Discount Gambling

It was bound to happen sooner or later that someone would invent a 3-Card Hold’Em carnival game. I first heard about this game from the Wizard Of Odds last week. Since they actually have this game at my nearby Santa Ysabel Casino (min $2 Ante, $1 Bonus), I thought I’d figure out a strategy, and give it a try.

The game is pretty simple, and the Wizard lists the full rules. Like Hold’Em, each player has two hole cards, and combines them with a community board to make his best 3-Card Poker hand. The board consists of the Flop (2 cards), and the River (1 card). To form a hand, the player must use at least one of his hole cards (i.e., he cannot play the board).

Rules

1. The player bets an Ante to start the hand.
2. Each player and the dealer receive two face-down hole cards.
3. The player decides to either wager the 1x Flop bet, or fold his hand and Ante.
4. Two community cards are dealt to the board (the “Flop”).
5. The player decides to either wager the 1x River bet, or fold his hand and all his bets.
6. One last community card is dealt to the board (the “River”).
7. The player decides to either wager the 2x Play bet, or fold his hand and all his bets.
8. At showdown, the dealer must have a pair to qualify, else the Ante, Flop, and River bets automatically win, and the Play bet pushes.
9. If the dealer does qualify, then all bets receive even-money action against the dealer hand.

Simple Strategy

The theoretical house edge for this game is 3.22%. The simple strategy described here returns 4.0%, which isn’t bad, considering the complexity of draws, and possible dealer hands against various boards. The simple strategy is extremely easy to remember. The game is fun and easy to play, because you only fold really bad hands (they’re rare).

Flop Bet

According to the Wizard of Odds, the player should play everything except 22 and 25o. Using my simplified strategy, you should also fold 26o.

River Bet

To see the river, you should 1x bet any of the following hands (fold everything else):

• Any pair (that beats the board), or better.
• Bet two or more draws (e.g., two flush draws, or two straight draws, or a straight draw and a flush draw).
• Against a paired flop, bet any straight draw, any flush draw, or 3rd nut kicker.
• Bet a lone gutshot against an offsuit, gapped flop.
• Bet a single flush draw against a gapped flop.

* “gapped flop” means the flop isn’t a pair, or connected (e.g., 6-7 is connected, while 6-8, 7-2, A-6 are gapped)

Play Bet

To go to showdown, you should Play (2x) any of the following hands (fold everything else):

• Mid pair or better.
• If board is not paired and all different suits, play anything (i.e., bet that dealer doesn’t qualify).
• If the board shows a flush (3 of same suit), and there are no one-card straights, play anything.
• If board is paired, bet your kicker if there are less than 21 cards that beat you (the lowest possible kicker is a 9 or T; it increases by about one level for each one-card straight).
• Bet bottom pair unless both a one-card dealer flush and a one-card dealer straight are possible.

Examples

You have 2s3c and the flop is 5dKh. You have a lone gutshot draw (you need a 4 on the river). You bet the gutshot draw, because the board isn’t suited nor connected.

You have 8d5h and the flop is Kh2c. You only have a flush draw. You bet the flush draw, because the board is gapped.

You have garbage. The board is 5d6h7c. You bet 2x hoping the dealer doesn’t qualify, because the board is rainbow and not paired. (There are 5 possible one-card straights, but that’s ok.)

You have 9h2c. The board is 6s6dAh. You can bet 2x your 9, since the board is rainbow, and there are no one-card possible straights.

You have Kh2c. The board is 6s6dAd. You can bet 2x with the K, since there are only 19 cards that beat you.

You have Qh2c. The board is 6s6d5c. You can bet 2x with the Q, since there are 21 cards that beat you.

Collusion

I can’t believe this game doesn’t lend itself to collusion between players sharing hole card info. I thought there’d be a lot of opportunities for collusion, like the Flop bet decision, if confederates hold your adjacent cards (very important for straights). Or, at showdown, when you call with nothing against an unpaired, rainbow board. But my analysis shows confederate hole card info doesn’t help much at all 😦 I really thought that card info would be important, because in 3-card poker, one card often makes a hand.

I Played It!

I went out to Santa Ysabel Casino, and played the game for a few hours. It was really fun! The minimum Ante bet is only $2! So, the most you could lose in a hand is $10, and the house edge is only about $0.08/hand. The strategy is really easy to implement. You only fold if you have absolutely nothing, so it’s pretty easy to play (sometimes you even 2x Play bet nothing!). I usually only looked at one card to make my Flop and River bet decisions. Sometimes, I didn’t even need to see both cards to make a 2x Play bet decision. It was a lot of fun. The only time I ever needed to think was on the Play bet decision with kickers against a paired board (subtracting from 6th nut kicker for one-card flushes and straights).

While it’s easy to play the strategy, most of the other players probably have difficulty figuring out the right move on the fly. So, you’ll enjoy being the expert at the table.

I recommend the game, because it’s fun, and you’re usually betting 5 units to either win even money, or 3-to-5 if the dealer doesn’t qualify. That makes the house advantage per average bet fairly low (4.0%/4.6 units) < 1%.