Don't be so quick to judge you might be surprised. I am not jokingI am serious: you have not understood yet any of Uri's and my posts on that specific issue. You are too fast IMO. Uri's clarification was precise, and he never said something different. A main problem may be that "counting" or "not counting" shorter games has several different meanings, and you will only get the right meaning from the context.
Read again, please. I am not joking.
Then please try to answer my open questions. I hope everything will be cleared up soon.
No you misunderstood.There is a possible source of your misunderstanding. Uri used the word "increment" but in the sense that shorter games are handled the same way as full-length games (for both types the total_games counter is incremented). So since total_games includes shorter games there is no such "total_games + 1". And this is the same he wrote before.
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Sum = ((legal_games) / (total_games + 1)) * U(1) * U(2) * U(3) .... * U(13)
And I explained to you in my previous post why I think that this formula is not "wrong" (U(i) covering all ever possible games including also shorter games).
My legal_games, and total games are being incremented as each game is being played that is both starting from 0.
You can fix the total_games from the start but it doesn't matter. The point is those shorter games should not be in the total games count period.
Say I have counters legal_games=5 and total_games=100 that is I already played 100 games and 5 of them are legal (with no shorter game encountered so far) , and then suddenly I got a shorter win game when I play one more game i.e on my 101th test, how do you increment now ?
I am saying you leave both as they are as in (a) below
a) legal_games = 5, and total_games = 100
If you do
b) legal_games = 6 and total-games = 101
c) legal_games = 5 and total_games = 101
it becomes _biased_. And I can prove it to you but please say which one you do (a) , (b) or (c), before we continue.