Discount Gambling

House Money BJ Side Bet @ Pala Casino

Posted in blackjack sidebets by stephenhow on August 28, 2012

Hooray, another game that I did the math for hits the floor! House Money is a blackjack side bet created by Roger Snow of ShuffleMaster. It’s unique because it allows the player to cap his main blackjack bet with his side bet winnings. The side bet pays when your first two cards make a pair, straight, or straight flush. So, if you’re dealt a suited A-K, the side bet pays 9:1. You always have the option of taking the proceeds (10 units in this case), and adding it to your main blackjack bet. In this case, your BJ nets you a profit of (3:2)(10) + 9 = 24 units on the side bet. (If this reads too much like a paid advertisement, skip to the section on counting for this bet.)

For a 6-deck shoe game with good rules, and the correct capping strategy, the house edge for this side bet is only 2.6%. The basic strategy of when to cap your main bet with your side bet proceeds is presented below.

The game is currently available at my nearby Pala Casino, the Siena in Reno, and the Drift On Inn in WA.

Rules

The rules for the House Money side bet are as follows:

  • The player makes the optional side bet wager before the hand is dealt.
  • The side bet pays for the initial 2-card player hands according to the paytable below.
  • The player has the late (after dealer peeks for BJ) option of capping his main blackjack bet with an amount up to the entire side bet proceeds.
  • The player completes the main hand following normal blackjack rules.
2-Card Hand Paytable
Hand Payout
AK suited 9-to-1
Straight Flush 4-to-1
Pair 3-to-1
Straight 1-to-1
Nothing lose

Basic Strategy

The table below tells you when you should cap your main bet with the winning proceeds of your side bet. “Y” means to cap the bet with the proceeds, because the EV of the hand (after the dealer peeks for BJ) is positive. “N” means not to cap the bet, but just to collect your winnings, because the post-peek EV of the hand is negative. After the capping decision, play your hand according to blackjack basic strategy.

Capping Strategy for House Money Blackjack Sidebet
Hand Dealer Upcard
2 3 4 5 6 7 8 9 10 A
Straights and Straight Flushes
AK Y Y Y Y Y Y Y Y Y Y
KQ, QJ, JT Y Y Y Y Y Y Y Y Y Y
T9 Y Y Y Y Y Y Y Y Y Y
98, 87, 76 N N N N N N N N N N
65 Y Y Y Y Y Y Y Y Y Y
54 Y Y Y Y Y Y Y N N N
43 N N N Y Y N N N N N
32 N N N N Y N N N N N
A2 Y Y Y Y Y Y Y N N N
Pairs
A-A Y Y Y Y Y Y Y Y Y Y
10-10 Y Y Y Y Y Y Y Y Y Y
9-9 Y Y Y Y Y Y Y N N N
8-8 Y Y Y Y Y Y N N N N
7-7 N N Y Y Y N N N N N
6-6 N N Y Y Y N N N N N
5-5 Y Y Y Y Y Y Y Y Y Y
4-4 N Y Y Y Y Y N N N N
3-3 N N Y Y Y N N N N N
2-2 N N Y Y Y Y N N N N

Countability

This side bet is only slightly countable, using the counting coefficients (2 => +1, 3 => +1, 4 => +1, 5 => 0, 6 => 1, 7 => 1, 8 => 1, 9 => 1, T => -1, J => -1, Q => -1, K => -2, A => -2) and a true count threshold of 3.1. From a 6-deck shoe with 1 deck behind cut card, you’ll have +EV betting opportunities about 13.4% of the time, with an average edge of +3.4%/bet. So betting $25 when the count is good will yield a profit rate (13.4%)($25)(+3.4%) = $0.11/hand. At 100 hands per hour, this yields $11/hr, which isn’t worth anyone’s time or effort.

Lunar Poker @ Pechanga Casino

Posted in +EV, collusion, lunar poker by stephenhow on August 24, 2012

Well, someone is finally bringing the infamous Lunar Poker (aka Russian Poker) to the US, starting at my nearby Pechanga Casino. The game is a very interesting version of the old Caribbean Stud Poker, with a lot more options like drawing cards, buying an extra card, buying insurance, and forcing the dealer to draw (all for a price).

The game has been infamous, because the many player options result in an incalculable number of possible hand combinations (6.27x 10^20 according to the WoOs), and because of the absence of a published strategy. It sounds like people have played this game by the seat of their pants for years in Europe and Asia. But a lot of us won’t play a game without first knowing the basic strategy and house edge. So I grinded out the analysis, just in case you run across this game.

Rules

The rules follow the basic structure of Caribbean Stud Poker. You place an Ante before the hand starts, and the players and dealer each receive five cards. The dealer exposes one of his cards. You eventually decide to either Raise 2x, or fold your Ante. The dealer turns up his hand, and needs Ace-King or better to qualify. If the dealer doesn’t qualify, then the remaining Antes are paid even-money, and the Raise bets push. If the dealer qualifies, then the Antes push, and the Raise bets are paid according to a paytable.

So far, these rules are just like Caribbean Stud, except here, the Ante only pays when the dealer doesn’t qualify.

Now, Lunar Poker offers the following player options before the Player makes his 2x Raise decision:

  • The player may either receive an extra (6th) card, or may replace 2-5 of his cards, for the cost of 1x the Ante.
  • With three-of-a-kind or better, the player may take even-money insurance against the Dealer not qualifying (up to 1/2 the amount of the winning payout).

The players make their 2x Raise or Fold decision, then the dealer turns up his hand. If the dealer doesn’t qualify, the Antes and Insurance pay even money. If the dealer qualifies, then the player must beat the dealer to win his Raise bet and push his Ante. Else, the player loses his Ante and Raise. Insurance loses if the dealer qualifies and the player wins. If the dealer qualifies and the player loses, Insurance pushes. (Note: Pechanga lets you can take Insurance on up to the full amount your potential win.)

Finally, if the dealer doesn’t qualify, the player has an option to:

  • Pay 1x Ante to force the dealer to replace his highest card with a draw from the deck.

If the dealer qualifies after the draw, then the player’s Ante and Raise resolve as before. If the dealer doesn’t qualify, then the Ante and Raise push. Note: if you decide to Force the dealer to draw, then you forfeit the pay on the Ante you would normally receive. (It is expensive to Force the dealer; you forfeit your win on the Ante, AND you have to pay 1x!)

Paytable

For winning hands against a qualified dealer hand, the Raise bet pays according to the following paytable. More importantly, you are paid on a second hand from the paytable, when the second hand uses at least one different card from your first payout hand. (Note: “hands” do not include kickers; e.g., a three-of-a-kind hand contains only 3 cards for purposes of the paytable.) I’m not going to provide examples of the second payout, as this is described elsewhere.

Hand Payout
Royal Flush 100-to-1
Straight Flush 50-to-1
Four-of-a-Kind 20-to-1
Full House 7-to-1
Flush 5-to-1
Straight 4-to-1
Three-of-a-Kind 3-to-1
Two Pairs 2-to-1
One Pair 1-to-1
AK 1-to-1

Basic Strategy

I worked out a simple strategy for the game that simulates at a 1.43% house edge. That’s not bad as far as carnival games go, but it looks like their claim of “House Advantage Under 1%!” is false.

Draw Decision

The first decision on what to hold and draw is presented in the table below.

Draw Decision for Lunar Poker
5-Card Hand Decision
Royal Flush
Straight Flush
Flush
Straight
Always buy 6th card.
Four-of-a-Kind Stand.
Full House Buy 6th card unless dealer upcard copies you.
Three-of-a-Kind Stand if 4-of-a-kind not possible,
else hold trips and exchange 2 cards.
Two Pairs Stand.
One Pair w/ AK Discard 2’s or 3’s (hold AK and exchange 3) against higher upcard, Queen or lower,
else stand.
One Pair Buy 6th card for open-ended, flush draw, or gutshot.
Hold pair and exchange 3 if pair below upcard,
else stand.
AK Buy 6th card for open-ended, flush draw, else
Buy 6th card for perfect gutshot to 6-card straight, else
Buy 6th card for gutshot straight draw against A or K upcard, else
Hold AKs and royal cards higher than dealer upcard, else
Hold AK and exchange 3
Nothing Buy 6th card for open-ended or flush draw, else
Buy 6th card for perfect gutshot to 6-card straight, else
Hold AKs and any Royal cards, else
Hold two or more Royal cards higher than the dealer upcard, else
Hold three straight flush cards higher than the dealer upcard, else
Hold A against K upcard or lower, else
Hold K against J upcard or lower, else
Hold Q against copied J upcard or lower, else
Hold Q against 5 upcard or lower,
Else fold.

where open-ended straight draws include double-gutshot straight draws.

Insurance

It’s only correct to take insurance in a few cases. Never insure your hand against an Ace or King upcard. Otherwise, take insurance when you copy the dealer upcard 2 or more times. If you only copy the dealer upcard once, then take insurance when you also hold 2 or more Aces or Kings in your hand.

2x Raise / Fold

You should 2x Raise any pair or better. Fold any non-qualifying hand. Otherwise, play AK according to the table below.

2x Raise Decision
Hand Decision
Pair or better Raise 2x.
AK Call with any copies of the dealer upcard, Q or lower, else
Call with AKJ83 or better with any copies of the dealer upcard (including A, K), else
Fold all others.
non-qualifying Fold.

Force Dealer Bet

Your potential Raise payout and the possible dealer outs determine when you should try to force the dealer to draw. The table below tells you when to pay 1x to replace the highest dealer card with one from the deck. Remember, you’re forfeiting your instant Ante win by Forcing the dealer to draw. Plus, you’re paying 1x for the Force, so you need at least a 4:1 payout to make it profitable (i.e., don’t Force trips-only hands).

Force Draw Strategy
Potential Payout Conditions
3-to-1
or lower
Never force.
4-to-1 Don’t force dealer flush or open-ended draws that beat you unless all dealer pair outs are available, else
Don’t force if you hold 2 or more of the dealer’s pair outs,
else force.
5-to-1 Force unless you hold 4 or more of the dealer’s pair outs.
6-to-1
or higher
Always force.

Simple Two Player Collusion

If you’re friendly with your table-neighbor, you can slightly modify basic strategy to get a +EV return of +0.43% on the Ante. The drawing decision is modified accordingly:

Buy/Exchange Decision for Two Player Collusion
5-Card Hand Decision
Three-of-a-Kind Stand pat if your neighbor holds your quad out, else
hold trips and exchange 2 cards.
One Pair
w/o AK
Buy 6th card for open-ended or flush draw, else
Buy 6th card with over-pair (above dealer upcard) and gutshot if all straight outs remain, else
Buy 6th card with under-pair (below dealer upcard) and gutshot if any straight outs remain, else
Stand pat against dead upcard (3 copies) Q or lower, else
Hold under-pair (below dealer upcard) and draw 3 if all outs remain, else
Stand pat for all others.
AK Buy 6th card for open-ended or flush draw, else
Buy 6th card with 2+ outs to perfect gutshot (6-card straight), else
Buy 6th card with 3+ outs to gutshot against A/K upcard, else
Stand pat against dead upcard (3 copies), Q or lower, else
Hold two or more royal cards, exchange rest, else
Buy 6th card with at least 2 gutshot draws to AKQJT, else
Hold AK and exchange 3 cards.
Nothing Buy 6th card for open-ended or flush draw, else
Buy 6th card with 2+ outs to perfect gutshot (6-card straight), else
Stand pat against dead upcard (3 copies), Q or lower, else
Hold two or more royal cards, exchange rest, else
Hold your highest card, 9 or better, higher than the upcard and not copied by your neighbor, else
Hold 3 straight flush cards higher than the upcard, else
Fold all others.

Only take insurance when you and your neighbor hold 3 total copies of the upcard, Queen or lower. Never insure against an Ace or King upcard.

Finally, modify the 2x Raise decision:

  • Call any 2:1 pay or better, else
  • Fold pair deuces against uncopied upcard 3 thru Q, else
  • Call any other pair, else
  • Call any hand when you and your neighbor hold all 3 copies of the dealer upcard Queen or lower, else
  • Call AKJ83 or better when you and your neighbor hold any copies of the upcard, else
  • Call AK when you and your neighbor hold 2 copies of the dealer upcard Queen or lower, else
  • Fold all others.

Improved Six-Card Poker Collusion Strategy (+EV)

Posted in +EV, six card poker by stephenhow on August 11, 2012

I’ve been playing a lot of Six Card Poker at my local Viejas Casino, which gave me the chance to think about a better collusion strategy. When I first posted about this game, I was disappointed that the theoretical limit for collusion would yield only around +1.2% on the Ante bet. So I didn’t try too hard to make a good collusion strategy.

But it’s a pretty fun game, since the dealer shows half his hand, and with a full table, you’ll know 39 of the 52 cards. You can get the rules of the game from the WoOs.

After thinking it through, I boiled down the 6-way collusion strategy to the following three rules:

  • fold any hand already beat by dealer
  • fold any qualifying hand when there are 4 or more remaining single-card outs that beat you
  • fold any non-qualifying hand when a kicker out remains that beats you, or there are 3 or more remaining pair outs for the dealer

This collusion strategy simulates at +0.43%, which isn’t bad. It’s pretty easy to count remaining dealer outs among the confederates. People just have to chime-in on how many copies of the dealer cards they have. The strategy is extremely simple, and the variance is pretty low given the 1x call, and the help in folding -EV hands.

SuperPeek Texas Hold’Em @ Suncruz Casinos

Posted in hold'em by stephenhow on August 6, 2012

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.

Follow

Get every new post delivered to your Inbox.

Join 90 other followers