Fascinating stuff, the perfect 1980!!! Tell me please, what is the HA on the roll, immediately following the established point, being a seven?
What would probability say about that same sequence happening multiple times consecutively?
DJTeddyBear: The Rule of 495 allows only seven losses in 495 PL outcomes. Isn't that what the 244/251 purports to show to create the 1.41% HA? The example provided those seven losses in the first 20 outcomes leaving 220 outcomes to be consecutive winners. If there were more losers during the next PL outcomes the HA would be greater based on the additional number of losers produced. OR after there are seven PL losers, whenever they occur, does a new 495 PL outcomes start??
I think you are confused with "net losses" versus "actual losses" here. This rule accounts for 251 losses and 244 wins in a 495 PL outcome scenario. Seven losses in 20 trials would not account for an expected result of 220 wins, nor would 50 consecutive losses. Each PL bet resolved has an expected house edge of 1.41%, but what happened previously has no effect on what will happen in the future. As multiple people before have posted, the idea of actually hitting 244 winners and 251 losses over a given 495 PL bet stretch is fairly slim, but over a much larger figure this will be accurate.
Think of it this way. The oddsmakers for sports contests are tasked with taking in an enormous amount of information to create a "line" that they feel will be the closest to the actual result as possible. These people are the best in the world at what they do, but there are variables in such a short timeframe (one week of a season or a single game) that they cannot account for. How many times do the games match the spread exactly (+ or - .5 points)? Far fewer than when they do not get it exactly right.
The house advantage is not a steadfast rule since you cannot experience a 1.41% loss on your pass line bet, and you will either experience wild variation in the expected value no matter what happens with that single bet. If you win, you are experiencing results that are 101.41% over the expectation but if you lose that one bet, you are 98.59% under expected value. Thus, the rule can only apply for the long-term.
First, while we are speculating because your set-up is wrong, a 495 sided coin would be almost impossible to mint in a size small enough to fit into the average human's pocket. Also, with an odd number of sides, it would likely be very difficult to create a roll to package the coins in for banking purposes.
The coin is mental, not literal, representing an abstraction of the game. A toss of the coin is one settled Pass Line. The concepts are equivalent.