Author: Vincent Diepeveen
Date: 16:56:41 03/26/01
Go up one level in this thread
On March 26, 2001 at 18:02:44, Christophe Theron wrote:
Now please let your calculations shine over a quad.
I simply search 2 ply more on a quad as on a single cpu machine.
a) bigger hashtable
b) memory completely parallel
c) harddisks are about 20 times faster as my slow IDE harddisks
d) because of the big crap the processors search you hardly
doubt in your mainline so you skip a lot of expensive researches
at different plydepths, of course that's the reason you get 2 ply
more as from speedup viewpoint it shouldn't be 2 ply.
Most important is that instead of 10 to 11 ply i search 12 to 13 ply.
Of course for Tiger which already gets 14 ply single cpu the different
from 14 to 16 will be less significant as it would be from 10 to 12!
This last is especially a thing which you shouldn't forget in your
calculations.
Getting from 5 to 7 ply is hell more important as getting from 15 to 17!
But in general i agree that faster hardware is less important as
getting yourself a bug in evaluation fixed!
Greetings,
Vincent
>I have seen a lot of messages recently from people who want to buy a dual
>processor computer or motherboard and are asking what is the best around.
>
>Out of curiousity, I sat down in front a sheet of paper, grabbed a calculator
>and started some computations.
>
>I wanted to have a better idea of how much better is a dual processor computer
>for chess, over a single processor one.
>
>Here is the result of my homeworks:
>
>
>
>
>
>HOW MUCH FASTER ?
>-----------------
>
>Experts (Bob included) say that with current parallel algorithms, the SMP
>efficiency ratio for a dual processor computer running a chess program is 1.7.
>
>That means that a biprocessor computer (a "dual") is going to compute
>1.7 times faster than a single processor computer, assuming a SMP chess
>program is running on both and that the processors are identical.
>
>From this we can estimate the ELO difference between the two computers.
>Assuming the generally accepted fact that doubling the speed of a computer
>adds 70 ELO points to its playing strength (and this might actually
>be less when we go to higher and higher frequencies), the formula
>to compute ELO increase from speed increase is:
>
> ELOdiff = 70 * log( SpeedRatio ) / log(2)
>
>So if SpeedRatio=1.7, we can expect a 53.6 ELO points increase (rounded to
>the first decimal) from a chess program running on a dual machine rather than
>on a single processor one. Keep in mind: assuming same processors and same
>processor frequencies.
>
>
>****************************************************************************
>** We expect a 53.6 ELO points difference between a single processor **
>** and a dual processor computer (both running at the same clock freq.) **
>****************************************************************************
>
>
>
>WHERE CAN I BUY ONE ?
>---------------------
>
>Unfortunately, while it is possible to get the highest available frequencies
>for single processor computers, it seems that it is not possible (at a non-
>astronomic price) to get these frequencies for dual motherboards.
>
>As I understand from discussions on CCC on the topic, while you can easily
>get an AMD ThunderBird 1.2GHz single processor machine for a reasonnable price,
>it seems to be almost impossible to get a dual MB with this processor. Looks
>like you'll get a dual AMD TB 1GHz at best, if you are ready to put your
>money on it (but then forget about the latest and sexiest Nokia, the money
>for it will go into the dual :).
>
>So now we should re-compute the speed ratio to get real world figures.
>
>On one hand you have a 1.2GHz single processor machine, on the other hand you
>have a dual 1GHz one. The dual is much more expensive than the single.
>
> SpeedRatio = 1.7 * 1 / 1.2 = 1.417 (rounded to 3 decimals)
>
>The corresponding ELO increase is:
>
> ELOdiff = 70 * log( SpeedRatio ) / log(2) = 35.2 (rounded to first decimal)
>
>
>****************************************************************************
>** So the expected ELO difference between a single 1.2GHz processor **
>** and a dual 1GHz one is about 35 elo points. **
>****************************************************************************
>
>
>
>35 ELO POINTS BETTER, REALLY ?
>------------------------------
>
>There's something else that should be taken into account. Unless your dual
>pet has 2 HD controllers and 2 independant hard disks, your processors are
>actually going to share a single hard disk when they begin to acess endgame
>tablebases.
>
>So in the endgame, you can expect tablebases to be less efficient (twice as
>less efficient) on a dual computer. Experts say that tablebases generally
>increase the strength of a program by 20 to 40 ELO points. From this it is
>possible that you lose 10 ELO points when you are using a dual processor
>computer with only one hard disk.
>
>
>****************************************************************************
>** So in the end the ELO difference between the fastest **
>** single processor PC and the fastest available dual **
>** processor PC might be 25 ELO points, maybe less if **
>** doubling the speed does not give a 70 ELO increase **
>** on nowaday computers. **
>****************************************************************************
>
>
>
>NOW LET'S COUNT OUR BEANS
>-------------------------
>
>What does it mean, 25 ELO points ? What are we talking about exactly ?
>
>A difference in ELO points in real life turns into a winning percentage.
>That's exactly what ELO means, and how it is computed.
>
>For winning percentages above 20% and under 80%, there is an approximated
>formula that works pretty well:
>
> ELOdiff = ( WinPercentage - 50 ) * 7
>
>From this you can deduce how to compute WinPercentage if you have the ELOdiff:
>
> WinPercentage = ELOdiff / 7 + 50
>
>If ELOdiff=25, then WinPercentage = 53.57% (we are between 20% and 80%
>so our above formula applies).
>
>So we are talking about a difference of 3.5 games each time you play 100.
>
>
>****************************************************************************
>** When you play 100 games with your dual 1GHz against **
>** your single 1.2GHz, you can expect the dual to win typically **
>** by a 3.5 games margin. **
>****************************************************************************
>
>
>
>HOW MUCH GAMES SHOULD I PLAY TO DEMONSTRATE THAT MY DUAL IS BETTER ?
>--------------------------------------------------------------------
>
>However, you must also take into account randomness. As you know, a chess
>match has some randomness (some luck is involved, either in the choice of
>the opening, of during the game itself in very unclear positions).
>
>For example, if you want to be 90% sure about the result of your 100 games
>match, it is wise to account for a +/-6.5 percent margin of error. If we take
>the aforementionned match, which is likely to end in a 53.57% win for the dual
>(in a perfect world! :), then it means that you will routinely get results
>between 47% (the dual actually loses!) and 60% (the dual wins clearly).
>
>So obviously, running a 100 games match dual against single is not enough
>to demonstrate the superiority of the expensive dual.
>
>Let's have a look at statistical tables. What we need, obviously, is to have
>a margin of error under 3.57%, so every time we play a match dual against
>single, the dual has the most chances to win (more than 50% chances to
>win).
>
>Here it is: you need to play at least 400 games. For 400 games, the margin of
>error for 90% reliability is 3.34% (for 300 games it is 4.72%, which is still
>too high).
>
>
>****************************************************************************
>** If you want the dual to win 90% of the matches against **
>** the single processor computer, then you need to play **
>** 400 games matches. If you play shorter matches, the **
>** single processor computer actually has significant **
>** chances to win the match. **
>****************************************************************************
>
>
>
> Christophe Théron, March 26th, 2001.
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