Discount Gambling

Texas Hold’Em Plus Deluxe @ Palms, Las Vegas

Posted in hold'em by stephenhow on March 27, 2012

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.


  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.
Ante Bet Paytable
Hand Payout
Royal Flush 100:1
Straight Flush 20:1
Four-of-a-Kind 10:1
Full House 1:1
Flush 1:1
Straight 1:1
Others push


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.


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

Hand Decision
AXs, KXs, QXs, JXs, TXs Discard 7 or under.
9Xs, 8Xs Discard 6 or under.
7Xs Discard 5 or under.
6Xs, 5Xs, 4Xs, 32s Discard lowest.
AXo, KXo, QXo, JXo Discard 9 or under.
all others Discard lowest.

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).

Bonus Bet Paytable
Hand Payout
Royal Flush 250:1
Straight Flush 100:1
Four-of-a-Kind 40:1
Full House 10:1
Flush 6:1
Straight 4:1
others lose

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.

Three Card Hold’Em @ Golden Nugget, Las Vegas

Posted in three card hold'em, three card poker by stephenhow on March 25, 2012

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.


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.


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.)

Hand on Turn Turn Bet Requirements
Straight or better Always bet.
Flush If scare straight AND scare flush board, only bet 4th nut flush.
One Pair If not scare straight nor scare flush board, bet your pair of Jacks or better, else
if not scare flush, bet your pair with 2 or more GSDs, else
if not scare flush, nor scare straight, bet your pair with 4th nut flush draw or better, else
if not scare flush, bet your pair of 6’s or better, if you have any GSDs and any flush draws, else
if the board is paired, bet your nut flush draw.
No Pair If not scare straight and not scare flush, bet 4 GSDs and 9th nut flush draw or better, else
if not scare straight and not scare flush, bet 2 GSDs and two flush draws with a 7th nut flush draw or better.
Simple Strategy for Turn Bet.

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.

Hand Payout Frequency Probability Return
AKQ-suited + pair 100 276 0.000106 0.010620
AKQ-suited 40 4428 0.001704 0.068150
Straight Flush 10 49628 0.019015 0.190953
Trips 9 58848 0.022643 0.203787
Straight 1 569268 0.219037 0.219037
Others -1 1916512 0.737415 -0.737415
Total 2598960 1.000000 -0.044868
Straight-or-Up Final Hand Side Bet

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

Hand Payout Frequency Probability Return
AK-suited 30 4 0.003017 0.090498
AA 20 6 0.004525 0.090498
KK 10 6 0.045249 0.045249
Pair 4 66 0.049774 0.199095
Suited 1 303 0.232278 0.232278
other -1 936 0.705882 -0.705882
Total 1326 1.000000 -0.048265
Pair-or-Suited Hole Card Side Bet

Barred From Barona: A Win-Win Outcome

Posted in +EV, mississippi stud by stephenhow on March 14, 2012

Well, I finally got barred from table games at my local Barona Casino. Some of you may have seen this coming, and I probably should have too, especially after the multiple private warnings from their director of table games. When they first came by to talk to me, I didn’t think they’d worry about a $5 player like me. I mean I don’t even take my $5 action seriously. So when they talked to me, I thought they were just stopping by to talk shop (they work in a casino, I live in a casino). But I eventually got the vibe that they were kind of watching me. Well, they were certainly reading this blog, and the day I posted the Mississippi Stud calculator (all 6 hands seen), they came by and nicely told me I couldn’t play tables games anymore.

I figured they wouldn’t like that post. The calculator showed all the players hands face-up, like it’s played at Barona, and showed you the exact value of your hand, and the best decision (3x, 1x, or fold). I guess if the regulars saw it, and all started playing optimally, it’d be a problem. But that will never happen; I’ll bet any amount of money on it. People don’t play optimal strategy, that’s not why they’re there. People play the way they want to, and that’s the way it should be. I pretty much just wrote the calculator for myself, and one or two guys who wanted to see it.

At any rate, someone at Barona thought it best to bar me, and I can’t argue with their decision. I doubt I influenced any players about the game, but everyone got the idea that I played tight. (People also thought I played too aggressively at Ultimate Texas Hold’Em.) Worse-case, I took up a weekend seat playing tight $5 Antes, and locked out a bigger player when the game was full. Best-case, I “prop’ed” up the game on weekday nights, when an additional player helps build up critical mass in the game. (Everyone agrees it’s better to have more players and see more cards per hand.)

Like I said, being barred is a “win-win” situation. They’re happy, and don’t have to worry about me meddling with their Mississippi Stud game. I’m happy, since getting barred was the only way I’d stop playing 60 hrs/week there. So instead of coming back from the casino every night until 3am, I go downstairs and take hour-long walks through Little Italy and Balboa Park. Although it was pointless, it was easy playing a game with a 1.5% tailwind. It’s like being the house, but without all the expenses, and with comp’ed food. But it was just an attractive nuisance, something that draws you in, but ends up harming you.