But rolls tend to even out in a much longer race,
[snip] Rolls, are in fact, the only reason I would ever be able to beat Shane in a race to 11.
Now if I played him in a race to 100, I would never get enough rolls to win that match.
Definitely agree that longer races even out the rolls.
My main point is mainly that the race doesn't need to be as long as people think.
100 is usually overkill. The bigger the skill gap, the less necessary it is.
Let's say you shoot pretty good and are capable of beating shane 40 out of 100 games.
Yes, in a race to 100, you got almost no chance.
But in a race to 11, your chances still suck... Only 17%.
So my point is, do we REALLY need a race to 100 for BieberLover vs. SVB?
if you said "I will only play a race to 11. Nothing longer."
then Shane should have no problem saying "Bet."
you just proved mine and others points to some extent.
[snip] Shane should win a race to 11 around 5.8 out of 10 times.
Now change that to a race to 100 and Shane wins it 7.2 out of 10 times. That difference is HUGE.
Well, I can see where people would feel 14% is not trivial. Fair enough.
The math is actually clearer if you use 7 sets.
Race to 11: underdog wins almost exactly 3 out of 7.
Race to 100: underdog wins almost exactly 2 out of 7.
If you KNOW you will only have *one* chance to play this underdog, and you're the better player,
then of course you want the longer race.
But if you know they will be willing to play you several times, it might actually be more profitable
in terms of dollars won per hour, to just stick with the short sets. You're winning more often than
you lose either way, so why invest 9x more time and effort (race to 100 vs. race to 11)
to get [probably] the same result?
I'm not sure where you're grabbing your statistics from [snip]
Here's how I'm doing the math. Others have called it bullshit it's cool if you think the same
If you can calculate a player's edge as a percentage (like, say, Shane is 4% better than Dennis)
then you can get an exact probability for Shane to win any given game. Which would be 52%.
In other words if they played 100 games the likely outcome is 52 wins for Shane, 48 wins for Dennis.
Once you have the odds of winning a game, you can calculate the odds of winning a set.
The formula for figuring that out is here:
http://www.mathwords.com/b/binomial_probability_formula.htm
But the easiest way to do it, is to use this online calculator:
http://stattrek.com/online-calculator/binomial.aspx
What we're interested in, is figuring out how likely it is for the underdog to score an upset,
for various races.
So on the calculator page, you put in Dennis' odds of winning (
0.48) as the
'probability of success in a single trial'.
Convert "Race to" into a "Best of" in your head - Like race to 11 is the same thing as best of 21.
Race to 100 is the same thing as best of 199.
So to get Dennis' odds in the race to 100, just plug in
199 for the number of trials.
Plug in
100 for the number of successes. Click
calculate.
The last figure is what we're looking for... that's the odds of the underdog winning 100 or more games.
That's IF the odds of winning each game is truly 48% and never changes for the entire set.
But of course we know momentum, mood, and other intangible stuff can change everything.
The main point I was trying to make is not "race to 11, race to 100, meh, pretty much the same".
I'm just saying that for MOST cases, race to 100 is overkill, (see SVB vs. Bieber above).
In cases where have two very close players (SVB vs. Orcullo),
it doesn't REALLY guarantee the better player will win.
70/30 is good but I wouldn't bet my life savings on it.
If you wanted to make the race long enough that the better player wins 90% of the time,
even a race to 1000 wouldn't get you there. Close but not quite.
Once you accept that, then you might as well stop worrying about
"let's make the race so long that the better player
always wins" because that's nearly impossible.
Instead, play around with the rules or equipment to ensure the cream rises to the top.
Or stop worrying so much about making sure the better player wins, and just look at the race as
"Here's who happened to play the best on that particular day" rather than
"Here is absolute proof that Joe is better than John".
We didn't need 100 to know Shane plays better than Mike D.
And 100 wasn't long enough to guarantee Shane always beats Alex Pagulayan.
