Discount Gambling

Earlier this month, I saw a new 3-Card Hold’Em poker carnival game at the Golden Nugget in Las Vegas. I wrote down the rules, and finally got around to analyzing the game today. Coincidentally, I found a reader of this blog playing the game at the Nugget. We were joking about the game, when he flops the nut straight (he has AK, and the Flop is a Q). So he bets the Turn and River blind, and the board comes runner-runner spades. I figure he’s ok, because a straight beats a flush in 3-card poker. Then the dealer turns up her hole cards, and uses both of them to make a straight flush. Unbelievable.

Rules

The game is played between the dealer and each player. Each player and the dealer receives two hole cards, and combines them with the community cards on the “board” to make their best 3-card poker hand. You do not need to use any of your hole cards to make a hand (i.e., you may “play the board”).

1. Player posts an Ante before the start of the hand.
2. The Player and the Dealer are each dealt two hole cards.
3. The dealer turns up the Flop card on the community board.
4. The Player decides whether to 1x bet the Flop, or to fold his hand and lose his Ante.
5. The dealer turns up the Turn card on the community board.
6. The player decides to either 1x bet the Turn, or check.
7. The dealer turns up the River card, then turns up his hole cards.
8. The Dealer requires a pair of 4’s or better to qualify, else the Antes push.
9. All remaining bets receive even-money action against the Dealer hand.

Strategy

I constructed a reasonably simple strategy, and was very surprised to see it simulate at only a -0.60% EV! This is pretty good for a carnival game, which usually has between a 2.5% to 3.5% house edge. My simple strategy isn’t very optimal, and I estimate the actual house edge is very close to 0. (The error EV of my simple strategy simulates around 0.5%, so an optimal strategy would yield close to 0 EV.)

On the Flop, you should always make the 1x bet (never fold your Ante).

On the Turn, use the following table to decide when to bet your hand, else check. You should only bet a pair under the stated conditions, and when your hand beats the board by more than just kickers, except when betting the nut flush draw.
(Glossary: “scare straight” means the board has connected cards; “scare flush” means the board is suited; “good straight draws” (GSDs) mean the number of River card ranks that make you a straight, excluding the “idiot end” straight draws. For example, if your hand is Kc 6h and the board is Qd 7s, then your 3 GSDs are {A,J,5}. Note that an 8 is not a GSD, but an “idiot-end” draw, because a dealer 9 would beat your 8-high straight. Basically, a GSD is an out that makes a straight which can’t be beat by a single dealer hole card.)

This simple strategy decisions are occasionally wrong by more than 10% of the Turn bet, but overall, it works out well enough. The mistakes are pretty obvious when you look at them, it’s just not worth optimizing the strategy unless you want to play it seriously. The game will probably be gone in a few weeks anyway, I just wanted to see what a reasonably strategy would yield.

Bonus Bets

The Straight-or-Up bonus bet has a 4.49% house edge, which isn’t too bad, as far as side bets go.

The Pair-or-Suited side bet on your two hole cards is a little better, costing only about a 4.8% house edge.