### Take risk when leading ? Einstein forum

5 replies. Last post: 2007-03-28

• Carroll ★ at 2007-03-27

Suppose you are playing an opponent in your range (50% winning probability) and you achieved 2-0.

Will you play more agressively ?

Suppose you manage to get a position with win/lose option, for example put a slow pawn (2/6) one away from goal and your opponent has his unique pawn left (6/6) one away from his goal. Is this bad position for you ?

No because p being the probability you win this set in one move, you have (p+3)/4 global probability which is here (1/3+3)/4 or 5/6 to win this match !

So how much risk should you take to get to this, do program here include this twist ?

• Carroll ★ at 2007-03-27

OOps in this case it is even higher because your probability to win this set is about 3/8, so global probability is 27/32…

• Carroll ★ at 2007-03-27

Hum erratum errata…

The formula :

If q (1st player) and r (2nd player) are different and position is equivalent if none won:

P(1st player win)=1/(1+r/q -r)

I applied it wrongly as if q=1/3 and r=5/6, but here r=6/6 and the first figure of 5/6 was correct.

• Jörg Günther at 2007-03-27

So what is the question?

If it is good to play some risky moves with the opportunity to win in few moves this one game and with that the match?

No, you should not. Play the move with the highest winning probability at any given time and you will maximise your global winning probability.

• hanfried_c at 2007-03-28

Since there are no draws and winning is always better than loosing there is nothing “to optimize”. As JÃ¶rg said, you should alway choose the move which maximizes your winning probability.

There is some ting “to think about” if you are much more better or worse than your opponent. For instance, if you are weak in endgames, you should try to win earlier.