Discount Gambling

Spanish 21

Posted in by stephenhow on February 24, 2009

Introduction

spanish21-logo
Spanish 21 is a variation of blackjack, played with a “spanish” deck that contains no Tens, but offers many liberal rules and options that generally yields better odds than blackjack.  Basic strategy is a little more complicated, but almost all casinos allow the use of strategy cards, so you’re a lot better off playing Spanish 21 if your house offers it.  Some of the liberal rules of the game are:

  • double on any number of cards
  • re-doubling (sometimes up to 3 doubles)
  • double after split
  • surrender after double
  • all player 21’s pay immediately, regardless of dealer hand
  • bonus payouts for 6-7-8, 5 card 21’s, etc.

Basic Strategy

The basic strategy for a 6-deck shoe game, where the dealer hits on soft-17, and up to 3 doubles are allowed is presented in the strategy card below.  The card is color-coded, where red stands for hits, white stands for surrender, yellow means stand, and blue means double.  The exceptions to the color-coded rules are indicated by special notations in the box.  There are no exceptions to hit or surrender, or any decisions after doubling.  There are a few exceptions before doubling, where yellow stand boxes indicate when you should hit instead.  Also, there are blue double boxes that indicate when you should just hit the hand.

Basic strategy for Spanish21.

Basic strategy for Spanish21.

Stand Exceptions

The yellow boxes with a number or * ‘ ” symbol in them mean you should hit the hand when you’re drawing for a bonus payout.  For example, say my hand is 7-8 offsuit, and the dealer is showing a 2. I have a hard total of 15. The strategy table shows a yellow box with a 4* in it.  The * tells me I should take a hit, because I’m drawing to a 6-7-8 offsuit bonus hand (pays 3:2).

As another example, say I have 2 3 2 3 2 2, a six-card hard 14, and the dealer is showing a 6. I’m drawing to a 7-card 21, which pays a 3:1 bonus.  The strategy table has a yellow box with a 6″ in it, meaning I should take a hit and draw to either the 7-card 21 bonus, or the 6-7-8 suited bonus.  I have the former, so I take a hit.

Double Exceptions

Sometimes, it’s better to just hit a hand than double it, depending on how many cards you have.  This is because you have a chance of drawing to a multicard 21 bonus (remember, there’s no bonus after double, and it gets very expensive to see another card after doubling).  For example, if I have a 3-card 11 total (e.g., 4-5-2) and the dealer is showing a face card, the table shows a blue double box with a 3 in it, meaning I should just hit my hand, because I’m holding at least 3 cards.  This makes sense, because if my first draw is a 3, then my total is 14, and I’d have to surrender if I doubled.  But if I just hit to the 4-card 14, then I have an easy hit to the 5-card 21 bonus (I need a 7).  Even if I don’t hit my bonus, I have a “free” draw to improve my hand, instead of surrendering the hand.

Some Observations

Double and Re-Doubling

All double-down opportunities are on-average winning hands (+EV).  That is, a decision to double-down is never the “least of two evils” (i.e., lose less by doubling).  You double because it’s the way to maximize the win from the hand.  However, some re-doubles are losers, and you’re redoubling-down to lose less than surrendering the hand 😦

For example, one of the weakest doubles are player hard-9 against a dealer 3.  Doubling still yields a winning net of approx 7.8% of the initial bet, whereas the hitting yields only 5.5%.  So, passing up on this opportunity to double will cost you about 2.1% of your initial bet.  That’s a huge edge you can’t afford pass up.  As another example, consider soft-18 vs. a dealer 4.  Doubling in this case yields a 14.3% return on your initial bet, while hitting returns only 8.4%.  That’s a whopping 5.9% advantage you cannot forfeit.

So while I often see people passing up on their double-down opportunities, I also see people doubling-down when they’re not supposed to.  A lot of people want to double soft totals against a dealer 2 or 3.  Of course, you only do so against a dealer 4/5/6, and doing otherwise will cost you money.  For example, doubling down on an A-3 (soft-14) vs. a dealer 2 will turn a winning hand into a losing hand.  Just hitting in this case returns an average 5.4% profit on the initial bet.  Doubling down erroneously here will result in an average loss of -0.2% of the initial bet.  Yet again, a doubling mistake costs 5.6% of your initial bet.  This is throwing money away.

Some of the re-doubling opportunities are the “least of two evils”, where you’re just trying to lose less on average.  For example, say you doubled-down on a 4-6 (10 total) against a dealer 8, and you drew a 2.  Now, you have 12, and are faced with either surrendering (-100% of initial bet), redoubling (-98.5%), or standing (-101.5%).  The basic strategy says to re-double, because you’ll get a little return on your redouble (1.5% of your initial bet).  The worst case is to stand, where you’ll lose a little more than if you surrender.  But practically speaking, since you’ve already doubled your bet, this +/- 1.5% initial bet difference between your options is reduced to a +/- 0.75% difference relative to your doubled bet.  So it’s not a huge mistake to go any way you want to here.

Dealer 4/5/6 Upcard

I get  happy when I see a dealer 4, 5, or 6 upcard.  I really get happy when I have a low soft total, because this is a chance to double and redouble your bet a few times.  In all cases, opportunities to double increase your average win from the hand.  In general, with a dealer 4/5/6 upcard, take all the opportunities to double and split, as they all return more expected win (i.e., they’re not “least of two evils” moves).

For example, you split 3-3 against a dealer 3, because you lose less (-7.5% of the initial bet) than if you took a hit (-11.1%).  But if you have 3-3 against a dealer 4, taking a hit is still a loser (-7.2%), while splitting becomes a +1.5% average winner.  Of course, you have to bet more (and may have to double it), but you can’t afford in the long run to cost yourself this 8.7% mistake.

All the doubles and redoubles with soft totals, even against a dealer 4 are winners.  For example, if you have an A-3 (soft 14) against a dealer 4, doubling will return a 15.2% profit on your initial bet, while hitting will yield just 9.1%.  This 6.1% difference includes the possibility of redoubles down the line.  Even A-7 (soft 18) against a dealer 4 yields more for doubling (14.3%) vs. just hitting (8.4%).  As I said before, all redoubles against a dealer 4/5/6 increase your winnings vs standing.  For example, if you (re)double to a soft 18 against a dealer 4, you’ll eek out a little more profit (28.7% of initial bet) by redoubling than by standing (23.7%).  Of course you’re putting a lot more at risk by doing this, especially if this is your third double.  I tend to start with a small initial bet, so I don’t care if I have to 8x it.  But, risking an additional 4 initial bets to extract out a gain of 5% of the initial bet may not be worth it to you.  You’re really only getting 5%/4 = 1.25% return on your 4x redouble bet.

The examples given against a dealer 4 upcard are even more pronounced against a 5 or 6 upcard.  The bottom line is: a dealer 4/5/6 upcard is good stuff.  I especially like the 6 upcard, and doubling down with low soft totals.

Breaking The Rules

Almost all of the people I play with don’t believe in math, and they display nothing but contempt for it.  I really learned to keep my mouth shut on the matter.  You can get into a fight over this, believe me. At best, I’ll say indifferently, “well, the book says …”.  They don’t believe in math, but they believe in the existence of the book.   The only math the players practice at the table is “would-of” calculations to see who to blame  for taking/not-taking a dealer bust card, or low card that gave the dealer a good total.  It’s really complicated stuff.  They see a lot of patterns in the cards, and hold a lot of superstitions.  Like if the dealer has a weak upcard, they still believe someone at the table has to hit (I guess take a low card), otherwise the dealer won’t bust.  People go ballistic over this stuff, especially at Spanish 21, where you’re supposed to hit hands like 14 against a dealer 3, and 12 against a dealer 6.  All of this just results in more blame opportunities than regular blackjack.

Common Mistakes

Some of the plays in the basic strategy table are overlooked by a lot of players, and these mistakes are significant, however infrequent.

Hand Correct Mistake Cost (of initial bet)
9 vs. dealer 2 hit double 1.8%
17 vs. dealer A hit stand 1.8%
8-8 vs. dealer face card hit split 4.1%

Gambling More

Sometimes, you just want to gamble more, despite the odds.  The best thing to do in this case is to choose the better gambling opportunities.  Of course these are often double-down or split opportunities, where you can get more money into play.  Some of these optional plays are listed in the table below, along with their cost, in terms of the initial bet.  The higher the cost, the worse the mistake is.  Note that there’s a wide range in the cost of mistakes that you’ll see at a table.

Hand Correct Mistake Cost (of initial bet)
A-3 vs. dealer 3 hit double 0.04%
3-3 vs. dealer 6 hit split 1.1%
3-card 11 vs. dealer face card hit double 2.3%
A-8 vs. dealer 6 stand double 7.8%
doubled 12 vs. dealer face card surrender stand 7.9%
12 vs. dealer 6 hit double 13.2%
doubled 12 vs. dealer 6 stand re-double 13.8%
doubled 17 vs. dealer A surrender stand 13.9%
doubled 12 vs. dealer 9 surrender re-double 18.3%
A-9 vs. dealer 6 stand double 24.4%
doubled 12 vs. dealer face card surrender re-double 25.2%
doubled 13 vs. dealer face card surrender re-double 42.7%

For example, you can decide to gamble and double an A-3 vs. a dealer 3.  The end result of the hand, assuming you finish the hand correctly, is only worst by 0.04% of the initial bet, had you just hit, then finished out the hand correctly.  That’s a very small cost for gambling it up, and getting some more money out there.  It hurts a little in the long run (which is too long for any of us to actually see), but in the short run, it’s just increasing your bet.

Often I see people re-double 12 against a dealer 6.  I guess they figure if you’re supposed to hit all 12’s, might as well double on them too.  In reality, the hand is a loser, and you’ll only get 62.6% of your amount bet back by standing.  Re-doubling will lower the return to 48.4% (of the amount bet before the last redouble).   It’s a bad bet, but some people like to gamble.  They can get lucky, by not busting.  At that point, they’ve doubled their expected return on the hand.

Gambling Less

Sometimes, you don’t care what the odds say, you just don’t have the appetite to re-double or split a hand that you don’t really like.  Your fears are generally well-founded.  In these cases, you have to put more money down, sometimes just as the “least of two evils”, to improve the return of a losing hand.  Below are some of the plays that fall into this category, along with the cost of  the mistake, in terms of the initial bet.  The realistic cost of the mistake probably needs to be divided by 2 in the case of a split, and by the amount of the (re)double bet in case of a double.

Hand Correct Mistake Cost (of initial bet)
doubled 12 vs. dealer 8 re-double rescue 1.7%
doubled soft 18 vs. dealer 4 re-double stand 5.0%

More Articles

posts categorized under Spanish 21:

Buying Surrenders @ Spanish21

Posted in spanish21, sycuan by stephenhow on April 12, 2009

I’ve been shooting an angle at the Spanish21 blackjack tables at my nearby Sycuan Casino for the past few weeks, but finally “management” got wise to it, and shut me down 😦 However, it’s still good, and you’ll probably have the chance to do it yourself, provided your casino isn’t retentive about these types of things.

Here’s how it works. I noticed that people tend to over-surrender at Spanish21, because they get used to surrendering from rescue after double, and they figure if its good then, it must always be good. Of course, there are people that never surrender, even after double (they’d rather redouble a 14 against a dealer Ace), but that’s a different story. So I’d see people surrendering 14 against a dealer Face, and all kinds of nonsense. It was okay to pass chips around the table to back someone’s double, and play someone else’s match, so I figured they’d let me “buy” people’s would-be surrender hands.  So, they surrender to me, I pay them half their bet, and they play the hand out for me.  I own the hand at this point, and if it wins, I get all the proceeds, including the original bet. It’s very simple in practice. When you see someone start to signal for surrender, you say “I buy” and show them the money. They say, “ok, you buy”, take the chips, and now its your hand.  Of course, they have to signal to the dealer for the hit, because of the house rules.  Hopefully, you improve the hand with the hit, and stand.  If you bust, the player feels good about their surrender.  If you win, make sure the player doesn’t feel like a sucker (say something like “I gambo”).  This transaction is somewhat normal for the Asian players, because of the concept of “color buy” in Paigow.  They’re also very adept at keeping track of various intra-player transactions (e.g., “come-come” bets). With American players, hopefully you can simply explain the proposition. Usually though, just have the right amount of chips ready, and use hand gestures to demonstrate your intentions.

Of course, every such opportunity (except for the 16 & 17 against a dealer Ace) is positive EV. Here’s a few examples of what I was getting before they put the kibash on it:

Hand EV(hit) Cost Profit
16 vs Dealer Face .516306 0.5 3.26%
15 vs Dealer Face .566478 0.5 13.3%
14 vs Dealer Face .61956 0.5 23.9%
16 vs Dealer 9 .546484 0.5 9.30%
15 vs Dealer A .543541 0.5 8.71%
doubled 13 vs Dealer 7 .532753 (stand) 0.5 6.55%

There’s one guy (an Italian guy named Robert), who surrender more than anyone could fathom. We got along well, so he’d gladly surrender to me. Unfortunately, he’s a bad chronic donor, so I didn’t see him enough. Besides, he would have caught on sooner or later.

From the table, the worst offer is the 16 vs. the dealer Face. Of course, it’s the most common opportunity, and only yields 3.26%. That’s a great return, but might be more variance than you like to assume.  Maybe you can only buy the small bets on these hands.  Anything else is pure gold.

Anyway, the retard floor manager on the day-shift saw me doing it, and sternly told me I couldn’t do it. I guess that means if I continue doing it, I’ll get in more serious trouble. Plus, they’ll probably have a staff meeting / memo on the issue, and all the dealers will be instructed to prohibit it. Geez, what a bunch of killjoys.  This was the best thing ever.

Does Card-Counting Work For Spanish21?

Posted in spanish21 by stephenhow on February 24, 2009

I’ve heard all the stories about card-counting, and almost managed to watch the entire movie “21”, but I never really saw how card-counting could help against a 6-deck shoe.  Well, since it was really easy to add to my Spanish21 program, I devised a simple hi/lo balanced count:

Cards Value
2, 3, 4, 5 +1
J, Q, K, A -1

Next, I wanted to see the correlation between the running count of the shoe, and the expectation value (EV) of the next hand out of the shoe. So I ran the simulator for a million shoes, and plotted the average hand net result vs. the running count:

Simulation of simple hi/lo count for Spanish21.

Simulation of simple hi/lo count for Spanish21.

I was surprised to see the very linear correlation between the running count of the shoe, and the profitability of the next hand out of the shoe. Counting works. I never saw this data before (probably because few people want to see this type of thing), but it’s the clearest way for me to see the benefits of counting. And these results were obtained by playing the unmodified basic strategy for the game. Note that the player has almost a 2% edge when the count is +10. And the game is always profitable when the count is positive.  (Oh, if we could only sit out while the deck is negative …) Obviously, results will improve by implementing more complicated counting systems (e.g., true counts, based on shoe depth, modifying basic strategy for the count, etc.). But, it’s nice to know that the most basic type of counting yields a positive edge for the game.

As another simple experiment, I added a simple modified betting strategy based on the count:

Condition Bet
count ≤ -5 0 (sit out)
-5 < count < 0 1x
0 ≤ count < 10 2x
10 ≤ count < 15 3x
count ≥ 15 4x

where a bet of 1x indicates your standard bet, and 2x is twice your standard bet, etc. This simple betting strategy using the simple running hi/lo count, and the unmodified basic strategy made the game net profitable (+0.41% of the 1x bet), vs. the normal -0.45% loss rate.

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Spanish21 @ Sycuan Casino, CA

Posted in spanish21 by stephenhow on February 18, 2009

One of the best games in San Diego is Spanish 21 at the Sycuan Casino. The dealer hits on soft 17, but the player can double a hand up to 3 times. This comes in handy with a game that allows doubling on any number of cards, even after splits. I wrote my own program to find the basic strategy for this game, and verified it through simulation.  The game at Sycuan yields a small 0.4% edge for the house. That’s really good, considering normal blackjack yields at least 0.6% house edge, and the carnival games and “bonus” bets yield anywhere from 2%-8%. As far as discount gambling goes, this is as good as it gets … it costs you only $.02 per $5 bet. This level of action will hardly pay for the casino lights ($.02/hand @ 60 hands/hr = $1.20/hr).

Here’s the results I obtained from my program. The table almost exactly with The Wizard Of Odds, except for a few cases like 8-8 vs. a dealer 10 (you should just hit), A-3 vs. dealer 3 (you should just hit), and a three card 10 (e.g., 2-3-5) against a dealer 8 (you should just hit). There’s an inconsequential difference on the after doubling table too.

Basic strategy for Spanish21.

Basic strategy for Spanish21.

I wrote the program in C++, and used a recursive algorithm to walk all possible player options and their outcomes against a given dealer upcard. The code is very compact, because of its recursive nature, but it’s a little slow. I speeded up the algorithm a bit by saving intermediate decision EVs, and using them to automatically prune off improbable option branches. For example, it took my Intel-based Mac Mini over 6 minutes to solve the basic strategy play for player 5 6 vs a dealer 2 upcard:

Macintosh:Debug show$  time ./spanish_21  -u 2 5 6
dealerHand: 2
playerHand: 5 6
EV +0.348048
double

real    6m15.242s
user    6m10.942s
sys     0m0.799s
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Six Card Poker Bad Beat Bonus

Posted in six card poker by stephenhow on June 25, 2013

sixcardI 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 …

Six Card Poker Two-Way Bad Beat Bonus
Beat Hand Combinations Probability Payout
(to-1)
Return
Straight Flush 1,967,920 1.0320E-08 10,000 0.000103
Four-of-a-Kind 150,323,712 7.8830E-07 5,000 0.003941
Full House 18,331,506,888 9.6130E-05 500 0.048065
Flush 57,651,601,832 3.0232E-04 200 0.060465
Straight 185,942,016,336 9.7508E-04 100 0.097508
Three-of-a-Kind 776,263,604,160 4.0707E-03 35 0.142475
Two Pairs 6,590,304,418,608 3.4559E-02 10 0.345595
Pair Aces 2,871,866,305,368 1.5060E-02 9 0.135540
Others 180,194,060,203,056 9.4494E-01 -1 -0.944935
Total 190,694,571,947,880 100% -0.111243

Triple Attack Blackjack (+EV) @ Barona Casino, CA

Posted in +EV, triple attack blackjack by stephenhow on August 14, 2011

My nearby Barona Casino opened up a new Triple Attack Blackjack game last month, and I tried it out this weekend. I really like this game, because of the weird, aggressive hitting like Spanish 21. But more importantly, the game allows you to double your initial bet after seeing your first card, and bet again after seeing the dealer upcard. You’re immediately paid on 21 or any 6-card total, and you can double down at any time. The house gets its advantage by paying even money on blackjack, and pushing on dealer 22.

For the full rules and basic strategy, see the Wizard’s analysis, which yields a 1.18% house edge. But for most cases, his basic strategy charts boil down to the following simple rules:

  • If your first card is an Ace, triple your bet.
  • If your first card is a Face, triple your bet against 2-9, else double your bet.
  • 3rd Attack 2 against a 6.
  • 3rd Attack 8 against 6,7.
  • 3rd Attack 9 against 5,6,7,8.
  • Double 10 against 3-6.
  • Double 11 against 7 and under.
  • The only soft total double is soft-18 against a 6.
  • Double all 5-card 14’s and under.
  • Double-for-less (split aces rescue) soft-17 and under, and soft-18 against 9 and A.
  • Hit all 12’s and 13’s.
  • Hit 14 except against a 6.
  • Hit 15 against a 2 or 3.
  • Hit 16 against a 2.
  • Hit 17 against an Ace, and for some 5-card totals.
  • Never split 4’s, 5’s, 6’s, 10’s.
  • Split 2’s and 3’s against 6,7.
  • Split 7’s against 4-7.
  • Split A’s and 8’s against everything except A.
  • Split 9’s against 6,8,9.

I really enjoyed the game. I also won about $400 in 3 sessions, which is unheard-of for me, since I flat bet for the minimum $5. I never vary my bet. However, in Triple Attack, you often end up betting 3 units, or even 6 or more, if you split hands like Aces. I don’t think I’ve ever won that much money playing blackjack before. The players all loved it, because they make more decisions, and their initial $20 bet can easily become a $120 bet on a good hand, or just remain a $20 bet on a weak hand.

Of course, it immediately occurred to me that card counting should be more effective in Triple Attack compared to standard blackjack. While you might dramatically increase your bet for a good count in regular blackjack, in Triple Attack, you only have to commit 1/3 of this amount on the 1st Attack, then another 1/3 only if you like your first card (an Ace or Face), and another 1/3 only if you like the dealer upcard. So, even though the count may be good, you can get away from a bad hand on the first card, and also if the dealer has a good upcard. Compare that to normal blackjack, where you bet huge on a good count, then get a 6, then the dealer shows an Ace.

Using basic strategy, I looked at the EV sensitivities of each of the card ranks (i.e., the effect of removing one card from the shoe). Interestingly, the effect of removing a Face card was very small. Removing a 5 improved the hand EV the most, but not by much compared to a 2, 3, 4, 6, or even a 7. By far, the Ace was the most powerful card, making the other cards insignificant.

So, I tried out a simple scheme, which only relies on the Ace count, compared to the expected number dealt. You subtract the number of actual Aces seen from the expected number of Aces dealt to get the Ace count. For example, after dealing 1/2 the shoe (192 cards), you should have seen 16 Aces. If you’ve only seen 12 Aces, then the count is +4. The Ace count is a measure of the “extra” Aces left in the shoe. Using a basic strategy simulator, I generated the curves showing the effectiveness of this simple Ace-Count system (including double-1-unit-for-less as Ace-split rescue):

Triple Attack Blackjack EV vs. Ace-Count and Shoe Depth

This effect is huge! Look at the green curve, which shows the effect of the Ace count after 3/4 of the shoe has been dealt (288 cards dealt). At this point, 24 Aces should have been dealt, on average. But if only 20 Aces were dealt, then the count is +4, and the next hand has a 4% player advantage. Similarly, a negative count tells you to bet the minimum, or even Wong (sit out) until the next shoe. The blue curve shows the effect after 1/4 of the shoe dealt (96 cards), and the red curve shows the half-way point (192 cards). You can see that generally speaking, it’s good to increase your bet any time the count is +2 or more (the shoe is “loaded” with 2 or more extra Aces).

We don’t need to look at the distribution of Ace counts to know that +1, +2, +3, +4, +5 counts happen all the time, especially at the end of shoe, where the effect if largest. Note that the green curve shows about a 1.25% EV improvement for each surplus Ace left in the shoe.

A simple counting strategy bets the minimum for the first 2 decks of the shoe, then a large bet if the Ace count is +2 or better. Using basic strategy, and assuming the cut card at 48 cards left in the shoe, the following returns are obtained:

Triple Attack Return vs. Large Bet On +EV Ace Count
Small Bet Large Bet Return
(relative to small bet)
1x 1x -1.10%
1x 5x +0.08%
1x 10x +1.60%
1x 20x +4.40%
1x 30x +8.80%
1x 40x +11.8%

On the other hand, the shoe is +EV about 20% of the time (+2 or better count) after the first 1/4 of the shoe is dealt. So, if you just like varying your bet on a good count, you’ll really enjoy this game. Overall, if you Wong and only bet +EV Ace counts, then you’ll extract about +17% total EV out of a shoe (i.e., +0.17 bets/shoe). The Ace-count system is very easy to implement (e.g., use the height of muck cards to estimate the expected Ace count), and is very fun. Some people have a good idea of when the shoe is Ace-rich or not. That’s all you need to know for this Triple Attack game!

And there’s no time to (possibly) bet big like the last hand of the shoe (purple curve, cut card @ 1 deck left):

Note that unless the Ace count is 0 (unlikely, only 22% of the time), you’re either a big favorite, or a big underdog on the last hand. It’s easy to get the Ace count right on the last hand, assuming the cut card was placed with 48 cards behind it. At the last hand, you should have seen 28 Aces. If you only saw 24, then you have a +4 count, and the EV of the next hand is almost 10% in your favor (a $100 1st Attack bet will return a $9.80 profit on average, including possible 2nd and 3rd Attacks, doubles, etc.). But, if you saw 30, then the count is -2, and the house has a 6.2% edge on the last hand, so bet the minimum, or Wong.

I suggest you simply count the number of Aces seen, even using chips if it helps you keep track. Compare your Ace count to the number of decks (48 cards/deck) seen in the muck rack. There are 4 Aces per deck. If the number of Aces seen is less than 4*(mucked decks), then the Ace count is positive. If your count is +2 or better, you’re +EV, and can increase your 1st Attack bet.

Get an idea of what a deck (48 cards) looks like in the discard rack. Ask the dealer for their estimate of the number of decks in the muck. You’ll find it’s pretty easy to estimate the number of dealt decks. Thus, you should be able to determine the Ace count very easily. Also, by watching the level of cards in the discard rack, you’ll know how powerful your count is (see above graphs for 1/4, 1/2, 3/4, and 7/8 shoe dealt depths).

Example: You look at the discard rack, and it looks like 3 decks have been dealt. This means that 4*3 = 12 Aces should have been dealt. Your actual Ace count is 15. The Ace count is -3, and you’re -EV, so bet the minimum. However, if the actual Ace count is only 9, then the Ace count is +3, and you’re +EV, so you should bet more.

This counting system couldn’t be any easier, or any more powerful. It doesn’t get much better than this.

Finally, I saw that at request, Barona increased the limits on the Triple Attack game to $25-$1000. I was locked out until the guy left, and the table returned to $5-$1000. In general, Barona is very flexible about increasing table limits.

Self-Bar @ Sycuan Casino, CA

Posted in spanish21, sycuan by stephenhow on July 12, 2009

Finally, after years of low-limit, “advantage-play”, life-in-a-casino degeneracy, I figured out the ultimate way to beat the casino this afternoon.

Of course, the story starts off that I was minding my own business, playing $5 Spanish 21 in pit 3 (non-smoking) at my nearby Sycuan Casino. I’d been doing this every weekend since I started this blog 5 months ago. I’d already played 10 hours for the weekend, which would likely total up to 20+ hours by Sunday night. Like clockwork, I’d also been toking out $10 per hour, giving each dealer $3 or $4 in $1 chips at the beginning of their push, and letting them play it anyway they wanted to.

I played at Sycuan an average of 4 days a week, for 30-40 hours a week, losing an average of $2/hr, plus toking out $10/hr to the dealers. So it cost me about $400/week, but I considered it cheap entertainment. The casino won $70/week from me, but they threw me about $10/week in loyalty rewards, and another $20-$30/week in food comps. So, my net donation to the casino was about $35/week, or $1/hr. However, there was no getting around the $350/week in dealer tokes ($10/hr). I was there for the socialization, and I wanted to treat the dealers fairly for standing up, dealing 400 hands/hr, putting up with the Idiots who somehow find it eminently reasonable to blame the dealer for their losing the rent money on their bad decisions, like playing with it in the first place.  And the casino forces them to be nice to the Morons, by spying on them with secret shoppers, even though they need to be nice to customers to make a living anyways (their paychecks are essentialy $0 after taxes, benefit deductions, and 401k).

In the thousand hours I sat playing Spanish 21 @ Sycuan, I never found a single player that employed basic strategy, or for that matter logical thought, to their gambling.  All my publishing of the odds, and my practical examples of 21 hour straight sessions, sometimes coming out ahead, could not convince people to hit a 14 against a dealer 2 or 3, or even to hit a 13 against a dealer 5.  Instead, I’d see the same thing that the dealers see every day.  People actually trying to figure out what the next card coming out of the shoe would be, or trying to figure out what the dealer down card was.  E.g., they say “she (the dealer) doesn’t have it”, and they stay on 15 against a dealer 9.  Or they think the dealer “has it”, and they surrender.  They clearly know they won’t improve their hand by hitting.

So anyways, I see this crazy behaviour every day, the way the players blame the dealer for drawing to 20, or 21, or otherwise not busting.  They anthropomorphize the cards coming out of the shoe as being controlled by the dealer, or the dealer’s properties at the time.  “The dealer is hot.  I’m going to sit out a few hands.”  Or, “the dealer isn’t busting”.  But while I enjoyed watching all of this (ok, I felt better about myself when I was playing with these people), I found out that the anger the losing players throw at the dealers ends up being rather hurtful, no matter how experienced the dealer is at handling it.  I think a particularly hateful way to treat the dealer is to sarcastically blame them for the losing hands, like “of course you make 21 when I have 20”, and disgustingly and dismissively violently gesture at them.  There’s a certain type of personality that ends up doing this when the losses get bad.

Anyways, the dealer has to make a living too, and I could afford to toke, so I do.  As I understand it, they’re taxed on about $18/hr in expected tokes, so for a 6-spot table, this works out to be about $3/hr per person.  Okay, so I toke at 3x the average.  But there’s a lot of people that don’t toke anything, so the average is made up by the people who do.  So since I toked $3-$4 on every down, and I could care less what the outcome of a $5 hand was, and I’d have reasonably intelligent discussions with the dealers about anything other than the game itself, and always had a good time playing, it made me a very good customer from the dealer’s perspective.  And, as they said, “especially in this economy.”

Ok, so finally, here’s the story I’m trying to get to.  No matter how good of a customer you think you are, an occasional moronic floor supervisor will do something completely stupid, and walk over with another floorperson, from another pit in another room, and indiscretely pull you out of your game in front of all the players to warn you about something minor you did in the previous week, or 35 playing hours, and 4 sessions ago.  The floor super told me I couldn’t buy surrenders from people, like I’ve described in my previous post.  I know they told me not to do this.  I refrained from doing it in general.  However, when you’re in the middle of a 21 hour session, in graveyard, and you’ve been friendly with the players for hours, and you’re trying to educate them about the game (i.e., teach them not to over-surrender), it feels like a pretty minor offence. Oh, and did I mention, I toke out $10/hr, win or lose?

So, I got pretty angry when they did this happened to me today.  I was really tired from my 7 hour session that ended at 3am the night before.  I was beside myself that they’d bring up something minor from last week and make a deal out of it.  I didn’t like being treated poorly for all the toking that I go out of my way to do.  I always state that I’m going to lose $1/hr to the house, and spend $10/hr on the dealers.  It’s been my stated policy all the while I’d been putting my 35 hrs/week into the place.

So I got indignant, and sarcastic.  I dismissingly agreed that I shouldn’t do it, and returned to my table, upset.  Everyone wanted to know what the fuss was about, and I said bad things about the way the house was treating the customers.  I told my fellow players that the house treats us poorly, and consider us suckers.  So the floor comes back into the picture, and tells me that if I say anything disparaging about the casino, she’ll bar me from playing.  Then I said, “please, bar me, throw me out”.  She told me just to sit down and play.  But I decided right then and there, that was the last thing I was going to do.  It was clear that I called her bluff, since they were way out of line relative to my good behaviour, as an extremely loyal regular customer.  What casino treats their regular donors like this?!  So she walked away, but I remained agitated.

Now, here’s the best angle to shoot when if you’re upset with the casino.  Threaten them that you’ll officially self-bar yourself.  By law, they have to take you seriously, and they’re all trained how to handle the request, and there’s a formalized procedure for processing it.  And the best part is that it’s irrevocable, except for a complicated appeals process that has to go through a state gaming commission hearing.  If you’re a good regular, the casino does not want to you threaten the nuclear option.  Sign the paper, and they lose revenue.  Do it in front of all the other customers, and it’ll put dangerous ideas in their heads.  Maybe it is a good idea to self-bar yourself from the casino.  I’d probably be better off, and save thousands.

Don’t threaten “I’m never coming back here”.  It doesn’t mean much coming from a degen gambler.  They send you some loyalty rewards in the mail, and you’re back the next day to redeem them.  Sign the “Sycuan Security Self-Exlusion Form”, say for a year, or 5 years, or permanently, and by law, they’ve lost all revenues from you during the exclusion period, or they’re liable for damages and penalties from lawsuits or the state gaming commission.  Thank g*d for consumer protection laws.

After the idea came to my mind, it sounded better and better as I thought it over for 30 seconds.  I asked the floor supervisor in my pit to sign me up.  I could tell he wasn’t happy with my decision, but he had to obey my request. I was going to save countless hours and money, and do something better with my time.  After all, there are 10 other places to gamble in town, and most of them are much nicer than Sycuan.  It was win-win for me.  Why the hell was I toking out so much money in the first place?  That visit from the floor supervisor was a wake up call to me.  Why was I wasting so much time in that casino?  How could I continue donating to a place that scolds you for your loyalty?!  I had no choice but to come to my senses.  I never would have thought of the self-bar unless I had been riled up by the confrontation, and I never would have executed it unless I did it on the spot, half in anger, half in brilliant insight.

They Sycuan staff were very nice as we started the ball rolling on the self-exclusion process.  Security staff came by with the forms, and had me cash out my chips at the table.  I think I’m the only person who enacted a one year self-exclusion from the premises while they were winning.  I won about $35 in my final session, and $45 from the night before.  After coloring-out at the table, security walked me over to the cage to cash out.  I toked the cashier as I put my $336 back in my wallet (I bought in for $300).  We walked outside, and I filled out the self-exclusion form, and they took a picture of me for their files.  Then one of the guards suggested I should cash out whatever cashback I’ve earned on my Club Sycuan loyalty rewards card before they confiscated it.  So, they walked me back into the casino, and in fact, we moved to the front of the line at the Club Sycuan desk.  They swiped my card, verified my picture ID, and filled out a voucher for $35 cashback.  Then security walked me over to the cage again to cash the voucher.  A lady saw my security escort and the voucher, put two and two together, and asked me how much I won (she thought the escort was for some big payout).  I told her it was for $35, and that she should check her card for cashback awards.  The security guard agreed with me, and told her that you never know what you might have accumulated.  We didn’t tell her that I was being escorted out of the building, for good.

I knew that security wouldn’t let me make a big show out of walking out with my hands/fist up in the air, celebrating my victory over the g**damn casino, but I knew they knew I was polite, and making the move out of principle.  In fact, the guard gave me a few Customer Satisfaction Survey forms, since they knew I wanted to file the reason for my self-bar from the casino.  So, I just walked by the tables in pit 3 for a last time, said “goodbye” to the dealers (I know them all on a first-name basis), and waved the Self-Exclusion Form in the air.  Everyone in-the-know is familiar with the nuclear option, but I’m sure they’re just a little shocked that I exercised it.

As I walked out of the casino, and through the parking lot for the last time, along the same path I’d followed over a hundred times in the last five months, I breathed in the warm summer afternoon air for the first time.  Usually, I made the walk in the dark, cold hours before dawn, after wasting a day or two at the Spanish 21 table.  With every step, I was feeling free again, and hours later, I would feel immensely grateful for the day.

Double Attack Blackjack

Posted in +EV, counting, double attack blackjack by stephenhow on March 29, 2013

wagerworks-double-attackThanks to reader John A. for pointing out this game to me. The game has been around (mostly in Atlantic City), but it’s new to me. It looks like the predecessor to Triple Attack Blackjack, as it’s based on a Spanish deck (10’s removed, J/Q/K’s remain) and the player may double his bet after the first card is dealt face up to the dealer. After this initial double attack option, the hand plays out normally with the total amount bet as the hand wager. (I.e., doubles and splits are based on the total amount bet after any double attack.)

The rules following the double-attack option are as follows:

  • Dealer stands on soft-17
  • Double-down at any time (no re-doubles)
  • Surrender at any time, including double-down rescue and after splits
  • No re-splitting of Aces
  • Blackjack pays even money

The house edge for the game is a reasonable 0.50% on the initial bet. The element-of-risk is even lower, as you double your wager 58% of the time (i.e., you double-attack vs. a dealer 2-8). The return is even lower still if they allow you to surrender after splitting Aces. The EORs are listed in the following table for removing a single card from a 8-deck shoe.

Double Attack Blackjack EORs (8 deck)
Removed Card EOR Balanced Unbalanced
Deuce +0.0832% +1 +1
Trey +0.1127% +1 +1
Four +0.1514% +1 +1
Five +0.1917% +1 +1
Six +0.1184% +1 +1
Seven +0.0341% +1
Eight -0.0560%
Nine -0.0895% -1 -1
Face -0.1466% -1 -1
Ace -0.0937% -1 -1

Basic Strategy

The basic strategy for the game was auto-generated by my analyzer program. You should double-down rescue 16 and lower against a dealer 8-thru-A, and 17 against an Ace. The strategy simulates at a -0.53% return, averaged over the whole shoe, very close to the analyzer’s calculated -0.50% return.

The unbalanced count in the above table yields 23.8% +EV betting opportunities (count >= +23) in an 6-deck shoe game with 52 cards behind the cut card. The average +EV hand returns +0.52%/bet. Compare this to the “Knockout” unbalanced count for 6-deck standard blackjack with cut card @ 5th deck, where 21.3% of the hands are +EV (count >= +17) with an average yield of +0.30%/bet.

Hand Dealer Upcard
2 3 4 5 6 7 8 9 10 A
Soft Totals
soft 21 S S S S S S S S S S
soft 20 S S S S S S S S S S
soft 19 S S S S S S S S S S
soft 18 S S S D D S S H H H
soft 17 H H D D D H H H H H
soft 16 H H H H D H H H H H
soft 15 H H H H H H H H H H
soft 14 H H H H H H H H H H
soft 13 H H H H H H H H H H
Hard Totals
hard 20 S S S S S S S S S S
hard 19 S S S S S S S S S S
hard 18 S S S S S S S S S S
hard 17 S S S S S S S S S R
hard 16 S S S S S H H H H H
hard 15 S S S S S H H H H H
hard 14 H H S S S H H H H H
hard 13 H H H H H H H H H H
hard 12 H H H H H H H H H H
hard 11 D D D D D D D D H D
hard 10 D D D D D D D H H H
hard 9 H H H H H H H H H H
hard 8 H H H H H H H H H H
hard 7 H H H H H H H H H H
hard 6 H H H H H H H H H H
hard 5 H H H H H H H H H H
Pairs
A-A P P P P P P P P P H
10-10 S S S S S S S S S S
9-9 S S P P P S P P S S
8-8 P P P P P P P P P P
7-7 P P P P P P H H H H
6-6 H H P P P H H H H H
5-5 D D D D D D D H H H
4-4 H H H H H H H H H H
3-3 H P P P P P P H H H
2-2 H P P P P P H H H H

About

Posted in by stephenhow on February 18, 2009

The author of this blog loves gambling. Or at least he likes obsessing over games, writing programs for them, and daydreaming about ways to beat the house. In reality he always bets the minimum amount, and lets the house take their $.02 edge per $5 hand (see Spanish21). Occasionally, there’s something worth sharing with players, so he posts it here.