Discount Gambling

Raise It Up Stud @ Pala Casino

Posted in Uncategorized by stephenhow on September 1, 2012

While visiting Pala Casino to check out House Money yesterday, I ran across the new ShuffleMaster game Raise It Up Stud. It has the familiar ShuffleMaster Ante, Blind, and 1x-3x Play bets, and there’s a 3-card community board. There’s no dealer hand; you’re just playing against a Paytable. You’re dealt 3 cards at the start of the hand, and you can bet 3x on your first 3 cards, or check. The dealer then turns up the first community board card, and you can now 2x bet your hand, or check. The dealer then turns up the 2nd community card, and you must either 1x bet to see the river, else fold. If you make a pair of Ten’s or better, you win even money on your ante, and odds on your Play bet. If you make trips or better, you win odds on your Blind bet. If you don’t make Ten’s or better, or if you fold, you lose all your bets.

I’d say the game plays like a more forgiving (easier) version of Mississippi Stud. You can raise a winning hand as soon as you make it, and you get paid odds on your raise. However, you can only make one bet per hand (in Mississippi Stud, you can bet a winner on all streets). But you can check until you make a hand, or have to call a draw. The Play and Blind paytables are listed below. Combining your three hold cards with the three community cards, you make your best 5 card hand.

This game is probably the long-awaited replacement for Let It Ride, which the dealers call “Let It Die”. They all hate the game, because they either stand dead at an empty table, or they just push back bets until someone occasionally wins on a 1x bet on the River. At Viejas, dealers keep their own tokes, so they hope the floor supervisor closes the game as early as possible, so they can go deal a game where they can make money. Hence, “Let It Die”.

Everyone was having a great time at Raise It Up last night, and the dealers were making lots of tokes. (Tokes are especially +EV on the Ante/Play bets; a nice little angle.) You make a lot more hands with 6 cards (compared to 5 in Let It Ride). Plus, you’re supposed to bet a lot more hands in this game than Let It Ride (small pairs, gut shot straight draws, 3 pay cards on 3rd St, etc.)

Raise It Up Stud Play Paytable
Hand Payout
Royal Flush 100:1
Straight Flush 20:1
Four-of-a-Kind 10:1
Full House 6:1
Flush 5:1
Straight 4:1
Three-of-a-Kind 3:1
Two Pairs 3:2
10′s or Better 1:1
Others lose
Raise It Up Stud Blind Bonus
Hand Payout
Royal Flush 1000:1
Straight Flush 200:1
Four-of-a-Kind 30:1
Full House 4:1
Flush 3:1
Straight 2:1
Three-of-a-Kind 1:1
Others push

Basic Strategy

The theoretical house edge for this game is 3.5022%. Below is a simple, intuitive strategy that simulates at -3.70%. The decisions on 4th and 5th Streets are fairly obvious, and you can easily learn the 3rd Street strategy.

Raise It Up Stud Basic Strategy
Street Play Bet Betting Hands
3rd Street 3x Any pair,
3 pay cards,
2 pay cards 1-gapped or less,
suited cards 2-gapped or less,
suited cards with 2 pays
4th Street 2x Any pair,
any straight or flush draw,
3 pay cards with 3 suited
5th Street 1x Any pair,
any flush draw,
open-ended draw,
gutshot draw with pay card

where “gap” is the sum of the distance between all cards (e.g., 456 is 0-gapped, 457 is 1-gapped, JT87 is 1-gapped, JT76 is 2-gapped, etc.).

Advantage Play

Even with ideal (computer) 6-way collusion, you can’t get the house edge below 0.93%.

Eliot Jacobson has published a simple hole-carding strategy that yields from +7.6% to +62.7% depending on which board card you see. Pala procedure places the bottom board card on 4th St, so I guess it’s only worth +7.6% when you see it.

Under-The-Gun 31

Posted in Uncategorized by stephenhow on March 28, 2011

Under-The-Gun 31 is a game developed and marketed by a pair of brothers who work at my local San Diego casinos. The game was on the floor at Viejas for a year, and it had a test placement at Pala too. The game is something of a cross between Blackjack and Three Card Poker. They designed the Ante bet with a small house advantage, while they pay good odds for the optional Bonus bet. The idea of the game is to make a hand total as high as possible, where only suited cards add together. Aces are always 11, and face cards have a 10 value. Since you can only add cards of the same suit, the maximum hand value is 31. The A-K-Q suited hand is a mini-Royal. The Ante pays a built-in bonus for a straight flush, a 31, or a mini-Royal.

To begin, the player makes an Ante bet. The Bonus bet is optional. The player and dealer both receive 3 cards. The looks at his hand, and decides to either fold, or to play the hand by betting an additional amount equal to the Ante. If the player stays, he also has the option to discard and draw one card. Once the action is complete, the dealer turns up his 3 cards. The dealer automatically takes a hit, and makes a hand from his 3 best cards. The player’s 31 Bonus and Stay-n-Play Bonus pay regardless of the dealer hand. The player’s Ante and Stay-n-Play bet pay even money against the dealer’s hand.

I know the game inventors, and wrote a playable Flash demo for them. They’d love to hear your feedback. Please try it out, and leave a comment about its playabilty, appeal, etc.. They’re working hard to get it out on the floor again. Click on the screenshot below to play:

Under-The-Gun 31 Game

Double Baccarat @ Sycuan Casino

Posted in Uncategorized by stephenhow on November 4, 2010

My local Sycuan Casino offers a unique game that’s a simplification of Pai-Gow tiles. Like the tile game, the players and the bank are dealt 4 cards each. Each hand is set into a front hand of 2 cards, and a back hand of two cards. The back hand must be greater than the front hand. Hand values are ranked by poker pairs, followed by Baccarat totals (0 thru 9). After the player hands are set, the bank turns over its hand and sets it according to “House Way”.

House Way
Hand Rule
Two Pairs Set large pair behind, small pair in front.
(Pair-Pair; never break pair).
Pair Aces Pair Aces behind (never split Aces.)
One Pair Pair behind if 5 or higher front, else
Split pair if can form (8,8), (7,9), (8,9) or (9,9), else
Pair behind.
No Pair Set (5,9) if possible, else
Set hand with highest front + back total, with minimum back – front gap.

Once all hands are set, the player or banker wins the wager if hands win/win, tie/win, or win/tie. In the case of tie/tie, the bank wins the wager. All other hands push the wager.

The player posts a minimum 1% collection before each hand. If all players push their bets, all collections are returned (“free collection”). This means in a heads-up game against the house, the player only pays the collection for a win or a loss, and gets free collection on a push.

I worked at optimizing a heads-up player strategy against the a house way bank, out of curiosity at what the house edge was. Of course, its an uphill battle against the collection (even when free for pushes), and worst, losing tie/tie. Using exhaustive combinatorics, I came up with the following near-optimal strategy (I only looked at the no-pair cases):

Heads-Up Player Strategy
Hand Rule
Two Pairs Set large pair behind, small pair in front.
(Pair-Pair; never break pair).
Pair Aces Pair Aces behind (never split Aces.)
One Pair Pair behind if 5 or higher front, else
Split pair if can form (8,8), (7,9), (8,9) or (9,9), else
Pair behind.
(6,9), (7,9), (8,9), (9,9)
front + back = 14 (7,7), (6,8)
front + back = 10 (5,5)
(4,6), (3,7), (2,8)
front + back = 9 (0,9)
(4,5), (2,7)
front + back = 8 (0,8)
(3,5), (2,6)
front + back = 7 (3,4)
(2,5), (1,6)
front + back = 6 (2,4)
Set hand with highest front + back total, with minimum back – front gap.

This strategy simulates at -1.46% heads up against house way, when minimizing collection to 1% of the bet amount. The frequency of ties simulates at 1.12%. So even if they eliminated the bank wins tie/tie rule, you’d still lose because of collection. As an additional note, if a heads-up player also plays the same House Way as the bank, the house edge increases to 2.0%.

Overall, the head’s-up game is about as good as a free-collection Pai-Gow game. (There are a few free-collection games at the card rooms town.) However, since the casinos don’t offer free-collection Pai-Gow, the head’s-up Double Baccarat game has better odds than the Pai-Gow game, for what it’s worth.

ShuffleMaster Ultimate Draw Poker Machine @ Viejas

Posted in Uncategorized by stephenhow on November 13, 2009

Table-Master_cutout_3There’s a new multi-player video “table” game at Viejas from ShuffleMaster, called Ultimate Draw Poker. (This game is different from the cards and table version of the game, which uses community draw cards.) The new Ultimate Draw machine seats up to five players, who play against a dealer hand. The game is “virtual single deck”, meaning that as far as any one player is concerned, you’re playing heads up against the dealer using a single deck. I’ll explain how they do this below.

The minimum bet (Ante) for this game is $3, and the maximum is $100. The video table is very nice, a single horizontal display for all player and the dealer hands, with nice visual effects (card animations, etc.). A vertical display is used to show a life-size dealer from the waist up, which is close enough to soft-core pornography to make you feel slightly uncomfortable. The dealer is dealt five cards face down, and also 5 replacement cards (not shown) from which she may draw. The remaining 42-card deck is then cloned for each seated player. Each player is dealt a five card hand of out a shuffled, 42-card cloned deck. The player decides what to discard, then draws from his cloned deck.

Once all players have discarded and drawn to their final hand, the dealer turns up her hand. The dealer applies a simple house-way discard policy:

  1. hold a pair or better, ELSE
  2. hold a four-card flush draw, ELSE
  3. hold an open-ended straight draw, ELSE
  4. hold all high cards (>= Jack), ELSE
  5. discard everything.

The dealer needs to make a pair or better to qualify. If she doesn’t qualify, you win 70% of your Ante bet. If she qualifies, then your Ante bet plays for even money against her hand.

Fortunately, “house-way” is a little weak, and a better player strategy exists (0.32% better than “house-way” vs. “house-way”):

  1. hold a pair of 3′s or better, ELSE
  2. hold a pair of 2′s unless flush draw w/ Jack or better, or unless kicker is King or better, ELSE
  3. hold a four-card flush draw (unless offsuit kicker better*), ELSE
  4. hold an open-ended straight (unless kicker better**), ELSE
  5. hold two highest cards >= Jack, ELSE
  6. hold JTs, ELSE
  7. hold highest card >= Ten, ELSE
  8. discard everything.

*Ace is better than four-card flush draw, unless draw contains Queen or bettter
*King is better than four-card flush draw, unless draw contains Jack or better
**the following table shows kickers better than open-ended straight draws

draw min kicker to hold
2345 Ten
3456 Ten
4567 Jack
5678 Queen
6789 King
789T Ace
89TJ Ace

The house edge is very small for this game, only 0.61% for the above player strategy. However, the bonus bet is really bad, since it pays something like a Jacks-or-better video poker game, but you’re playing a strategy to beat the dealer hand, not to win a bonus. For the following table, and above player strategy, the bonus bet has about a 14% house edge. If you want to play the bonus bet, go find a video poker machine, it’s faster and pays more.

Hand Win
Royal Flush 1000
Straight Flush 150
Four Of A Kind 25
Full House 8
Flush 7
Straight 5
Three of A Kind 3
Two Pairs 1
all others -1

There’s a small “collusion” opportunity in this game. Because the game is played with cloned decks, and each player acts in turn, a player acting last gets to see a lot of the 42-card cloned deck. For example, if you look at all the dealt player hands, you can see what’s available in the cloned deck (any card you see is in the cloned deck). And, when you see what’s drawn, you get more info of what’s available. There’s a few cases where this info would help you make a borderline discard decision. There’s probably aren’t enough situations like this to make it worthwhile, but I could be wrong.

Welcome Wizard of Odds Readers!

Posted in Uncategorized by stephenhow on November 2, 2009

I got a mention on the universally-known “last word on gambling” Wizard of Odds site. Needless to say, its nice to suddenly get much more page hits in a day then I used to get in a month. So welcome, especially if you’re here for the +EV angles I’m working to find. Well, if you’re in San Diego, there are two +EV games right now, Mississippi Stud @ Barona, and CSM (card) craps at Viejas. These games have been spread for a while, and the casino isn’t afraid of any advantage players. They’re making plenty of money with these games. No one is going to get rich from these small edges. Its a lot like card-counting in blackjack, but without all the hard work. I just re-wrote the page on the Viejas craps game, to make it easier to see the edge, and how to play it. Hopefully someone will actually try it. Welcome!

PlayCraps Example Session with Counting

Posted in Uncategorized by stephenhow on August 27, 2009

I thought I’d post a thorough description of how to play the PlayCraps game at Viejas, including how to account for the shuffle, using a fair-weighted counts for all the points.

First, here’s the value of each roll, and how it contributes to the counts for each point.

Point ΔCount
4 +4 if both cards ≤ 3, -4 if both cards ≥ 4, else 0
5 +2 if no Fives or Sixes, -1 if one Five or Six, -4 if two Fives/Sixes
6 +1 if no Sixes, -2 if one Six, -4 if boxcars
8 +1 if no Aces, -2 if one Ace, -4 if snake-eyes
9 +2 if no Ace or Deuce, -1 if one Ace or Deuce, -4 if two Aces/Deuces
10 +4 if both cards ≥ 4, -4 if both cards ≤ 3, else 0

Ideally, you’ll keep a count for each point. Of course, this is hard to do. I just wait for the point to come out, then I try to guess if I saw any key cards lately, and make up an initial count for the point. Then I adjust the count for each roll as in the above table. It’s very easy while the muck accumulates. Then, when the dealer shuffles the muck into the CSM, I keep counting as normal, for about 5 rolls (approx. buffer depth). After these five rolls, I start the count again, based on a guess of what’s in the muck.

simulated session with annotations after the jump! (more…)

Triple-Down BJ @ Texas Station, Las Vegas

Posted in Uncategorized by stephenhow on August 8, 2009

I’m finally getting to a reader’s request about a triple-down blackjack game at the Texas Station casino in North Las Vegas. Here are the relevant rules:

  • triple-down on first two cards totals of 9, 10, 11 (including soft totals)
  • blackjack pays even money (1:1)
  • blackjack is an automatic winner, if you stay
  • normal double-down rules
  • no triple after split
  • double-deck

The overall house edge for this game is 0.83%. The triple-down rule gives the player a +1.62% boost, but it’s not enough to overcome the even money blackjacks. The basic strategy is the same as double-deck, except that doubles on hard 9, 10, 11 are replaced by triples. Also, 9 vs a 7 upcard, and A-9 vs 4/5/6 are triples.

Interestingly, tripling a blackjack against a dealer 6 upcard isn’t too bad of an option. The EV is .998, instead of the 1.0 automatic winner for staying. It’s worth a gamble, if you feel like it. Tripling a blackjack against a dealer 5 upcard isn’t as good, as the EV here is only .946. That’s giving up 5.4% of your original bet, on average.

Someone should petition Texas Station to allow triple-down on any two cards. This still leaves the house edge at 0.59%, which is about equal to a liberal shoe game.

Easy Way To Beat PlayCraps™ @ Viejas Casino

Posted in Uncategorized by stephenhow on August 1, 2009

Ok, I just got straightened out on what the actual lay 4/10 vig is. You put up $41 to win $20, so this is better than I previously thought. So I fixed the OpenOffice spreadsheet, and my simulations:

Macintosh:Debug show$ ./laycraps -n 100000000000 -r -t 2 -m 15
max muck depth: 15, CSM buffer depth: 10, threshold: 2, seed: 1249092576
...  ...
roll: 61970000, net: 40131.900, return: +0.15%
roll: 61980000, net: 40184.350, return: +0.15%
roll: 61990000, net: 40218.950, return: +0.15%
roll: 62000000, net: 40254.550, return: +0.15%
roll: 62010000, net: 40231.850, return: +0.15%
roll: 62020000, net: 40243.700, return: +0.15%

Where the 0.15% edge is on the total action, which includes $41 for each roll the lay is ON. This is a pretty conservative way to state the return.

Another way to look at it is the edge for any given roll:

Running Count Lay 10 Player Edge
0 -0.29%
1 -0.04%
2 +0.23%
3 +0.48%
4 +0.76%
5 +1.01%

So, the easy way to play this is to lay the 4 and 10 when the count is good (at Viejas, you pay the vig up front). Then, while the count is good (i.e., RC >= 2 for the lay 10, and RC <= -2 for the lay 4), you leave the lay bet ON. When the count isn't good, you turn the appropriate lay bet OFF. Usually, this means both the lay bets are OFF, then when one of the counts gets good, that bet goes ON. When the count goes bad, both bet OFF. When the count is neutral (0), the distribution shows the odds are greater then 2:1 to hit the 4/10. However, the odds aren't good enough to overcome the vig. But, you can gamble, and turn both bets ON, and if 7 comes up, you win both bets.

It’s a little strange to have both lay bets up there, and turning them ON/OFF with every roll. The dealers might get a little irritated, and you’re only picking up a small edge. (While a lay bet is ON, you’re picking up from approx. 0.25 – 1.0% edge.) Too bad it’s not an electronic game :(

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PlayCraps™ @ Viejas Casino, CA

Posted in Uncategorized by stephenhow on July 31, 2009

There’s a new craps game at Viejas Casino, that I’ve been playing lately. It’s definitely my new favorite game, since it’s dealt to players seated at a table, and it provides the best odds in the casino. In fact, it’s a winning game for a player using basic strategy (yes, I know, sounds impossible, but read my full analysis). Although the game is beatable, you can only make a killing the normal way, by gambling and getting lucky. However, it’s always good to know the odds are in your favor.



If you haven’t read my full analysis yet, you’ll first need to know the player edge is on the don’t pass / don’t come side, and the house’s edge on the pass odds are higher than usual. So don’t rush out here and start betting the pass line and taking odds like you normally do. Switch over to the Dark Side first, if you’re not already over there.

If you like taking a shot a craps, come on out to Viejas, and have some fun. The layout of the game is really enjoyable, because it promotes fast action, and you get to sit while you play. It’s very relaxing, and there’s no stress of rolling the dice in front of a bunch of angry players. It’s just you watching the cards that come out, and deciding to increase/decrease your don’t pass or don’t come odds. Even for the best counts, you’re not really justified in buying any No-4′s or No-10′s, but at times, the odds overcome the vig.

If you like advantage play, and can enjoy playing the Don’ts, read up on this game, and come on out. It’s not every day that a game is beatable by basic strategy.

No-Bust Blackjack @ Ocean’s 11, CA

Posted in Uncategorized by stephenhow on March 3, 2009

By chance, I learned that the Ocean’s 11 cardroom offers a no-bust version of 21. As usual, I got myself worked up on the slim possibility that the game was better than intended, and set off to crack it. You can probably guess how the story ended. On the positive side, I improved my C++ programs to include a general BlackjackAnalyzer class, where you just subclass the Hand and DealerHand classes for any blackjack variation (just a few lines per rule). I also cleaned up some small bugs, and improved performance tremendously by making some small approximations. The analyzer returns the EV for the game in seconds, without simulation. Yay!

The bottom line is the No-Bust Blackjack yields a -0.18% edge for the bank, that is, before 1% house collection. So including collection, it has about twice the house edge as a typical 6-deck shoe game. See my O11 No-Bust BJ page for details and a basic strategy table. The game is characterized by a few different rules:

Rule ΔEV
Blackjack pays 6:5 -1.39%
3-card lower bust pushes +1.22%
surrender at any time +0.29%
double on any number of cards +0.24%

I spent a few days on the programs, but it was worth it. I’ll post them one day, to save others the effort of re-coding this common tool.

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