Discount Gambling

Thanks to reader K. for pointing out this obscure game available on the Suncruz Casino boats. It’s an interesting Hold’Em-based carnival game where you get to see the two dealer hole cards. Here are the rules:

• Player wagers Ante before game begins.
• Dealer reveals his two hole cards.
• Player must bet either 2x or 4x his Ante, based on the dealer’s two hole cards.
• Player receives his two hole cards, and decides to either 1x Call, or to surrender half of his 2x/4x bet (keeps Ante).
• Dealer reveals community flop, turn, and river.
• If final Player hand beats Dealer hand, the Ante and 2x/4x bet pay even-money. The 1x Call bet pays even-money for a flush or higher, else pushes.
• If the final Dealer hand beats the Player hand, all bets lose.
• Regardless of Dealer Hand, a 1x called Player hand qualifies for an automatic bonus (50:1 for Royal, 25:1 for Straight Flush, 10:1 for Quads, 1:1 for Full House and Flush).

The following strategy is within 0.61% of optimal. There are two decision points. The first decision is whether to wager 2x or 4x against the dealer hole cards. The second decision is whether to surrender half your 2x/4x bet, or to 1x call the hand and see the river.

After seeing the dealer’s two hole cards, you should:

• 2x against any dealer pair.
• 2x against any dealer Ace or King.
• 2x against a Queen, except 4x against Q3o or lower.
• 2x against a Jack, except 4x against J3s/J5o or lower.
• 2x against a Ten, except 4x against T5s/T6o or lower.
• 2x against a Nine, except 4x against 96s/97o or lower.
• 4x all others.

Once you see your hole cards, make the 1x call decision according to the prioritized strategy:

1. Against a dealer pair, call two over cards or an equal pair, else surrender.
2. Call any pair, except against a higher dealer pair.
3. Call any hand higher than or equal to dealer.
4. Call a 4x bet if you copy one card with the dealer, but the dealer’s kicker is 7 or lower.
5. Call a suited hand copied once with dealer, against an offsuit dealer hand with 7 or lower kicker (e.g., call 63h against dealer 73o).
6. Call two live cards when your low card beats the dealer’s low card, AND (you’ve made a 4x bet OR you’re suited OR you’re 3-gapped or less).
7. Call two live cards for a 4x bet when the dealer cards are less than 9, not suited, and 3-gapped or more.
8. Call two live suited cards when your high card beats the dealer’s low card, AND (the dealer is not suited OR you’re 3-gapped or less).
9. Call two live suited under cards for a 4x bet when you’re 4-gapped or less, AND (the dealer is not suited OR the dealer cards are of a different suit).
10. Else, surrender all others

The game is good, and you should play it if you find it.

You know there’s too many Hold’Em based carnival games out there when their names start to include words like “Plus” or “Deluxe”. Well, this game that I saw earlier this month at the Palms Casino has them both. I took a rack card home, and finally got around to analyzing the game. (Check the game publisher for current placements.)

The game is interesting, because it allows you to discard and replace one of your hole cards before deciding to see the flop. However, you have to pay to see each street (1x to see flop, 1x to see turn, 1x to see river), otherwise you fold. The Ante in the game resembles the Blind in Ultimate Texas Hold’Em, where it only pays for a player’s winning hand according to a paytable, when both hole cards play. But, there’s no qualifier on the dealer hand, so your Flop, Turn, and River bets all get even money action against the dealer hand.

I worked out a fairly simple strategy for the game, which simulates at 3.0% house edge. That’s not too bad, and is comparable with UTH and Texas Hold’Em Bonus.

Rules

1. The Player must wager an Ante before the hand begins.
2. Each Player and the Dealer receives two hole cards.
3. The Player may discard one of his hole cards, and receives a replacement card from the deck.
4. The Player either 1x bets to see the Flop, or folds.
5. The Flop is dealt to the community board.
6. The Player either 1x bets to see the Turn, or folds.
7. The Turn is dealt to the community board.
8. The Player either 1x bets to see the River, or folds.
9. The Dealer turns up his hand, and the Flop, Turn, and River bets receive even-money action against the Dealer hand.
10. If the Player beats the Dealer, the Ante pays according to the paytable if both player’s hole cards play, else the Ante pushes; if the Dealer beats the Player, the Ante loses.

Strategy

The following strategy is fairly simple, and probably doesn’t sacrifice much EV. I’ll guess that the optimal strategy (non-colluding) is better by less than 0.5%, at most.

Discard

Never break a pocket pair. Use the following table to decide whether to replace your lowest hole card:

Flop Bet

Play any pair. Play any suited hole cards, except for 72s, 62s, and 32s. Play T2o or better. Play offsuit {9,8,7,6} with a 5 or better. Fold all others.

Turn Bet

You bet almost all hands on the flop. Bet any hand that beats the board, bet any draw, bet if trips on board. If the board is paired, bet your 86 or better hole cards. If the board is suited, bet your Jack hole card or better, else bet your 96 or better hole cards.

River Bet

You bet most hands on the turn. Bet any hand that beats the board, bet any draw, bet if trips on board, bet if board is double-paired, bet if scare straight on board. Bet your 8-high hole card or better. You can still bet garbage hole cards if the board is paired, and the on-board kicker is 3rd nut or better.

Bonus Bet

The game also has a final hand bonus with the paytable below. It’s interesting that the bonus bet allows you the discard, and it still pays on “folded” hands. However, the discard strategy for the main game is not optimal for the bonus bet. The bonus bet simulates at a 9.9% house edge using the discard strategy for the main game. If you optimize the discard strategy for the bonus bet, then you’ll reduce the house edge to about 3.5% (while destroying your main game EV).

My Blind Review

I have no idea if this game is any fun. I haven’t played it. I know I don’t like the 9.9% house edge on the Bonus bet, but I don’t play most bonus bets either. Of course, you can mess around and bet $5 on the Ante and $100 on the Bonus, and discard for bonus (never break suited cards or pairs; keep 0-gap connectors except for AK, KQ, 43, 32, A2; otherwise keep the card closest to an 8 and discard the other). That’ll get the floorman’s attention.

It’s simple enough to follow the above strategy, but it’s not very poker-like. You make a lot of “crying calls” with nothing (e.g., you call to draw to a pair of 8’s on the river, even against a scare board). I guess the discard option is fun, but I can see breaking A7s, and getting a worse hand more than half the time.

If anyone out there tries it, tell us how you liked it.