Discount Gambling

WPT3X All-In Collusion (3 Players)

Posted in collusion, wpt3x by stephenhow on July 27, 2011

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).

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.

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