Pushing this old thread of mine back to the top hoping to show those interested that in fact the "math" of the game defines it as negative, with some bets definitely "better" than others. One thing that perhaps is not obvious about the'Table of the Game' is that the "Win probability with number rolled vs, Seven out" (Column 2) defines statistics that apply only during the come out roll, so that Craps numbers give zero win probability and Naturals are guaranteed winners. This is corrected for in column 3, the probability that a number is rolled. This probability, and the way it relates to the same probability for the seven, defines the odds of the numbers in the game. Now think about this. A naked pass or come bet, without odds is 49.3% likely to win. Logically, these bets are 50.7% likely to lose. Because with place bets there is no opportunity for a come out winner, percentages are: 3 out of 9 = 33.3% likely winner on the outsides, 66.7% loser 4 out of 10 = 40.0% likely winner on the odds, 60.0% loser, and 5 out of 11 = 45.5% likely winner on the insides, 54.5% loser. All such wagers are significantly worse than the contracts, mathematically speaking. Their benefit involves the non-contracted nature of the bet. I am not much of a place bettor. To those who are: is the benefit worth the mathematical disadvantage?