While visiting the TCSJohnHuxley booth at G2E last week, I played at the Lucky Draw Baccarat demo table. It’s a fun game that plays like midi-baccarat, where you can squeeze your draw card. Each player wagers an initial bet, and receives their own 2-card starting hand. Everyone plays against the bank hand, whose first card is exposed. Each player may wager an optional 1x Draw bet to receive a 3rd card, or otherwise stand pat. After the action is complete, the banker reveals his hole card. The bank draws a 3rd card when his two-card total is less than five points. Otherwise the bank stands with 5 points or more.
The game is fun, because winning hands pay odds for drawn 7, 8, and 9 totals. The player makes a decision based on his 2-card total, and the exposed bank upcard. Winning hands pay even-money on the initial wager, and odds on the 1x Draw bet according to the paytable:
|Outcome||Paytable 1||Paytable 2|
|Lucky 9 (3-card 9)||3-to-1||3-to-1|
|Lucky 8 (3-card 8)||2-to-1||2-to-1|
|Lucky 7 (3-card 7)||2-to-1||3-to-2|
|6 or less||1-to-1||1-to-1|
I analyzed the game to check the house edge, and to run EORs. The outcomes for an 8-deck shoe and optimal player decisions are listed below.
|Win w/ Lucky 9||134,129,168,192,512||0.053669||4||+0.214675|
|Win w/ Lucky 8||98,365,258,946,560||0.039359||3||+0.118076|
|Win w/ Lucky 7||93,724,551,243,776||0.037502||3||+0.112506|
|Win on draw||260,100,744,978,432||0.104074||2||+0.208147|
|Lose on draw||976,828,113,772,544||0.390856||-2||-0.781713|
|Tie on draw||165,885,343,716,480||0.066375||0||+0.000000|
|Win on stand||471,832,788,590,592||0.188794||1||+0.188794|
|Lose on stand||195,977,691,906,048||0.078416||-1||-0.078416|
|Tie on stand||102,355,476,404,736||0.040955||0||+0.000000|
The house edge for Paytable 1 is 1.79%, and 3.34% for Paytable 2.
The basic strategy for the Paytable 1 game is shown in the table below.
The computed single-card EORs for an 8-deck game with Paytable 1 are fairly low. Still, I checked the countability of an 8-deck shoe, assuming only 15 cards cut off the end. For the simple count below, the game gets advantageous only 3.2% of the time (count is +40 or better), and for an average of only +0.23%/bet. That’s essentially worthless. You might pick up some additional edge with indexed plays, or better yet, using a computer and full knowledge of shoe composition. But overall, this game is surprisingly uncountable, given the options and the odds on the Draw bet.
If I haven’t been posting a lot lately, it’s either because I’m gambling too much, or the edges are too good to post publicly. While both these reasons would normally apply to Galaxy Gaming‘s new Lucky Win Baccarat Side bet, Eliot Jacobson just found out about it, so it’s a free-for-all while it lasts. Hopefully, you can still find a placement in the UK.
I picked up the literature for the game at Galaxy’s booth @ G2E last week. Lucky Win is a baccarat side bet that pays out for wins on low totals. When you bet on Lucky Player, you’re paid when the player wins with 5 points or less. If you bet on Lucky Banker, you’re paid for a banker win with 4 points or less. The top end of the paytable is very nice.
|With With||Lucky Banker
|1 in Spades||500||500|
The basic house edge is computed in the following tables (8 deck shoe). The Lucky Player has a nominal 12.04% house edge, and the Lucky Banker has a nominal 10.46% house edge.
|Banker win w/ 1 in Spades||373,248,411,648||0.000075||500||+0.037337|
|Banker win w/ 1 Suited||1,119,745,234,944||0.000224||200||+0.044804|
|Banker win w/ 1 Offsuit||22,798,126,252,032||0.004561||30||+0.136833|
|Banker win w/ 2||44,681,581,871,104||0.008939||20||+0.178784|
|Banker win w/ 3||72,927,778,568,192||0.014590||12||+0.175083|
|Banker win w/ 4||163,359,790,133,248||0.032682||8||+0.261459|
|Player win w/ 1 in Spades||378,622,455,808||0.000076||500||+0.037874|
|Player win w/ 1 Suited||1,135,867,367,424||0.000227||200||+0.045449|
|Player win w/ 1 Offsuit||23,124,703,715,328||0.004626||30||+0.138793|
|Player win w/ 2||44,328,525,111,296||0.008869||20||+0.177371|
|Player win w/ 3||62,946,423,310,336||0.012593||12||+0.151120|
|Player win w/ 4||86,165,771,096,064||0.017239||8||+0.137909|
|Player win w/ 5||122,838,277,197,824||0.024576||5||+0.122878|
The calculated EORs are pretty high, and lend to a very simple unbalanced count. One count nicely fits both the Lucky Player and Lucky Banker bets, for spade and non-spade cards.
Using the simple unbalanced count above (Four thru Nine => +1, Ten thru Ace => -1), and starting at 0 for a new shoe (don’t forget to count the burn card!), you should bet both the Lucky Player and Lucky Banker side bets when the count is +34 or better. For an 8-deck shoe with 15 cards behind the cut card, you’ll be able to bet 6.0% of the hands. The Lucky Player bet has an average edge of +14.0%, and the Lucky Banker bet has an average edge of +10.5%. That’s a whopping combined +1.47% edge per dealt hand. That’s insane. You can see how good the bet gets in the graph below.
Normally, I would never post about something this good. But Eliot is posting today, so the cat’s out of the bag. My apologies to any APs already hitting this game
For now, Viejas is offering a liberal interpretation of the Free Bet Blackjack rules, where they’ll now let you free double on two card soft 19, 20, and 21. The rules printed on the felt say free doubles only on hard 9, 10, and 11, but they’ve interpreted A-8 to mean hard 9, A-9 to mean hard 10, and A-Ten/Face to mean hard 11. This is only slightly helpful to the player.
The Viejas rules are:
- Free double on two card hard 9, 10, 11
- Free double on two card soft-19, soft-20, and Blackjack
- No re-split of Aces
- No surrender
- Free double after free split
The house edge is 0.88%, which isn’t too bad. Without the free doubles on the soft totals, the house edge would be 1.10%. I guess the free doubles on the soft totals make up for the lack of surrender. The basic strategy for the non-free-split hand is listed below. Refer to the original post for the basic strategy for free-split hands.
My local Viejas Casino just installed Free Bet Blackjack, a game I worked on for Geoff Hall and ShuffleMaster. There’s a side bet on the game called “Push 22″, that I did not work on (until I got back from Viejas last night). I figured I’d check if it was you-know-what.
The bet has some nice payouts, and is a natural match for a game where the dealer pushes all bets on a 22 bust. For a 6-deck shoe, the game has a 5.85% house edge. Not too bad, considering the odds it pays.
|Suited Dealer 22||0.003327||50-to-1||0.166345|
|Same Colour Dealer 22||0.011659||20-to-1||0.233174|
|Other Dealer 22||0.058551||8-to-1||0.468405|
|Dealer Not 22||0.926464||lose||-0.926464|
Of course, I had to check the EORs (for a single removed card), which showed promise:
With the unbalanced blah, you should blah for +24 or better. This will happen 5.1% of the time, with an average +3.6% blah.
I end up playing a lot of this game at my local Viejas Casino, mostly because it’s a really cheap game if you stick to the just Ante bet (~1.5% house edge). Of course, everyone else plays the Aces Up and Two-Way Bad Beat Bonuses, and you pretty much get ostracised from the table for not betting them. The other players just shake their head at you, and g-d forbid you should lose with a bad beat without betting the bonus. I don’t know where else you’ll ever experience such negative communal disapproval. It’s about as bad when you hit your 12-15 against a dealer 6 upcard in Spanish 21 (you should). On 3rd base. Every hand.
Anyway, everyone just loves the Two-Way Bad Beat Bonus. They don’t care what the house edge is. That’s why they’re there. They just want to hit a 35:1 or higher payout. And it happens frequently enough, especially when you play it every day. It’s the crack cocaine of bonus bets.
I saw the WOO’s numbers for the Two-Way Bad Beat were a little different than mine, but they’re pretty close. The 11.1% house edge is more than I’m usually willing to pay. I’ll bet it once or twice an hour, and consider it an occasional treat. But, unless I made a mistake, it’s not impossible for your straight flush to get beat (1 in 100 million). So you’re telling me there’s a chance …
While I was playing Six Card Poker at my local Viejas Casino, another player told be about the Wild Six Card Draw that he plays in Colorado. It’s a poker game with two wild Jokers in the 54-card deck, and the player gets 5 cards plus one free replacement card vs the dealer’s 6 card hand. I ran a Monte Carlo analysis to see if ideal 6-way collusion would yield any edge (you never know, the game has two Jokers after all). But even with 6-way collusion, you can’t get the house edge below 2.2%. I guess that makes sense, since it’s probably rare where you’d chose a weird draw over the more obvious discard. Anyway, it’s really easy to check these things, and you never know what you’ll find.
Some readers asked about a Baccarat side bet called “Super Six” which pays 15:1 for a dealer wins with a 6 total. It’s really easy to analyze the countability of any Baccarat side bet. The ideal return for this bet with a perfect (computer) count of an 8-deck shoe game with 15 cards behind the cut is only +24% of a fixed bet per shoe (2.6 bets per shoe at an average +9.2% advantage per bet). A simple unbalanced count (six => -2, seven, eight, nine => +1) and betting when the running count is +34 or higher yields only +12.2% of a fixed bet per shoe on 2.77 bets/shoe, and +4.41% edge/bet. It really doesn’t seem worth the effort, even if you had an ideal count (e.g., mobile app). You’d go crazy waiting around for less than 3 bets per shoe.
You probably know that I’m not much into advantage play based on edge-sorting cards. That’s the realm of Phil Ivey and Eliot Jacobson. It’s a pretty cool technique, but it’s way too involved for my attention span, regardless of the payoff. However, I did watch Warren Beatty in Kaleidescope, if that counts for anything.
Anyways, a reader who saw Eliot’s post on Edge Sorting (Jacks in) Mississippi Stud asked me if it’d be worthwhile to also sort the Queens, Kings, and Aces. That’s a pretty interesting question, since I can see how Eliot would start out with just the Jacks, as you’d know when you had a sure winner. But, maybe sorting the other “pay” cards would improve the return. You might not know exactly when you had a winner, but you’d have a good idea, and much more often.
I realised a Monte Carlo analysis would easily yield the ideal return for any selected sorting group. I modified a few lines of code, and violá, I simulated the estimated theoretical max return for the following sorted card groups in Mississippi Stud:
|Sorted Card Group||Ideal Return|
|Jacks & Queens||+48.9%|
|Jacks, Queens, Kings||+59.0%|
|Jacks, Queens, Kings, Aces||+63.4%|
(I use the paytable that pays 5:1 for a straight.)
So it’s probably worthwhile to sort all the “pay” cards, unless it really complicates the practical strategy (not too likely).
While it’s easy to get the return for an ideal strategy for any sorting group, it takes time to work out a practical strategy. It’s straightforward, but tedious, so I’m not doing it. (Well, I actually did it for a reader, so it’s his now.)
Paigow Dan told me about the new Lucky Stiff side bet his friend recently placed at the 7 Cedars Casino in WA. It looks fun, because you’re paid 5:1 when your initial 12-16 hard total ends up winning the main hand. Also, blackjack pays even-money on the side bet, and an initial pair of 8-8, 7-7, and 6-6 instantly wins 10:1. Anyways, I ran the bet through my BJ analyzer, to see if it was interesting in any way. I understand that 7 Cedars lets you bet $5 on the main hand, and up to $25 on the side bet. So I ran the analysis for a 5:1 side-to-main ratio on a 6-deck, H17, SP4, SPA4 game. The return showed a house edge of 3.5% of the combined (main+side) wager. The optimal strategy for the 5:1 side-to-main ratio only has a few differences with basic strategy.
The EORs are fairly small for the 5:1 side-to-main ratio. They’re about only 1/3rd as effective as the EORs for a standard 6-deck shoe main game. So it’s not worth your time to count this side bet. For a single card removed in a 6-deck game, the EORs are as follows:
This bet looks like fun. If you bet an equal main and side bet (1:1 side-to-main ratio), the house edge is 4.66% on the combined 2 unit bet (2.33% element-of-risk). That’s not too bad for a carnival-like odds. If you make a small side bet 1/5th of your main bet (e.g., a $1 side bet to a $5 main bet), then the house edge on the combined 1.2 unit bet is 1.38%. That’s not bad for a little bit of fun.
I saw this blackjack side bet in the Venetian last month, and it looked pretty you-know-what. I forgot to post about it until now. I’m pretty sure they use 8-deck shoes at the Venetian.
|Removed Card||EOR||Balanced Count||Unbalanced Count|
Using the unbalanced taps, the bet is +EV for RC >= +34 (assuming two decks behind the cut card). This yields 16% betting opportunities, with an average edge of +2.8%/bet. The theoretical max (using full shoe composition, including suits) is 17% opportunities @ +3.0%/bet. It’s not worth much.