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I read through the review, finally (took me a while) and, though it mostly looked like a good review, I noticed these little quirks, which are counter to what I have learned and believed about the game.  I don't really have much to discuss, but I'd like clarification on these two points:

Quote from: The ReviewSo, if one player rolls 5, 3, 3, 2 while another rolls 4, 2, 2, 2, the first player has 3 victories.

It's only one victory, right?  Not 3?  Player 1 only rolled one die higher than a 4 (the highest of player 2).

Quote from: The ReviewWhat kind of dice does Sorcerer use? That is entirely up to the players and GM, so long as all the dice are the same type. Just bear in mind that, the more sides your die of choice has, the harder it is for someone with low stats to defeat someone with high stats.

I was told in a recent thread (and I believe the book says so too, but I don't have the book here at work with me) that the smaller the dice size, the greater the skew towards a higher statistic winning.  Now she's saying "the bigger the die, the less chance the lower-stat person has of beating the higher-stat person."

I guess what I'm asking is, in both situations, am I mistaken, or is the reviewer, or are we both?

1) she was wrong.  Its only 1 success.

2) Sorcerer mechanics have a fairly high chance of the lower pool winning.  A single lucky 10 against an opponent who rolls all 9s and 8s is good enough for victory.  Contrast this with Target Number and count successes dice pools where given the same TN the odds skew much more heavily towards a bigger pool.

In other words you have to be lucky in Sorcerer for a 3 die pool to beat a 7 die pool...but not as lucky as you'd have to be in Riddle of Steel.

Smaller die sizes increase the likely hood of ties.  If the high dice are tied you go to the second and then the third etc.  That means when ties are involved it isn't enough for the small pool to get a single lucky die...you have to get several lucky dice.  The more likely ties are the more of an advantage the larger pool has, because the more likely the smaller pool is to run out of high dice...or in the extreme...run out of dice altogether.

So smaller die sizes make "upset" rolls less likely.  Larger die sizes make "upset" rolls more likely.  The difference even between d10 and d6 is pretty noticeable in this regard.  Ties become common place with dice pools of 8-13 dice rolling d6s.

Quote from: ValamirSorcerer mechanics have a fairly high chance of the lower pool winning.  
....
In other words you have to be lucky in Sorcerer for a 3 die pool to beat a 7 die pool...but not as lucky as you'd have to be in Riddle of Steel.

This is correct.  3:7 would have about a 25% chance of success in Sorcerer.  I don't know what the TROS odds are off the top of my head (or if TN makes a difference), but I'm guess its is much smaller.

QuoteSo smaller die sizes make "upset" rolls less likely.  Larger die sizes make "upset" rolls more likely.

I'm not sure that is true.  The only factor that controls the overall probability of success or failure in Sorcerer is the relative size of the die pools.  The number of successes produced is influenced by the absolute size of the die pools (2:1 has the same odds as 4:2, but 4:2 may produce more successes) and also the size of the die used (smaller dice increase the odds of extreme results).  The die size effect becomes most noticable when the number of dice in the largest pool exceeds the number of faces on the die.  So it seems to me that smaller die sizes would make upset rolls *more* likely, since the smaller pool has the same odds of winning regardless of die size, but has slightly higher odds of pulling more successes if they *do* get a victory.

Hey Rafial,

QuoteI'm not sure that is true. The only factor that controls the overall probability of success or failure in Sorcerer is the relative size of the die pools.

Does that really work out? I'm a little rusty on my probability, and I haven't run all the numbers, but it seems to me that Ralph's assessment seems more on target for this. If we're rolling d4s and I have one die, and you have four, I've got a 25% shot at getting a four, and the probabilities for you are pretty much a win. If we're in the same situation with d20s, I've got a 1/20th shot, and you've got 1/5th. My overall odds are worse, but my odds of getting a 20 when you haven't, have increased, right?

Like I say I haven't run all the numbers and the devil is always in the details when it comes to heavy permutation situations like these, but am I missing something more obvious than that?

-Tim

Tied dice are removed from the pool.

In a 3 vs 7 situation, the larger pool is 2.33 times bigger than the smaller
If the high die ties the pools become 2 vs 6 and the larger pool is 3 times bigger.
If the second high die ties the pools become 1 vs 5 and the larger pool is 5 times bigger.

Thus each time the high die ties, the odds of winning between the pools that are left increases for the larger pool.

Since smaller die sizes increases the likelyhood of ties, they increase the number of times during the game the above scenario plays out.

Ralph's original statment is true, smaller dice favor the winner. This is well documented. That said, the effect is not really very pronounced, amounting to a shift of, at most, a couple of percent. And the effect gets less and less as the dice increase in sides. d20 v d100 is less different than d6 v d10 (ties just become even more infinitesmally unimportant). You probably ought to stay away from flipping Coins, though even that wouldn't be too big a deal. To get any real distortion in the curve, you'd have to roll dice that had some result that occured more often than .5, meaning doing something silly like rolling a d6 and counting 1-5 = 0, and 6 = 1.

Basically, given Sorcerer's priorities, it's a complete non-issue. The system works just as well, overall, with any dice.

Mike

I'd have to see the numbers crunched to buy that Mike.  My admittedly rough stab at it indicates that the effect...while not overwhelming, is significant enough to be noticeable to the "naked eye".  

While I agree fully that the system works just as well with any dice, I am at this point convinced that players who play several sessions with d10s and then switch to d6s will experience a noticeable reduction in the number of times the smaller pool wins.

I'm all confused now. Are we talking about how often the one pool wins over the other, or the degrees of difference by which it wins?

Best,
Ron

In my case, I was talking about how often one pool wins over another.  My results are based on a python program that I let run for several days (100,000 rolls if I remember correctly).  If there is an effect of die size on how often one pools wins over another, it is less than the "noise" in my results, >1% over the range of d6-d20, with pool sizes ranging from 1-10 dice.  The only variable I saw affect the overall odds of which pool won was the ratio of the pools.

I totally grant that the absolute size of the pools and the die type used affect the degree of difference by which one pool will win over another.

Brilliant! This is why I'm never good with these problems. I inevitably attempt to do it formulaically and can't remember the method in anything but the simplest of cases, for whatever reason I never think to do it experimentally. Does your script just dump pure winning percentages, or does it give an indication of the margin of victory averages as well?

-Tim

Quote from: talexDoes your script just dump pure winning percentages, or does it give an indication of the margin of victory averages as well?

It does give margin of victory, in fact I even have nifty graphs made with GnuPlot, but the data I have right now on margin of victory is not correct for this discussion, since it uses the Donjon varient of adding back matches to the number of success after victory is determined.  This inflates the average number of successes on victory, but does not alter the overall win/lose percentages.

Very slick. In the interest of not entirely highjacking the review thread (though we're a bit far gone at this point,) I'll drop you a private message. I'm a perl monkey, not a python guy, but I'd like to have a gander at it to see about modding it for Sorcerer. I think it'd be useful to get some probability info on the margin of winning at various die sizes.

-Tim

Quote from: talexVery slick. In the interest of not entirely highjacking the review thread (though we're a bit far gone at this point,) I'll drop you a private message. I'm a perl monkey, not a python guy, but I'd like to have a gander at it to see about modding it for Sorcerer.

It's a one line change.  Don't add back the ties.

However, I'm glad you brought it up, because it caused me to go and pull up the data files that are sitting on my disk.  I hadn't looked at them at a long time, and in reinspecting them I see my original contention that the overall die size does not affect overall win/lose percentages may not be correct.  In fact, it looks like a smaller die actually increases the chances slightly for a smaller pool.  I'll look at the data in more detail tonight.

I've done the same experiment a couple of times using spreadsheets. And repeatedly I've found the same results.

In any case, what Rafial and I both agree on in terms of results is that the differences in outcome are so small as to be unimportant. A player isn't going to notice less than a 5% difference in frequency of success. And the differences are always less than that. We can quibble about the fine details if we like, but that's the only important conclusion to be drawn.

Even if it did make a larger difference, would it matter then? Which way makes more "sense" for Sorcerer? Disparity in pools meaning more likely success, or less likely success? I can't think of any reason why it's pertinent.

Mike

Mike you are correct.  I'm baffled by how badly I misinterpreted my data when I first generated it six months ago.

I regenerated my data sets last night using the sorcerer method of discarding ties, and built the graphs into a web page for everyone's amusement.

Pool ratio is still definitely strongest overall factor in determining odds of success, but its now clear to me that die size does have an effect, which grows in step with absolute pool size.  In the ranges I ran (1-12 dice), the difference in outcomes between d20 and d6 looks to be around 5%, with smaller die sizes favoring the larger pool, as originally stated on this thread.  I stand corrected.

Also, larger absolute pools at the same ratio favor the larger pool by a slight margin.