Discount Gambling

Simplified +EV Collusion For WPT-3x All-In (4 Players)

Posted in +EV, collusion, wpt3x by stephenhow on May 30, 2011

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)

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.

Ultimate Texas Hold’em Arrives @ Barona

Posted in ultimate texas hold'em by stephenhow on May 20, 2011

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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