Discount Gambling

Champion Poker @ Circus Circus, Las Vegas

Posted in champion poker by stephenhow on July 30, 2011

On a Vegas trip a few years ago, I saw a non-standard Hold’Em based carnival game at Circus Circus. My friend played a few hands and won, without knowing anything about the basic strategy. I called up and found it’s still there, and it’s called Champion Poker. It’s a simplified version of Texas Hold’Em Bonus, where you only make one real decision, whether to bet 1x on the flop, or check. The house edge is a little high, and it’ll cost you about 7.8% of the Ante to play (i.e., $0.39/hand for a $5 Ante bet). However, this includes a mandatory bonus bet (that pays odds), so the “element-of-risk” is arguably lower, at 7.8%/(avg 3.5 Antes bet) = 2.2%. The per hand cost is comparable to a $5 UTH game, when playing the 8-7-4-3 Trips bet (2.3% + 3.5% = 5.8%/hand).

The Rules

The game is played as follows:

  1. Before starting, the player must make an Ante bet and an equal, mandatory Bonus bet.
  2. The players and the dealer each receive 2 hole cards.
  3. The player looks at his hole cards, and decides to either 1x Play his hand, or to fold his Ante bet (the Bonus bet is never folded.)
  4. The flop (3 community cards) are dealt.
  5. The player decided to either bet his hand (1x Raise bet), or to check.
  6. The turn and river community cards are dealt.
  7. The dealer and player determine their best 5 card Hold’Em hands.
  8. The player’s 1x Ante, 1x Play, and 1x Raise bets receive even-money action against the dealer hand (no qualifiers).
  9. The player receives a Bonus for Trips or better, depending on the Bonus bet paytable.

Basic Strategy

The player always makes the 1x Play bet. He never folds his hand. Even 23o is worth -0.6 if played (vs. -1 if folded), so play anything.

The flop (1x Raise bet) is played exactly the same as for Texas Hold’Em Bonus. Read the flop strategy on the Texas Hold’Em Bonus page; it’s too long to reproduce here. The theoretical return for the even-money bets (Ante+Raise+Play) is +16.66%. My strategy yields about +16.3%, which isn’t too bad, considering the complexity of the types of possible hands.

As you’ve noticed, the even-money bets are +EV, which is why the Bonus bet is mandatory. Depending on the paytable, it’s return is about -24%. The following paytable is currently on the floor at Circus Circus, and returns -24.1%.

Champion Poker Bonus Paytable @ Circus Circus
Hand Return
Royal Flush 100-to-1
Straight Flush 25-to-1
Four-of-a-Kind 15-to-1
Full House 7-to-1
Flush 5-to-1
Straight 2-to-1
Three-of-a-Kind 3-to-1

So the net of the Bonus plus the even-money bets (Ante, Raise, Play) is -24.1% + 16.3 = 7.8% overall house edge.

The 1x Raise bet itself has a +EV of 33.3%, and any improvements due to collusion add directly to the bottom line, since there’s no qualifier on the dealer hand. I’ll look into the collusion gains in a later post.

Face Up ™ Three Card Poker @ Casino Pauma, CA

Posted in three card poker by stephenhow on July 30, 2011

Three Card Poker Logo
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.

Face Up ™ Three Card Poker Basic Strategy
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)

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.


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).