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The Unbalanced Over/Under card counting system, developed by Arnold Snyder, identifies profitable betting opporunties on the blackjack Over/Under Side Bet. The Over/Under side bet can provide blackjack players with an edge far greater than the edges attainable through normal card counting. In fact, the edge available with Arnold Snyder's <i>Unbalanced Over Under Count</i> is in the neighborhood of 2-3%. The Over Under side bet originated in Nevada casinos but is primarily available in casinos in Asia and Eastern Europe right now. Unbalanced card counting systems can provide close to the full power of balanced card counting systems, including for the Over Under side bet.
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By Arnold Snyder
[From Blackjack Forum Vol. XI #1, March 1991]
© 1991 Blackjack Forum

It’s been a year and a half now since I published my Over/Under Report. [Editor's Note: The Over/Under Report is now available in the Blackjack Forum Online library.] Since that time, the number of casinos offering the over/under rule at their blackjack tables has continued to climb. Not a few serious players have also discovered the many cruise ships that are offering the over-under rule. Since cruise ship games are typically heat-free, allowing min-to-max spreads without countermeasures, card counters who can afford $100 bets are finding that the potential win on “cruises to nowhere” more than justifies the cruise expense. Prior to the introduction of the over/under rule, the otherwise lousy rules on cruise ships, always in shoe games and usually with unexceptional penetration, failed to attract serious players.

According to Caesars Tahoe pit boss, Ken Perrie, who invented the over/under rule and markets the distinctive over/under table layout, more and more casinos all over the world will be opening over/under tables in the near future.

The Huxley Corporation (London) handles marketing of the over/under rule in foreign casinos. They report sales of over/under table layouts to casinos in Yugoslavia, Poland, Turkey, Czechoslovakia, South Africa, Canada and the Isle of Man. Ken Perrie is currently negotiating with casinos in the Bahamas and Aruba to begin testing the over/under rule on some tables. He has also been negotiating with all of the Atlantic City casinos to begin field testing over/under games. Two riverboat casinos running out of Iowa now have the over/under rule on all blackjack tables—the President’s Cruise Line and the Dubuque Belle. There are also 10 to 20 over/under tables scattered throughout various of the Deadwood, South Dakota casinos. As previously reported, the Ojibwa Indian Reservation Casino in upper Michigan also has over/under tables.

All of the blackjack tables on the Royal Caribbean Cruise Lines ships now offer over/under bets, as do all tables on the Dolphin Cruise Lines. The Carnival Cruise Lines have some over/under tables available on all ships. The Norwegian Cruise lines, Kloster Cruise Lines, Atlantic Maritime Cruise Lines, and Princess Cruise Lines offer over/under games on some, but not all, ships.

In Northern Nevada, you’ll find over/under tables at Caesars Tahoe, Hyatt Lake Tahoe, and coming soon to Harrah’s (Stateline), Harvey’s and the Horizon (formerly High Sierra). In Reno, over/under bets are still offered on all tables at the Comstock Casino and on one two-decker at the Peppermill. The Comstock has recently undergone a management change, and according to one dealer, their over/under games will be restricted to the new shoe games they are installing. Bally’s has taken out one of their two over/under tables and the other is reportedly open only in the evenings. You’ll also find an over/under table at Stockmans (in Fallon) and at the Red Garter (in Wendover).

In Las Vegas, you’ll find over/under tables at Caesars Palace, the Golden Nugget (which has more over/under tables coming—hopefully with higher limits!), the Holiday, Whiskey Pete’s, the Silver Nugget, and coming soon to the Tropicana.

In the fifteen years I’ve been observing casino blackjack, I don’t recall any new rule spreading so fast or so widely. The reasons for the popularity of the rule are many. It’s an easy rule for players to comprehend; it’s easy for dealers to incorporate into the game; it has no significant effect on any other aspect of the game; from the players’ perspective it’s an attractive betting option; from the casinos’ perspective, the house edge is four to five times higher on over/under bets than on the regular blackjack hand.

The rule attracts amateur counters and wannabe counters like flies because it seems so easy to beat. In fact, very few over/under bettors make any money on their over/under bets. Standard blackjack card counting systems just don’t work very well for over/under bets.

I’ve been receiving many letters from players who have purchased, or are considering purchasing, my Over/Under Report. I’ve recently used John Imming’s RWC simulation software to answer the three most common technical questions I get.

Question #1: “All of the predicted win rates in your Over/Under Report are derived by mathematical analysis using your calculated effects of removal with Hi-Opt I frequency distributions. I’d love to believe your estimates, but couldn’t you run some computer simulations to back up your predictions?”

Using the RWC software to test the 1- and 2-deck Reno games, with both 67% and 75% shuffle points, what follows are the win rates after 40+ million hands each, using the Over/Under Count, as published in the Over/Under Report. I used a flat-bet strategy, a 1-to-2 spread, and a 1-to-4 spread.

  Flat 1-to-2 1-to-4
67% dealt: 1.66% 2.49% 3.25%
75% dealt: 2.15% 2.97% 3.62%


  Flat 1-to-2 1-to-4
67% dealt: 0.53% 1.12% 1.70%
75% dealt: 0.87% 1.55% 2.16%

You can see here why I advise counters in hand-held over/under games to flat bet, especially if there’s decent penetration. You can get a healthy edge with a flat bet and you’re less likely to wear out your welcome.

Caesars Tahoe has 6-deck over/under tables. They’ve also recently made their rules better: Vegas Strip rules with double after splits and late surrender (just like Caesars Palace in Las Vegas). The following chart shows what the over/under count gets in the Caesars game. The over/under count surrender indices were not published in the Over/Under Report. Use these:

  9 X A
16 +1 -2 -1
15 +3 -1 +2
14   +3  


  Flat 1-to-2 1-to-4
67% dealt: 0.01% 0.22% 0.57%
75% dealt: 0.18% 0.50% 0.97%


I also simulated the standard (no surrender) 8-deck Atlantic City game, with the typical 2 decks cut off (75% penetration), but I put in the over/under option:


  Flat 1-to-2 1-to-4
75% dealt: -0.06% 0.20% 0.55%


If you compare these computer simulated win rates with those predicted in the Over/Under Report via mathematical analysis, you’ll find that the mathematical analyses were quite accurate.

The next most common question I get is: “Wouldn’t it be helpful to know the over/under indices for ‘standard’ card counting systems? I use the Hi-Lo Count, and I can’t see learning a whole new counting system for the few over/under games available. How much potential gain is there for the Hi-Lo Count with optimal over/under bets?”

Using the Hi-Lo Count, you should place the over bet if your true count is +5 or higher, and you should place the under bet if your true count is -8 or below. Let’s compare the win rates of a player using the Hi-Lo Count with and without these over/under indices in the 6-deck Caesars Tahoe game (using Wong’s Professional Blackjack strategy indices for other playing decisions), along with the win rates of a player using the Over/Under Count, as published in the Over/Under Report.

This is how the count values compare:


  2 3 4 5 6 7 8 9 X A
Hi-Lo +1 +1 +1 +1 +1  0  0  0 -1 -1
O/U +1 +1 +1  0  0  0  0  0 -1 +1


And, these are the win rates:


  Flat 1-to-2 1-to-4
Hi-Lo (no o/u) -0.23% +0.05% +0.41%
Hi-Lo (with o/u) -0.14% +0.16% +0.52%
O/U +0.18% +0.50% +0.97%


So, in this 6-deck game, a Hi-Lo counter can get about a tenth of a percent extra if over/under bets are allowed. Hi-Lo players should note that there is virtually no gain whatsoever on the under bets. Although the under bet should be placed at a true count of -8 or below, which rarely occurs, you should not increase your bet until your true count is -11 or below, which will almost never occur in a shoe game. Until your count gets to -11, the expected loss on your blackjack hand exceeds the expected gain on the under bet. From -8 to -10, the under bet just acts as a hedge to reduce your loss.

For this reason, if you typically table-hop with the Hi-Lo Count, you should continue to do so in over/under games, but take advantage of the over bet at +5 or higher. With the Zen Count, place the over bet at a true count of +6 or more. With Hi-Opt I, make the over bet at +4 or more. If you side-count aces, with an ace-neutral count (like Hi-Opt I), adjust your ace into the plus count cards for over/under bets. If you side count aces with an ace-negative count (such as the Hi-Lo), double the adjustment you usually make to neutralize the ace, so that the value applied to the ace is reversed to a plus count. (If this doesn’t make sense to you, you probably shouldn’t be attempting to side count aces!)

If you find yourself playing in over/under games frequently, you should probably learn the Over/Under Count. The potential gains are that substantial.

With or without the over/under bets, a Hi-Lo counter would not want to sit through all negative counts in this 6-deck game with a small spread. An Over/Under counter may obtain a decent win rate in this game, even sitting through the negatives with a small spread. Deeper penetration would be desirable for any counter (natch!).

The third most common question I get is “Can’t you develop an unbalanced running count system for the over/under bets? I’ve gotten so used to the ease of the Red 7 Count that true count adjustments and strategy tables put me off.”

The main problem here is that I can’t come up with any easy running count method that will take advantage of both the over and under bets. Using the RWC simulation analyses, however, it’s easy to see that even with the over/under count, the significant gains in multi-deck over/under games come from the over bets. Since most of the over/under games available in casinos are shoe games, we can develop running count systems for taking advantage of the over bet only.

Here are three unbalanced running count systems that will work very well on over bets in multi-deck games:

  2 3 4 5 6 7 8 9 X A
Sys. 1: +1 +1 +1 +1  0  0  0  0 -1 +1
Sys. 2: +1 +1 +1  0  0  0  0  0 -1 +2
Sys. 3: +2 +1 +1  0  0  0  0 -1 -1 +2


If you are familiar with the Red 7 Count (from Blackbelt in Blackjack), these counts work the same way, except that in each of these systems, the “pivot” equals 4 times the number of decks. In other words, in a 4-deck game, the pivot equals +16, while in a 2-deck game, the pivot equals +8, and so on.

All betting and strategy decisions for these counts are made at the running count pivot. In other words, at the pivot or higher, raise your bet, take insurance, place the over bet, and alter these basic strategy decisions:

Stand on 16 vs. 9, X and A

Stand on 15 vs. X

Stand on 12 vs. 2 & 3

Double down on 10 or A vs. A

Surrender 15 vs. 9 and A

Surrender 14 vs. X


Use basic strategy for all other decisions.


This is an easy system to remember. In the 6-deck game, all betting and strategy changes occur at a running count of +24.

I computer tested System #3, which is the best of these counts, in the 6-deck Caesars Tahoe game. We’ll call this unbalanced running count system the “Over Count,” as opposed to the “Over/Under Count,” and compare it to both the Over/Under Count and the Hi-Lo (with the optimal Hi-Lo over/under indices +5 and -8).

  Flat 1-to-2 1-to-4
O/U: +0.18% +0.50% +0.97%
Over: -0.03% +0.31% +0.80%
Hi-Lo: -0.14% +0.16% +0.52%


So, even though the unbalanced Over Count is placing no under bets, the gains on the over bets are so substantial that the player may play basic strategy through all negative counts and still get the lion’s share of the potential gains in this game.

A player using the Over Count would enjoy even more substantial gains if table hopping to avoid negative counts. Despite the fact that the Over Count is a level-two counting system (aces and deuces count +2), in my opinion it is quite a bit simpler to learn and play than either the Over/Under Count or the Hi-Lo. With just a few strategy decisions that change at the same running count, as professional level systems go, this one’s a piece of cake.

The unbalanced Over/Under Count is also effective, but substantially less effective, than the Over/Under Count in hand-held games. These are the single-deck win rates:


RENO 1-DECK, 67% Dealt
  Flat 1-to-2 1-to-4
O/U: 1.66% 2.49% 3.25%
Over: 0.93% 1.60% 2.17%


RENO 1-DECK, 75% Dealt
  Flat 1-to-2 1-to-4
O/U 2.15% 2.97% 3.62%
Over: 1.28% 2.05% 2.69%


So, if you ever play single-deck over/under games, I’d advise learning the Over/Under Count with the complete set of strategy indices published in the Over/Under Report. The simplified Over Count will take substantial gains in this game, but no running count system is comparable to a balanced true count system for hand-held games.

One other question I’m frequently asked, which I’m going to answer succinctly without charts and tables: “Can I use the Over/Under Count for regular blackjack games that don’t offer over/under bets?”

Unfortunately, unless you normally play in deeply dealt single-deck games with a small spread, this is not advisable. Both the Over/Under Count and the Over Count correlate poorly to your betting decisions in regular blackjack games. If you find it impossible to learn and use two different counting systems, one for regular blackjack and one for over/under blackjack, then you’re going to have to make some kind of compromise.

Maybe you should just stick with your regular counting system and take the small gains available with over bets when available. Maybe you should learn to side count aces so that you may adjust the ace to the plus or minus side as appropriate to the game. Maybe you should take up gin rummy. The casinos are putting more and more of these over/under tables in because they are beating the majority of the players who place over/under bets, including the card counters.

The fact remains that if you have access to over/under games, and you know how to play them, these games offer the most profitable opportunities for card counters to be found anywhere. ♠

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  Red 7 card counting system  Arnold Snyder's Over/Under Report presents an even stronger balanced Over/Under system, with analysis on the edges attainable from the Over/Under side bet in games with various numbers of decks and levels of penetration. The Over/Under Report is available at Gambler's General Store in Las Vegas.