With the increasing and continued bluster over biased dice, it causes me to think about why I never won a game of Monopoly. It's has to be bias dice!  
 
If the manufacturing of casino dice is so careless as to produce bias dice, I have to question the efforts put into the making of dice for board games. Board game dice must be out of compliance. No way for backgammon to be fair either. I mean, really, who's going to spin balance the dice for board games and measure whether they are square with a micrometer. Okay, besides my cheating little sister ... Parker Brothers' you're crooks.  
 
It amazes me, all the attention that casino dice receive, and how they are increasingly linked to casino cheating. If the "Players Union" is dead set on bringing cheating casinos to their knees, why not go after real, identifiable roots of cheating. What's that, about which I speak? My friends, it is the damn rules by which we willingly submit to, like lemmings waddling to sea ... the house odds. Even to play with true odds, a craps game would be difficult enough for the player. But no one wants to hear that, cause changing the rules ain't gonna happen bro. The house vigorish guarantees that the oil well will keep pumping. So, let's all play as an ostrich, and deny the obvious cheating in the game of craps. It's kind of like giving the Yankees two and a half runs when they play the Red Sox. The Yankees don't need the 2.5 runs to beat the Red Sox, but they'll take them, just in case. It's not the stripes. It's the Yankee's vig.  
 
I just don't get the "how come". "How come" place bettors are happy to receive less than they deserve? How come the same place bettor is so concerned about the minuscule indifferences of biased dice and, at the same time, succumbs to the vigorish like it's a part of the game? Oh, right, it is?  
 
Seriously now, let's expose the problem with place bets. When the Place Bet does win, it pays less than the true mathematical odds. In the case of the 6 and 8, the pay-out is 7/6 instead of 6/5. These two deficiencies explain why the casino's best customers are Place Bettors. Hits on the six or eight, are only going to pay around 1.17 units (7 to 6). Second, over 36 rolls, if a place bettor bets $12 on the six every roll, he will win 2.27273 times. The Place Bettor should receive a payout of $14.40 ($12 x 1.2). Instead, however, the place bettor gets a payout of $14.00. Over 36 rolls this amounts to a ($0.4 x 2.27273) or $0.91 tax for the $12 place bettor on the six, and the eight too. It gets worse for the other box numbers. Do you see how it is a game with the numbers? Do you see how, over a lifetime career of playing craps the house-advantage works against the player on every roll for every bet? The higher the house odds, the higher the tax the player pays. Does that cause you to cringe more than wondering about microns? (one-thousandth of a millimeter, 0.001 mm, or about 0.000039 inches)  
 
Wait a minute, where's that math come from? Okay, here,s the rest.  
 
Let's look at the six. As we know, 5 times out of 36, the shooter will establish six as a point. If he does roll a six for a point, there are 5 ways to roll a six before a seven (the shooter wins) and 6 ways to roll a seven before a six (the shooter loses). So the chance over 36 rolls of a shooter winning on a six is (5x5/11), or 2.27273 times.  
 
The chance for a shooter to seven-out (having established six as the point) is (5x6/11), or 2.72727 times. Note that 2.27273 + 2.72727 = 5 and recall that 5 is the number of times over 36 rolls that a shooter will establish 6 as a point. Cool?  
 
The math for the eight is, of course, the same as the math for the six.  
 
I guess if toy dice are good enough for Monopoly, the only real concern about cheating is my little sister ... and that's why I decided to quit playing the game. You can't beat cheaters, so there's not point in trying.  
 
Michael Vernon - Copyright 2013  
 
PS If you still insist on playing Monopoly, do not watch this clip.  
http://www.youtube.com/watch?v=e71mQWoNtTQ
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