With all the recent discussion about betting on random-rollers, I thought you might like to see how frequently multiple 7-Out’s will occur in a randomly thrown game.
To better understand why it’s easier for a random-roller to 7-Out than it is for him to repeat his Passline-Point; we have to look at how those wins and losses actually happen.
On an individual basis, a random-rollers PL-Point has the following chance of being repeated before a 7-Out.
Ø When the PL-Point is either a 4 or 10, there is a 33.3% chance that a random-roller will make his Point, and a 66.6% chance that he won't.
Ø When the PL-Point is either a 5 or 9, there is a 40% randomly-tossed chance that it will be repeated before a 7-Out, and a 60% chance that it won't.
Ø When the PL-Point is either a 6 or 8, there is a 45.4% chance of being repeated, and a 54.6% chance that it won't.
All of this means that, on average, a random-roller has a blended 39.56% chance of repeating his PL-Point before 7'ing-Out...and a 60.44% chance that he won't.
So let's first consider the chances of a random-roller throwing multiple PL-Point winners in a row:
~Well, we know that, on average, a random-roller has a 39.56% chance of repeating his PL-Point...and a 60.44% chance of not being able to do it.
~There is a 15.6% chance of a random-roller throwing TWO PL-Point-repeaters in a row. That means 1 out of 6.4 random-shooters will successfully roll two PL-Point winners before 7'ing-Out.
~There is a 6.2% probability of a random-roller making it three PL-Point-repeaters in a row (about 1-out-of-every-16 shooters). That equates to about one shooter out of every rotation of the table.
~Thereafter, a R-R has a 2.4% chance of completing four-in-a-row (1-in-40 shooters), while only 1% will roll five PL-Point winners in a row. Yes, that is only 1 out of 100 shooters who will make it this far.
~Out of them, only 0.4% (1 out of 250 random-rollers) will successfully complete their sixth PL-Point.
~When you combine the 1-in-250 shooters who will make six PL-Point winners in a row, you can see by its relative rarity why the occurrence of a random-roller throwing six PL-Point winners in a row is such a cause for raucous celebration and an abundance of high-fives.
That brings us to the main question; of How frequently do multiple 7-Out’s in a row occur in a randomly thrown game?
~There is about a 60.44% (6-out-of-10) chance that a random-roller will 7-Out before repeating his PL-Point.
~There is a 36.5% chance that two random-rollers will 7-Out one right after the other.
Now individually, any given random-roller’s average chances of 7’ing-Out before he’s able to repeat his PL-Point remains at 60.44%; however when you look at the cumulative probabilities of several events in a row happening (or not happening) over an extended number of trials; then we can determine, on average, how frequently multiple non-PL-Point-repeating 7-Out’s occur in a row.
~There is a 22% chance that three random-rollers will consecutively 7-Out in a row.
~There is a 13% chance that four random-rollers will consecutively 7-Out in a row.
~The chances that five random-rollers will 7-Out in a row, is 7.8%.
~There is a 4.7% chance that six random-rollers will consecutively 7-Out in a row.
~There is a 2.8% chance that seven random-rollers will consecutively 7-Out in a row.
~Finally, there is a 1.7% chance that eight random-rollers will consecutively 7-Out in a row.
Now obviously these figures do not include C-O winners or losers...only PL-Point repeaters. I'll save those C-O winners and losers figure for another day and another discussion.
In the meantime, when someone comments about how chopping or cool the table-conditions seem to be, or you start to wonder why your 'enlightened' random-betting is not generating the kind of money you believe it should be; then consider How Frequently MULTIPLE Random 7-Out’s Occur in a Row; and perhaps you’ll want to completely re-evaluate the kind of bets that you currently make on random-rollers.
Good Luck and Good Skill at the Tables…and in Life.
The Mad Professor
Copyright © 2007
