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Problem with using the expected value to choose which variant to play next is, your current expected value assumes I will win the game unless it is unwinnable. That might be good for you, o mighty sir, but it’s highly unrealistic for me. How about two rows in your table, the EsubP you have now (P for perfect) and an EsubH (H for historical) which uses my actual historical win percentage on the variant to figure the expected result.

How about T (theoretical) and P (practical)? Can you give and example for P? Say 4x8; you have 38.25% and the therotical value 81.34% What should I do?

I dunno. I haven’t looked at what you are already doing, and also I’m not at all confident I know the right thing. Here’s my thinking: If Sw is the score you’d have by winning, Sl by losing, Pw is the probability of winning, and Pl the probability of losing, and S is your current score, then I guess I would have said that E = S + (Sw - S) * Pw + (Sl - S) * Pl Then set Pw to nr-winnables/32k for the theoretical and to the user’s current win percentage for the practical, and Pl to 1-Pw. I admit you don’t have climate-specific info for the practical but it isn’t going to make very much difference that you don’t. But like I say, I might be completely wrong here. So feel free to shoot it down.

I use different probabilities depending on the user's current level. Your 12x0 has these: win percent: 88.11% average time: 4:32 minutes approx. avg. streak: 8.4 Can %88.11 be used for all levels? Maybe you have a better winning percentage at level 7 or 8 than 88.11%.

I know. That’s why I said “I admit you don’t have climate-specific info for the practical”. But I do still think it would be useful. I played a bunch of 5x7s today because your table showed me they yielded the best new expected value. But history shows me, as captured in my win pct for 5x7 (and reconfirmed today, sadly), that i’m not capable of playing near enough to the theoretical 5x7 maximum to make that a true assessment. For such variants as 5x7 practically all of my plays are at climate 5 anyway, so there isn’t much climate difference to be had even if we did have it.

By the way, thanks for the table, it’s great! I only noticed it this weekend, has it been there a while?

I was planning to do it but free's stats were not complete. So after cellmate came up with the complete set, it was implemented. I have added an option for it. Since I am not interested in it, you need to check it (click '+' button to the upright) much like Denny's announcement checkbox (unchecked by default in this case).

My formula, which was supposed to always produce an E between the lose-value and the win-value, doesn't. *Self Bonk* I guess the real formula is just S + (Sw - S) * Pw. What was I thinking?

Sometimes you get higher expected values than the theoretical ones if your percent is higher than the expected percentage. For example check my practical values for 4x9, 5x8, 6x6, 8x3, 9x2 in (11-12-13) competition. I simply used this formula: E_p = Prob_for_win*score_if_won - (1-Prob_for_win)*score_if_lost

Hop, thanks for fixing it so reloading the page doesn’t forget which score-set you were looking at. That helps a lot! The e_p score really ought to be score-if-lost + ((score-if-win - score-if-lost) * prob-of-win), where the prob-of-win is just set to the user’s current win percentage of the variant. That way it can’t fall outside the range of (score-if-lost, score-if-won) since win percent is in (0,1). I looked at your code and I apologize for even asking, you went to a lot of trouble. I thought all those numbers were just lying around already. Sorry!

Isn't it similar to this one? The Expected Value of a Roulette Wheel Although there are many ways to bet on the 38 numbers of a roulette wheel, one simple betting scheme is to place a bet, let’s say $1, on a single number. In this case, the casino pays you $35 (you also keep your $1 bet) if your number comes up and otherwise you lose the $1. What is the expected value of this bet? SOLUTION: We can think of this betting scheme as an experiment with two outcomes: 1. Your number comes up and the value to you is +$35. 2. Your number doesn’t come up and the value to you is -$1. Because there are 38 equally likely numbers that can occur, the probability of the first outcome is and the probability of the second is . The expected value of this bet is therefore (1/38)*35 + ((37/38)*(-1)) = 0.0526 Hmm. Looking at this example, I think I should change it to: E_p = Prob_for_win*(score_if_won-current_score) + (1-Prob_for_win)*(score_if_lost-current_score) If rearranged: E_p = Prob_for_win*(score_if_won-score_if_lost) + score_if_lost-current_score Now it's very similar to yours but there should also be a current_score term in the equation. Do you agree?

As I see it, current score is already built into score-if-win and score-if-lose (the first two lines of your table.) It wouldn’t be correct to introduce it again. That’s kind of the mistake I made back in the third post.

"current score is already built into score-if-win and score-if-lose" No. My 11-sum results: HopDiriDiriDattiriDittiriDom (180.990) 4x7 5x6 6x5 7x4 8x3 9x2 10x1 11x0 New score if won: 210.123 191.242 181.863 181.930 181.355 181.546 181.721 185.722 New score if lost: 90.495 60.330 31.750 32.235 26.901 29.057 30.641 47.537 #unwinnables: 14.474 2.459 1.850 241 201 450 2.215 7.205 % to hit an unwinnable: 44.171 7.504 5.646 0.735 0.613 1.373 6.760 21.988 Expected value: -23.708 428 -7.602 -161 -583 -1.538 -9.481 -25.652 Expected value (P): -13.591 -2.216 -8.089 -7.696 365 -1.374 731 126 Time left to age off: 23h 46m 1d 11h 1d 11h 1d 11h 12d 13h 1d 15h 1d 13h 1d 12h For 4x7: Current: 180990 If-won: 210123 If-lost: 90495 ? (210123-180990)*(2^15-14474)/2^15 + (90495-180990)*14474./2^15 %1 = -23708.05444335937500000000000

Ok. For some reason I was seeing the expected value line as “expected resulting score”, in other words as if you added the current score back in again. You and I are in agreement since that line is really “expected change in score”. Don’t know why I saw it that way. Sorry.

I see the + on the upper right on Joey's standings page, but where do you find the expected value calculator there?

Do you mean "Joey's" option? If checked I use the user's win loss stats to come up with a probability as suggested by Joey. Then the calculation is as above.

Oded, Maybe I misunderstood you. Did you try to click player names?

Yeah right, forgot to do that, lol. Did you decide moving player names to the right?