said, on November 6, 2011 at 9:03 am

If the dealer was showing a King, and a player has King, how would this player convey the correct signal to his confederates? With just 1 red chip or with both a red chip and a blue chip?

• stephenhow said, on November 6, 2011 at 10:11 am

You would display a red chip (upcard copy), but you would *not* display a blue chip for this King. I worded the signaling instructions as “for each *remaining* Ace or King a teammate holds” to place a blue chip. By “remaining”, I meant that if you already signaled it as an upcard copy (red chip), don’t consider it for an A/K (blue chip). That’s a good question, thanks for providing the opportunity to clarify the situation.

9. Nick said, on September 7, 2012 at 7:25 pm

Hi Steven,

I have to say I couldn’t replicate your results. With a more accurate betting strategy that takes account of number of dealer’s card and number of A/K out, I could get -0.35 % (a disadvantage of the player) for 7 colluding players Carribean Stud. This came from the simulation of 1.000.000.000 trials.

This 1.12% edge comes from a simulation or from mathematical calculation?

10. Diego said, on April 10, 2015 at 8:29 pm

Hi. Great post and analysis. I found an exploitable game in my city(low stakes though, max about \$30) I have some questions about the legality of Caribbean stud collusion. Is it something just frowned upon by casinos (like card counting) and the worst consequence is being banned by the casinos, or are there any possible legal repercussions (like jail) if I get caught pulling this?

• Not A Lawyer But I Read A Lot said, on April 11, 2015 at 10:40 am

In defense of the author, he’s not a legal expert, he’s an expert on card statistics. You’re putting him on the spot by asking him this. If he says it’s okay, he could face legal liability.

There is no certain answer to your question. Rules could differ by region, and even then how law enforcement and casino decide to bend or enforce the rule is anyone’s guess. Even if you discover it is 100% legal, you could still find yourself in trouble. Read article in Wired Magazine about some guys that found a bug in video poker and faced massive legal trouble for simply hitting buttons on the display like any other player (and winning in the process). I believe all troubles were eventually dropped, but it wasn’t a smooth process at all.

That said, my advice, is that it’s probably not worth it for that amounts, but you PROBABLY wouldn’t get thrown in jail. Play at your own risk though. It’s sort of the murkiness of having big brother involved in gambling.