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The Free Odds Fallacy  
BY:  Mike Burger

Gambling charges an ignorance tax. Much of Las Vegas and similar places is based on this ignorance tax. People do not learn to play the games right, or intelligently. Examples abound. Such as the various pay tables on seemingly identical video poker machines which make one Jacks or Better machine worth playing and another one a terrible rip off right beside it.  
 
The game of Craps is an amazing study. It contains some of the best and worst examples of bets found in a casino. They all look alike until you start taking them apart. The math is not hard, but the exact wording of the problem and getting the calculations in exactly the right way is. You can easily get turned around.  
 
One example is the long stated belief that taking free odds behind the line on pass line and don't pass bets decreases the house advantage. You see this calculation bandied about everywhere. You appear to be a fool if you do not take maximum odds behind on such bets because such bets are paid at true odds, with zero apparent house advantage. A dead even bet.  
 

Zero Sum Games
 
 
A dead even bet is a "Zero Sum Game". That is where this all falls down. Zero. When a gambling game is matched to a betting system that exactly pays fair odds on the betting options, it must over time total out to zero. You will win exactly as much as you lose on either side of the bet. Unless something is not right, like crooked dice, people pocketing chips or other kinds of cheating. Here let's assume two things. First, no cheating. Second, square dice that are a true random roll.  
 
Ask yourself "why does the Casino allow free odds bets?" Is it because they love giving gamblers a fair shake? Not bloody likely!  
 
Since Casinos live and breathe by house advantage, even a slight tilt in the game could derail the Casino's cash flow. A rake is built into each possible bet, either by the definition of the way the game is played, which can be even a small inconspicuous special rule, or by just offering bets that do not match the true odds of the game. House advantage.  
 
Basic Craps at the Passline
 
 
In basic craps that house edge on passline bets is 1.41% approximately. For every $100 you bet on the pass line, the Casino will tax you $1.41 for playing. That is their "rake" on this particular action. This will happen because of many players playing many "hands" of a game whose mechanics and rules are defined to generate this slight tilt in the odds. Of course they offer an array of really crappy [pun] bets that pay them much better per "hand" and there are people betting on those, so overall the craps game cranks out a better percentage than that.  
 
It is a widely held belief that taking free odds behind the line after the comeout roll decreases the house advantage.  
 
You can easily crank out a calculation that seems to "prove" this. How it works is even easy to "understand". Any gambling calculation that is easy to understand is suspect!  
 
You are taking the basic craps passline bet with its 1.41% house advantage, and when you take odds behind, you are making a second bet at zero sum, dead even odds. If you take single odds, one line of reasoning says you now have (0% + 1.41%) / 2 or about 0.71% house advantage at the point where you take the free odds bet behind the passline. Since you do not get a chance to make the free odds bet on every hand (many are decided immediately by craps, 7 or 11) the actual alleged affect on house advantage is a bit different.  
 
But you get the fundamental idea. This is the basis of the taking odds strategy more or less regardless of which original bet you take odds on. The house loves it. This has to be a clue that something does not gel. Why would the house keep asking you, helpfully and cheerfully, if you would like to take odds?  
 
The critical point here is you are making a SECOND bet and it is a Zero Sum Bet. Bottom line? It ain't there! A zero sum bet is a dead wash for both parties. It does not change anything. The house is still going to extract that $1.41 from every $100 on the passline bet with or without the extra free odds behind. And the extra free odds bet is going to exactly win and lose for you in a dead heat, so it is going to end up being invisible in the long run.  
What does change is the amount of money you are risking. This is what confuses people. When you take odds you are putting more money into play. This is the part the house loves. Why is a bit hard to understand.  
 
You are now risking more money to lose the same $1.41 house advantage on each $100 that winds up on the passline. In a perfect world it would all be a wash on the zero sum side, the free odds bet part of this combined action. It is that "perfect world" part that is the key.  
The world is not perfect. That is where the Casino gets its invisible edge on free odds bets. It is a derivative value for them. They have the BIG pockets. They also look out onto an ocean of betters for each hand, while each individual looks in and sees only one Casino opponent. On any given hand there are winners and losers for the Casino. Even on a single hand, life is evening out for them towards their mathematically entitled $1.41 from each $100 bet on the passline.  
 
Any Zero Sum Bet is a Contest of Bankrolls
 
 
But for individual players, they do not have deep pockets. There is a limit to how negative an individual shooter can go before they have to stop one way or another. When a player is busted and forced out, it is all gravy for the Casino. Human nature causes winners to tend to keep playing with the predictable result that they start to drop back towards that inevitable house advantage equilibrium point. Virtually no individual player quits right at his or her maximum win point. But all players have to quit when they are hopelessly busted and tapped out. Casinos eliminate human nature with strict rules and highly trained and monitored employees.  
 
What the free odds bets does is increase the money in play for each player, the amount of risk they are exposed to, and increases the volatility of their winnings, and more importantly their losses, relative to their personal bankrolls.  
 
This increased volatility increases the chances of them being busted out in a given session. The Casino with its bigger pockets and its array of players on each hand, and flow of assorted good and bad players over just a 24 hour period, can handle the increased volatility easily. The individual player is at much greater risk from the increased volatility since he or she can easily be pushed too negative to afford to stick around, waiting for the swing back towards the equilibrium point for them personally.  
 
In effect, a free odds bet is a wash over the long run if the two sides of the bet are equally bankrolled. It is a zero sum bet. It will equal zero for both sides. The casinos do not fear a zero sum bet. They realize it increases volatility which they are economically set up to tolerate.  
 
But by encouraging players to bet more, it increases the individual player's exposure and increases the absolute value of the positive and negative swings they experience. It increases the chances of a player being forced so negative they have to abandon a session as a big looser, the best possible outcome for the Casino. Drain the player, move him or her out, and slide in a new one with fresh chips! The fewer hands it takes to do this, the better for overall cash flow.  
 
Meanwhile the other bet, the money laid on the passline, is puffing along like the "little engine that could." Cranking out its $1.41 of each $100 bet on the passline just like clockwork from the player's pocket into the casino's stacks.  
 
Think of it this way, by taking free odds behind the line, you are risking a lot more money to loose that $1.41 of every $100 you place on the passline. You are ensuring a higher volatility, larger plus and minus swings and the chances that one of those negative swings will be large enough to bust you out of a session.  
 
That is all. The $1.41 remains. It makes no sense to say because you put $30,000 on the layout in odds and passline wagers combined in a session you reduced the house advantage vs. just putting the same smaller percentage without odds (say $12,000) on the passline without making the free odds wagers. The only thing that really "played" was the passline wagers, and of that the house took $1.41 of each $100. All the free odds bets did was increase your exposure to volatility, which is great if you got lucky, but ended your session much faster if you did not.  
 
So What Does Make Sense?
 
 
Much of gambling strategy is clear thinking. Unfortunately gambling calculations while they are very easy math, typically, are the dreaded "word problems" that everyone learned to hate in High School! The evil word problems center on formulating the question. Stating them exactly right is key to the getting the correct answer and very difficult.  
 
You must decide in advance how much money you are going to risk in a given session vs. the amount in your gambling bankroll. This is what a casino does each and every moment of every day. They know mathematically how much money they need in reserve for the risk on all their games and are prepared to cover all the statistical swings so they can keep cranking out the income the inevitable house advantages guarantee to them. The individual must approach the problem the same way. You have a certain bankroll to risk.  
 
In craps, you must decide how much you can afford to risk on each hand you participate in.  
Once that number is decided, NOW you can decide to put a percentage of that number onto the passline etc. and then take the rest of it in odds on the first bet. This is a good strategy!  
 
What is NOT a good strategy is to be going along betting the $5 chips that your bankroll entitles you to risk on each hand, and hearing that "odds will reduce the house advantage", suddenly start taking an extra $10 in odds on each bet or whatever odds are allowed. What this does is suddenly double or triple the amount of money you are risking on each hand, without increasing your bankroll by the same amount. You are now certain to be wiped out by the increased dollar amount swings your bankroll cannot tolerate. Some casinos offer up to 100 times odds. This is why.  
 
· So, first decide how much you can afford on each hand you participate in.  
· THEN and only then, decide if you want to take a percentage of that number as odds.  
Done this way odds is a good tool for preserving your bankroll and increasing your session life. As long as you keep the total in original bets and odds equal to what you can afford to risk on each hand based on your bankroll.  
The second you allow the siren song of "Taking Odds" to lure you into doubling or tripling your average bet, out proportion to your bankroll, the Casino has you right where they want you. In over your head.  
 
New shooter coming out...  
June 2006  

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