# Discount Gambling

## Caribbean Stud Overlay @ Sycuan Casino, CA

Posted in sycuan by stephenhow on April 12, 2009

Update:
There’s no actual overlay for this game 😦 When I first saw the high hand bonus, I asked all the rules concerning it, and was assured twice by the floor that I didn’t need to make the \$1 progressive jackpot bet to qualify. Well, the next day as I was playing (the only person not making the progressive bet), the dealer told me I needed to bet the jackpot to qualify for the high hand bonus. They checked with the shift supervisor, who confirmed the rule. That killed the overlay, because the progressive was really low @ \$87,000. I wish they told me the right rule before I did all the work on this post 😦

Strangely enough, there’s a weekly high-hand prize in the Caribbean Stud Game at my nearby Sycuan Casino that makes the game profitable to play.  Of course, we know Caribbean Stud is a game with about a 5.25% house edge, but the overlay (additional favorable odds, e.g., through a promotion, or an exceptionally large progressive jackpot) makes the game profitable.  Here’s how it works: Sycuan offers a weekly prize of \$1500 for the highest hand made in Caribbean Stud, \$1000 for the 2nd highest, and \$500 for the 3rd highest hand. They post the three highest hands next to the game, so you can see what you’re up against. When the high hands aren’t so high, and it’s late in the week (the contest starts and stops at midnight Sundays), the added expectation value from the high-hand prizes makes it a winning game.

To calculate the overlay, you need to calculate the probability of making a high hand. We’ll assume it’s late enough in the week, so that if you make a high hand, it’ll stand up (i.e., no one will push your hand down, or off the high hand list). First, we need to know the probabilities of making the following hands:

Hand Probability
Straight Flush 1.54 x 10-6 per hand (e.g., 6-high straight flush)
Four-of-a-Kind 1.85 x 10-5 per hand (e.g., quad Tens)
Full House 9.24 x 10-6 per hand (e.g., 44433)

Then, take the current high hands in the contest, and calculate the probability and EV for beating them. Let’s take the following example, which were the high hands at the time of this post, with 24 hours left in the weekly contest:

Place Prize Hand Pr(beat) EV
1st \$1500 8-8-8-8-J 2.65 x 10-5 .00795
2nd \$1000 K-K-K-A-A 2.22 x 10-4 .04437
3rd \$500 J-J-J-T-T 2.40 x 10-4 .02402
total 4.885 x 10-4 .07634

First, we see we need to beat quad 8’s for first place. Any straight flush is good, or quads 9’s or better. The probability of making such a hand is (10)(1.54e-6) + (6)(1.85e-5) = 2.65e-05, for an overlay of (\$1500/\$5)(2.65e-5) = .00795.

For 2nd place, we calculate the probability of making a hand between the current 1st and 2nd place hands.  These are Ace’s full of anything, and quad 2’s thru 7’s.  The probability is (12)(9.24e-6) + (6)(1.85e-5) = 2.22e-4, for an overlay of (2.22e-4)(\$1000/\$5) = .04437.

Finally, we can make 3rd place with any full house between JJJTT and KKKAA.  There are 26 of them, for a probability of (26)(9.24e-6) = 2.40e-4, and an overlay of (2.40e-4)(\$500/\$5) = .02402.

Adding this all up, we see we get an total 7.634% overlay for this set of current high hands.  This more than overcomes the inherent 5.25% house edge for the game, leaving us with a net of almost 2.4%!  Of course, this is only valid until someone makes a high hand (possibly us), and changes the probabilities.  Don’t get too excited, because your chances of making the high hand board is pretty slim, at about 1-in-2000 hands.  Overall, the game is slow and pleasant.  Using the conservative strategy of playing only pairs or better, or even playing AKJ or better is a pretty slow bleed at about \$.25/hand house edge.  Its a fun, communal game at a full table.