Face Up ™ Three Card Poker @ Casino Pauma, CA
They’ve added a new Three Card Poker table to Casino Pauma, and I got excited when they said they exposed a dealer card. However, unlike the Three Card Poker at Ocean’s 11, they don’t pay the Ante if the dealer doesn’t qualify 😦 They remove the Ante bonuses, so while you get to see a dealer card, it still ends up being worse than regular Three Card Poker. The Wizard Of Odds posts an optimal strategy that yields a 4.3% house edge, while the simple strategy below returns a slightly worse 4.6% house edge. All-in-all, I’d rather have the regular game and it’s more reasonable 3.4% house edge.
| Hand | Decision |
|---|---|
| Losing hand | Fold |
| Pair or Better | Play |
| Ten-high or less | Fold |
| Jack-high | Play if your 2nd card higher than the dealer upcard; else Fold. |
| Queen-high | Play against a lower dealer upcard, and play Q-9 against a Queen upcard; else Fold. |
| King-high | Play against a lower dealer upcard, and play K-9 against a King upcard; else Fold. |
| Ace-high | Play against a lower dealer upcard, and play A-9 against an Ace upcard; else Fold. |
I looked into the benefit of collusion on Jack-high decisions, and found only a few tenths of a percent improvement. Unlike Caribbean Stud, where collusion improves the return by 6.5%, the effect of dealer qualifying is not that dramatic in Face Up Three Card Poker. So, there’s no practical point of colluding here.
WPT3X All-In Collusion (3 Players)
I’m headed out to Vegas next week with two friends, so I re-worked a 3-player collusion strategy for WPT-3X All-In. They probably won’t want to play the game, because one friend loves fast-paced, hi-limit blackjack, and the other friend doesn’t like gambling. Well, I like working out these collusion strategies, whether I use them or not. So, the following 3-player collusion strategy reduces the basic strategy house edge from 0.74% to a mere 0.05% (effectively zero). Of course, you usually raise 3x in this game, so the variance is high relative to the Ante. But, with the casinos increasing the minimum bets, and if you play for hours on end, a zero edge game is much cheaper over the course of a weekend.
In fine-tuning the strategy, I found that the low straight cards are important for weak hands like 5-2, and 3-2. For example, if you have 3-2, and are not copied, it’s also necessary that your friends don’t hold any 4,5, or 6’s. I’ve included this requirement in the strategy table, where the asterisks indicate the maximum straight cards seen.
Below is the 3-way collusion strategy table for WPT-3X All-In poker. The first table is for offsuit cards, and the second table is for suited cards. You should use the suited table ONLY IF your friends hold at most one of your suits. Otherwise, use the offsuit table. The yellow squares indicate basic strategy folding hands. The numbers in the boxes indicate the maximum number of copies allowed in order to raise the hand. The asterisks indicate the maximum number of straight cards seen, in combination with the max copies. One asterisk allows at most 1 straight card when max copied. Two asterisks requires no straight cards seen when max copied.
3 Player Collusion Strategy for WPT-3X All-In.
Examples
You have 32o. The chart says 0**. Your two friends don’t have any deuces or treys. You should 3x raise if none of your straight cards are seen (4, 5, 6). Otherwise fold.
You have 72o. The chart says 0*. You should raise if your friends don’t copy your hand, AND there’s at most one (3, 4, 5, or 6). Otherwise fold.
You have 52s. The chart says 1**. You should raise if your friends don’t copy your hand, regardless of straight cards. However, if you’re copied once, you should raise only if your friends hold no straight cards (3, 4, 6).
You have 54s. The chart says 2**. You should raise if your friends hold 0 or 1 copies of your card. If you’re copied twice, then you should only 3x raise if your friends hold no straight cards (2, 3, 6, 7).
You have T5o. The chart says you should raise if you’re copied up to two times. Otherwise, fold if you’re copied 3 or 4 times.
You have A2o. You should raise even if you’re copied 4 times (i.e., both your friends also hold A2, or they hold 22 and AA).
Easy Poker @ Huster Casino, Los Angeles
One of the dealers at Viejas told me about a weird Hold’Em carnival game at the Hustler Casino in LA, so I decided to check it out (over the phone). As with all table games in California card rooms, you have to pay a per-hand “collection” to the house in order to pay. You play against a 3rd party bank, which is always available whenever the game is open. (The 3rd party bank is usually a separate “corporation” with an arrangement with the casino, but the house is prohibited from directly banking the game.)
Anyways, here’s how the game works. All bets receive even-money action against the dealer, including the Ante. The dealer plays two hands against the player’s one hand. There’s no qualifier to the dealer hand, and if the dealer hands don’t make a pair (including the board), the player instantly wins all wagers. Specifically, the rules are as follows:
- The player must Ante before the hand begins.
- The player receives two cards, and decides either to (A) wager an amount equal to the Ante (1x) in exchange for the right to make additional post-flop bets, or (B) to just play the hand for only the Ante bet. (There is no folding in this game.)
- On the flop, the player may either bet an amount equal to the Ante (1x), or check. (Provided he wagered the 1x preflop bet.)
- On the turn, the player may either bet an amount equal to 2x the Ante, or check. (Provided he wagered the 1x preflop bet.)
- On the river, the player may either bet an amount equal to 2x the Ante, or check. (Provided he wagered the 1x preflop bet.)
- The dealer turns up the two bank hands (two separate sets of hole cards).
- If both the dealer hands are lower than a pair, the player automatically wins even money on all wagers, including the Ante and preflop 1x bet.
- Otherwise, the player receives even money action on all his wagers (including Ante and 1x preflop bet) vs. the best dealer hand.
The game is pretty weird in that you have to play against two dealer hands. I guess this resembles more of a poker game, in that you have to beat multiple players. However, you’re not getting 2:1 odds on your money, so it’s clearly worse. The only benefit to the game is that there’s no qualifiers on the action, and you automatically win if both dealer hands are lower than a pair. Plus, your Ante never folds.
Banking The Game
As I show below, the bank has about a 6.25% edge against a near-optimal player. Needless to say, most people will probably not even come close to playing this game correctly. Even though they can find this page on the web, they won’t bother to look for it, let alone read it, or god-forbid, follow it. I can only imagine how badly people play this game. I’m guessing they under bet pre-flop, over-bet the flop, and under-bet the river. And every post-flop mistake will cost the player at least 10% of the Ante, and there are up to 3 post-flop decisions per hand. Plus the sucker bonus bet that everybody plays.
According to the house rules, you can bank twice per round. When I talked to the floor over the phone, he says that “99.9% of the time” players don’t bank the game. So you’ll share banking privileges evenly with the corporation bank (and other bankers, if present). It costs $2/hand to bank the game, so even if there are 3 players playing $5 Antes, you’ll break even if each player averages a total of 13% of EV mistakes per hand. People probably bet top pair on the flop, which is around a 20% mistake, and they probably bet 2nd pair on a paired board on the river, which is another 20% mistake.
If you live in LA, you should probably give banking a shot, especially on the weekends. It sounds like you’ll only be competing with the corporation for banking rights, and you won’t need a huge bankroll to bank $5 Antes. You might need a minimum bankroll to cover paying off a possible Royal Flush (200:1?) on the bonus bet. But the bonus bet is pretty easy money, depending on the pay table.
Basic Strategy
I worked out a relatively simple strategy that’s probably close to optimal, since there weren’t many exceptions to the following rules. The following strategy simulates at a 6.25% bank edge.
- Preflop (1x)
- See below preflop tables.
- Flop (1x)
- If trips on board, bet pocket 3’s or higher, else check.
- If the board is paired, bet trips or better, pocket 10’s or higher, or top pair if King’s or higher.
- If the board is suited, bet trips or better, or top two pair.
- If the board is not suited nor paired, bet two pair or better.
- Check everything else.
- Turn (2x)
- If quads on board, bet nut kicker, else check.
- If trips on board, bet full house except under pair, else check.
- If two pair on board, bet if you beat board by more than just kickers, else check.
- If scare flush board, bet 4th worst flush or better, else check.
- If scare straight board, bet any straight or better, else check.
- If board paired, bet trips or better, top pair or over pair if no possible flush, or top pair with 4th nut flush draw or better, else check.
- Else, bet two pairs or better, and top pair or over pair unless gutshot board or possible flush.
- Check all other hands.
- River (2x)
- If quads on board, bet 2nd nut kicker, else check.
- If trips on board, bet full house unless under pair, else check.
- If two pair on board, bet any hand that beats board by more than kickers, else check.
- If scare flush board, bet 3rd worst flush or better, else check.
- If scare straight board, bet any straight or better.
- If board paired, bet trips or better, or top or over pair (or pocket pair higher than 2nd board singleton) unless gutshot board, else check.
- If board not paired, bet two pair or better, or top pair or over pair or 2nd pair unless gutshot board, else check.
where “top pair” means you pair with the highest singleton on board, and “2nd pair” means you pair with the 2nd highest singleton on board.
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | T | J | Q | K | A | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y |
| K | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | |
| Q | N | N | Y | Y | Y | Y | Y | Y | Y | Y | Y | ||
| J | N | N | N | N | N | Y | Y | Y | Y | Y | |||
| T | N | N | N | N | N | Y | Y | Y | Y | ||||
| 9 | N | N | N | N | N | Y | Y | Y | |||||
| 8 | N | N | N | N | N | Y | Y | ||||||
| 7 | N | N | N | N | Y | Y | |||||||
| 6 | N | N | N | N | Y | ||||||||
| 5 | N | N | N | Y | |||||||||
| 4 | N | N | Y | ||||||||||
| 3 | N | Y | |||||||||||
| 2 | Y |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | T | J | Q | K | A | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y |
| K | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | |
| Q | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | ||
| J | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | |||
| T | Y | Y | Y | Y | Y | Y | Y | Y | Y | ||||
| 9 | N | N | Y | Y | Y | Y | Y | Y | |||||
| 8 | N | N | Y | Y | Y | Y | Y | ||||||
| 7 | N | N | Y | Y | Y | Y | |||||||
| 6 | N | N | Y | Y | Y | ||||||||
| 5 | N | Y | Y | Y | |||||||||
| 4 | N | Y | Y | ||||||||||
| 3 | N | Y | |||||||||||
| 2 | Y |
Collusion Analysis For Wild 52 @ Las Vegas Flamingo
I got pretty excited last week about possibly exploiting Joker information for the new Wild 52 game at the Las Vegas Flamingo. Its a 7-card poker game with a Joker, where up to 6 players hold 5 cards each, and play against a dealer hand. There are 2 community cards, an Ante, and two 2x betting rounds. I figured it was a lock that sharing Joker Busy status with confederates, combined with an optimized strategy both, would yield at least a 5% player edge. So I worked it all out, and was shocked to find only a ~1% improvement from around a 2% house edge to a 1% house edge.
Honestly, I was thinking “Vegas trip”, and betting $25 or $100 Antes with my friends, winning thousands each until they shut us down. I thought it’d end up being obvious to everyone that knowing where the Joker would yield a huge player advantage. I figured they’d set up the game with a small house edge, and they didn’t foresee players sharing Joker information. Well, whether they looked into it or not, sharing Joker info didn’t help out much to change the overall odds 😦
Here’s how the game is played:
- The game is played with a 52 card deck plus one completely wild Joker.
- Each player Antes before the hand begins.
- Each player and the dealer receives 5 cards, dealt face down.
- The player looks at his hand, and decides to either Play it by 2x raising his Ante, or folding his hand and losing his Ante.
- The dealer then turns up the first community card.
- Based on his 6-card hand, each player either checks, or makes the Option bet (2x the Ante).
- The dealer then turns up the 2nd community card.
- Action is complete, and the dealer then turns up his 5 cards.
- The dealer’s 7 card hand (5 hole + 2 community) qualifies with a pair of 5’s or better.
- If the dealer does not qualify, the 2x Play and Option bets push, and the player automatically wins the Ante bet.
- If the dealer qualifies, then the Ante, Play, and Option bet all play even-money against the dealer hand.
Here’s a simple basic strategy that yields a 2.4% house edge:
For the 2x Play bet (5 card hand):
- Play any pair or better.
- Play any flush draw or straight draw (including gutshots).
- Play A-high, if 2nd card is at least a Queen, and 4th card is at least an Eight.
- Fold all others.
For the 2x Option bet (6 card hand):
- If the community card is a Joker, only bet trip-8’s or better.
- Bet any hand with a non-community Joker.
- Bet two pairs, if the community card is below your top pair, or if your top pair are 8’s or better, or if you also have a straight or flush draw.
- Only bet a pair of Kings or better if you also have any straight or flush draw.
- Check all others.
Effect of Collusion
I looked into the advantage obtained if 6 players colluded to share “Joker busy” information. This knowledge changed the 5th and 6th street strategies, but only at the margins, which don’t happen frequently enough to significantly change the overall EV 😦
The differences on 5th street are that:
- If the Joker is busy, you can play any Ace-high, or 4 cards higher than a Six.
- Else, if the Joker is hiding, you can only play a pair or better.
The differences on 6th street are that:
- If the Joker is busy, you can bet a pair of Jacks or better (and Ten’s if the community card is below a Ten).
- Else, if the Joker is hiding, you can only bet two pairs or better (Jacks up or better, or if the community card is under your top pair).
These differences only add up to a 1.2% improvement, and the house edge is still 1.2%.
This was pretty disappointing. I called my friends back to tell them we *weren’t* headed to Vegas that weekend 😦
Joker/Ace Collusion Analysis For Pai-Gow Poker
Experienced Pai-Gow players (i.e., those who play every day) often tell each other where the Joker and Aces are. At a full table, 6 players hold 42 cards, so if no one says “joker busy”, then the dealer probably has it (63.6%). Also, if the players don’t hold many Aces, then the dealer is going to have a stronger-than-usual hand. I’ve often wondered how practical and powerful a Pai-Gow collusion strategy would be, so I worked out an analysis of the problem.
Immediately, I saw that Ace/Joker info would help mostly for deciding whether to play “pair-pair” (small pair in front, big pair in back) or “two pair behind” (kickers in front, two pair in back). The two pair hands (or other “break/keep” decisions) occur about 20% of the time, frequently enough for a collusion strategy to have some promise. For these two pair decisions, I thought it’d be important to see how the Ace/Joker count affects the dealer front pair %, and the dealer two pair or better behind %. This seemed natural, because I figured if the players held 3 Aces, then the chance of a single dealer Ace was pretty high, which he’d probably play up front (the “3 Ace Effect”).
I ran the analysis (CA rules where the Joker is completely wild), and was amazed to see the following results!
Probabilities of dealer hands as a function of known Ace/Jack locations (6 players).
Sure enough, the expected results pop right out of the graphs. On the left side are hands where the Joker is “busy”, i.e., one of the players holds it, so the dealer cannot have it. On the right the Joker is not busy, and is probably in the dealer’s hand. The top graphs represent the strength of the dealer front hand vs. the known Ace count, and the bottom graphs show the strength of the dealer back hand vs. the Ace count.
As expected, the dealer hand is strong when the Joker is not busy. Also, the dealer front hand is weakest when the players hold 3 Aces. As I pointed out earlier, the “3 Ace effect” results from the high probability that the dealer has the remaining Ace, and will play it up front. This is the “sweet spot”. So, we see the weakest dealer hand happens when the Joker is Busy and the players hold exactly 3 Aces (12.5% front pair or better) and the strongest dealer hand happens when the Joker is not busy, and the players hold no Aces (80% front pair or better). This is a huge, huge difference, and suggests a big difference in the right way to play two pairs for these two cases.
So, by sharing Ace/Joker information at a full table, you learn when the dealer has either a very weak hand (Joker Busy, 3 Aces seen; most common case, 34.3% of the time), or a very strong hand (Joker not Busy, and 2 or less Aces seen; rare 3% of the time). You should alter your 2 pair decisions to take advantage of this information, as shown below.
Examples
The following examples show cases where Joker/Ace info would save you around 20% of your bet, on average.
Strong Dealer Hand
Let’s say you have two pairs, Jacks and 5’s, and no kickers: Jd Jh 5s 5d 8s 7h 3c. Normally, you’d play this pair-pair, with a pair of 5’s up front, and a pair of Jacks behind. No one in the world would play 8-high in front, and two pairs (Jacks and 5’s behind). But, in the rare (3%) case where the Joker is hiding, and the players have 0, 1, or 2 Aces, then you’re actually better off playing two pair behind!
| Aces Seen | EV(Pair-Pair) | EV(2 Pair Behind) | Decision |
|---|---|---|---|
| 0 | -0.72 | -0.52 | play 8-high front, J’s and 5’s behind |
| 1 | -0.57 | -0.36 | play 8-high front, J’s and 5’s behind |
| 2 | -0.34 | -0.25 | play 8-high front, J’s and 5’s behind |
| 3 | -0.06 | -0.24 | play 5’s in front, J’s behind |
| 4 | -0.11 | -0.26 | play 5’s in front, J’s behind |
Weakest Dealer Hand
Now, say you had the J’s and 5’s again, but this time you have an Ace kicker. This is a decision point that people may think about. Most house-way strategies will play two pair behind. You should definitely play two pair behind when the Joker is hiding. However, when the dealer hand is extremely weak because the Joker is busy and exactly 3 Aces are seen (“3 Ace Effect”), ignore your Ace, and play pair-pair. This is normally considered aggressive, but against the weakest dealer hand (the most common case, 34.3% of the time), you should go for it. The “3 Ace Effect” creates the “sweet spot” that minimizes the expected dealer front hand strength.
| Aces Seen | EV(Pair-Pair) | EV(2 Pair Behind) | Decision |
|---|---|---|---|
| 1 | -0.12 | +0.17 | play Ace front, J’s and 5’s behind |
| 2 | +0.18 | +0.30 | play Ace front, J’s and 5’s behind |
| 3 | +0.52 | +0.32 | play 5’s in front, J’s behind |
| 4 | +0.41 | +0.55 | play Ace front, J’s and 5’s behind |
How To Exploit Ace/Joker Info
It’s kind of pointless to work out the extreme details of the optimal Pai-Gow strategy given Joker/Ace info. Most people won’t remember the details, or even the broad strokes, given the gory details. However, it’s pretty easy to boil it all down to a simple collusion strategy. The players should first find out if the Joker is “busy” or not. If players have not seen the Joker, then they should play conservatively and favor two pair behind (like house way). If the Joker is hiding, check if there are only 0 or 1 Aces out. If so, the dealer has a very strong hand, so play extremely conservatively. For example, I would play no front and Kings and 6’s behind against the very strongest dealer hand. But the strongest dealer hand is rare 0.4%), so it’s not worth checking for, unless you have a huge bet out there. The Joker is busy 80% of the time. When the Joker is busy, and you have a possible two pair decision, find out if 3 Aces are seen, and thus the dealer has the weakest possible hand (the most common case, 34.3% of the time). If so, play two pair aggressively according to the below table.
Here’s a summary of the practical 6-player collusion strategy:
- If Joker is Busy
- If exactly 3 Aces seen, the dealer has the weakest possible hand (most common), so play aggressively.
- Else play normal.
- Else, Joker is Hiding
- If 0 or 1 Aces seen (extremely rare), dealer has the strongest possible hand, play super conservatively
- Else, play conservatively
| 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | TT | JJ | KK | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AA | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p |
| KK | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | |
| p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | |||
| JJ | AK | AK | pp | AK | AK | AK | p/p | p/p | p/p | |||
| TT | AQ | AQ | AQ | AK | AK | AK | AK | AK | ||||
| 99 | AJ | AJ | AQ | AQ | AQ | AQ | AK | |||||
| 88 | AT | AT | AJ | AJ | AJ | AQ | ||||||
| 77 | A4 | A4 | A8 | AT | AJ | |||||||
| 66 | A4 | A5 | A5 | A7 | ||||||||
| 55 | A4 | A7 | A8 | |||||||||
| 44 | KJ | KQ | ||||||||||
| 33 | K9 |
where “p/p” means always play pair-pair. Note that this table more aggressively plays pair-pair, because of the stronger-than-normal minimum front hand required to play two pair behind. Most tables require only an Ace for the larger pairs, and only a Jack or Queen for the lower pairs. However, the above table requires not only an Ace, but often AK, AQ, or AJ. Even the smallest pairs require K9 to play two pair behind. This is an aggressive table to play against a weak dealer hand that likely (87.5%) will not have a front pair.
Compare the above aggressive table to the more conservative strategy below, where the dealer hand is moderately strong (Joker is Hiding, and all 4 Aces are held by the players). Notice front hand requirements are much lower than the aggressive strategy. This means you end up playing “two pair behind” much more often. This is as you would expect against a stronger dealer hand. I don’t provide two pair tables for all Joker/Ace combinations, but provide these two to show the effect of expected dealer hand strength on how you play two pairs.
| 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | TT | JJ | KK | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AA | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p |
| KK | Ax | Ax | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | p/p | |
| Kx | Kx | Ax | Ax | Ax | p/p | p/p | p/p | p/p | p/p | |||
| JJ | 2p | Qx | Qx | Kx | Kx | Ax | Ax | Ax | Ax | |||
| TT | 2p | 2p | 2p | Qx | Kx | Kx | Kx | Ax | ||||
| 99 | 2p | 2p | 2p | 2p | Jx | Qx | Kx | |||||
| 88 | 2p | 2p | 2p | 2p | Jx | Jx | ||||||
| 77 | 2p | 2p | 2p | 2p | 2p | |||||||
| 66 | 2p | 2p | 2p | 2p | ||||||||
| 55 | 2p | 2p | 2p | |||||||||
| 44 | 2p | 2p | ||||||||||
| 33 | 2p |
where “2p” means always play two pair behind.
Summary
| Description | Strength | Frequency |
|---|---|---|
| Joker Hiding, 0 Aces Seen | Strongest | 0.02% |
| Joker Hiding, 1 Aces Seen | 0.4% | |
| Joker Hiding, 2 Aces Seen | 3.0% | |
| Joker Hiding, 4 Aces Seen | 8.6% | |
| Joker Hiding, 3 Aces Seen | 8.8% | |
| Joker Busy, 0 Aces Seen | 0.1% | |
| Joker Busy, 1 Aces Seen | 2.0% | |
| Joker Busy, 2 Aces Seen | 13.2% | |
| Joker Busy, 4 Aces Seen | 29.6% | |
| Joker Busy, 3 Aces Seen | Weakest | 34.3% |
| Total | 100% | |
Simplified +EV Collusion For WPT-3x All-In (4 Players)
I cleaned up my +EV collusion strategy for the World Poker Tour 3x All-In Hold’Em casino table game, because my old strategy was basically unplayable. I’ve simplified the strategy to focus on copied cards, and to ignore the high cards that only slightly lower the probability of the dealer qualifying. I optimized the strategy for four players, since I wanted a +EV worth playing for.
I always see the game at the Bellagio, when I walk through it on my way to the Forum Shops at Caesar’s. It’s also dealt at my local Sycuan Casino. I always tell my friends we should play it, but no one has any interest in +EV play, or carnival games. I figure someone out there sees the value in sharing hole card info for this game, since it starts with a mere 0.74% house edge. The following simplified collusion strategy simulates at a player advantage of about 0.31%.
The game is really simple, and other than the bad bonus bets, is not very exciting. Each player posts an Ante to start the game. The player then receives 2 down cards, which combined with the 5 card board, makes a Hold’Em poker hand. The dealer also receives two down cards, for his Hold’Em hand. You look at your 2 down cards and decide to either 3x raise “all-in”, or fold and lose the Ante. Once the players action is complete, the dealer turns up his hole cards. The dealer hand qualifies if it’s a pair, or has a blackjack value of 11 or greater. If the dealer doesn’t qualify, the remaining players win the Ante bet, and the 3x Raise bet pushes. If the dealer qualifies, then he deals the flop, turn, and river. The dealer’s Hold’Em hand is compared to each player’s Hold’Em hand. If the player has the higher hand, he wins even money on the Ante and the 3x Raise. If the dealer has the higher hand, the player loses both bets. If the hands are equal, the bets push.
The basic strategy is very simple. You’re supposed to 3x raise any pair or suited hand. The only hands you fold are 23o thru 28o, and 34o, 36o, and 37o. (That’s deuce-trey thru deuce-eight offsuit, and trey-four, trey-six, and trey-seven offsuit.)
The collusion strategy is also very simple. You 3x raise anything, unless you’re copied. Fold a weak hand (the basic strategy folding hands) if copied. Slightly stronger hands are still played if only copied once. You always play a Jack or better.
If four players share down card info, then the players have about a 0.31% edge over the house. The players need to know if their hole cards are copied by their neighbors. Here’s the modified strategy:
| Hand | Basic Strategy | 4-Player Strategy |
|---|---|---|
| Offsuit | ||
| 23o thru 28o | Fold | 3x Raise if no copies |
| 29o, 2To | 3x Raise | 3x Raise if no copies |
| 34o, 36o, 37o | Fold | 3x Raise if no copies |
| 35o | 3x Raise | 3x Raise if no copies |
| 38o | 3x Raise | 3x Raise if no copies |
| 39o | 3x Raise | 3x Raise if ≤ 1 copies |
| 3To | 3x Raise | 3x Raise if ≤ 2 copies |
| 45o | 3x Raise | 3x Raise if ≤ 2 copies |
| Suited | ||
| 23s thru 28s | 3x Raise | 3x Raise if no copies, or 1 copy and ≤ 1 suit seen |
| 29s, 2Ts | 3x Raise | 3x Raise if ≤ 1 copies, or 2 copies and ≤ 1 suit seen |
| 34s thru 37s | 3x Raise | 3x Raise if no copies, or 1 copy and ≤ 1 suit seen |
| 38s | 3x Raise | 3x Raise if ≤ 1 copies, or 2 copies and ≤ 1 suit seen |
| 39s | 3x Raise | 3x Raise if ≤ 1 copies, or ≤ 1 suit seen |
| 3Ts | 3x Raise | 3x Raise if ≤ 2 copies, or ≤ 1 suit seen |
Additionally, you should fold triple-copied offsuit hands T2 thru T6, 92 thru 96, 82 thru 85, 72 thru 76, 62 thru 65, and 54.
Simplified Collusion for Mississippi Stud (4 Players)
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
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
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.
Ultimate Texas Hold’em Arrives @ Barona
Finally, months after they sent out the “coming soon” mailers, UTH hits the floor at Barona, and it looks pretty good. They’re dealing it in the chipless (iTable) pit, which has some plus and minuses compared to the standard felt game. The only disadvantage of the iTable is that you will never get a dealer mispay, which can be a very significant component of the game, depending on where you play. (The last few times I played at Harrah’s Rincon, I’ve received a $55 mistake in each session. Instead of killing my 4x losing hand, the dealer paid it as a winner, which is a $55 difference for a $5 Ante bet. That +1100% payout goes a long ways against a 2.3% house edge.)
On the other hand, there are a few pluses to the Barona game. First, everyone is playing their hand face up, like they allow in their Mississippi Stud game. As I’ve written about in this blog, that’s worth about a 0.5% reduction in the house edge. Better yet, the Barona Trips paytable is the 9-7-4-3 type (9 for full house, 7 for flush, 4 for straight), which has a very small house edge of 0.9%. (All the other casinos in San Diego have the 8-6-5-3 paytable, which has a 1.9% house edge.) The game also goes quite a bit faster, since the iTable reads all the hands instantly, and makes the correct payouts. Also, I believe they’re able to open up as many UTH tables as they need in the iTable pit, whereas you can easily be locked out of the only UTH table at Viejas, or the two tables at Harrah’s Rincon and Pala. And, the Barona game is only a $5 Ante, even on weekend nights. Since it’s an iTable game, you can also bet $6, $7, etc. (does not have to be multiples of $5). That’s the only amount of pressing that I’m comfortable with 🙂
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