Probabilty

[oneinam]

If I have a 14% advantage over each of my opponents, then what is the probability of winning 6 matches in a row?

[Buenchico]

Assuming that there are only the 2 of you, and that a draw isn't possible, your criterion of a 14% advantage implies that the probability of you winning = 0.57 (57%) and that of your opponent winning = 0.43 (43%).

So the probability of you winning 6 times in a row = 0.57 raised to the power of 6 = 0.0343 (to 3 s f) = 3.43%

[oneinam]

Buenchico, Gracias. Thank for the statistical solution. So need 29/1 is profitable

[Gizmonster]

It all depends on your interpretation of "14% advantage".
If we take it, as Chris as, that you have a straight 14% points more, then 57% and 43% is correct.

There is, however, an alternative to consider:

Assuming that a draw isn't possible, we'll take a simple example of flipping a coin.
If you're evenly matched, you both have a 50% chance of winning.
If one has a 14% advantage (as in, they win 14% more flips), then the answer is given by:
x + y = 1

and

x = 1.14y

This yields x = 0.533 and y = 0.467

This holds, as x is 14% greater than y.
/
To win 6 games on the trot = 0.533 ^ 6 = 0.0229 = 2.29%

I'm not saying Chris is wrong, it all depends on what is meant by the 14% advantage.

[Buenchico]

Thanks, GM.

I struggled a bit with '14% advantage' as it's definitely not a phrase that I would have encountered when either studying or teaching probability theory. (It's simply not 'mathematical' enough). I'm happy to agree with your answer if the definition you've adopted is the one which was meant in the question (and I'll stick with my own if I've assumed the correct definition of '14% advantage').

[shoota]

'Each of my opponents' implies there is more than one opponent....

[Old_Geezer]

But does that matter ? 6 matches all against the same or different rivals.
shrug

Anyway there can never be two of me !

[shoota]

Although I suppose that if all the opponents were of an equal skill level it would be no different to playing the same opponent 6 times.

[shoota]

It would matter if the opponents skill level varied in that you would be less likely to beat a stronger opponent than a weaker one.

[sandyRoe]

Do the figures mean that the likelihood of winning six games in a row is less that 1 in 20?

[Buenchico]

Sandy:
Irrespective of whether you use my assumption (about the meaning of '14% advantage) or that of Gizmonster, the answer to your question is definitely 'Yes'.

[redparpyman]

14%=14/100
This means that the probability in a fraction=14/600
Using a calculator, you can solve this equation, which means the answer is 2.3 reoccurring percent.

[oneinam]

Buenchico....what syntax would u use to define an advantage in this context?
E.g. If a player is able to win 57 games out of 100, how would u express the advantage?

[oneinam]

Buenochico. Also lets say a player wins twice as many games as the opponent, what is the advantage?