Sorry, Fred, but hanisch was correct, in fact, exactly correct
With all due respect to John Scarne, his ability with cards and dice was legendary, but his mathematical accumen, at least in this case, is suspect. And also with respect to you as one of the most astute gamblers to ever post on this forum, I must tell you, having just reviewed the post by hanisch, that his math is right on target. Having just worked through the calculations myself (Hey, I've taught college level statistics!), I can assure you that the number of rolls for a fair (50/50) bet, is 3.801784 (the limit of the calculator I am using). This answer is the same to the sixth decimal place as the one hanisch provided. If my math isn't persuasive, just recall that Titanic took the other side of the bet! Maybe Scarne was talking about a slightly different bet?freddy the beard said:In John Scarne's book, The Complete Guide To Gambling, he determined the odds to this proposition by multiplying the odds to one by .693 for a single event. 5 to 1 times .693 comes out to 3.465 rolls needed to make the prop a break even bet. Using 2 dice you need 24.6 rolls to roll double six.
the Beard