Author: Christophe Theron
Date: 09:37:24 03/27/01
Go up one level in this thread
On March 27, 2001 at 08:09:48, Paul Petersson wrote:
>On March 26, 2001 at 18:02:44, Christophe Theron wrote:
>
>>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 :).
>>
>
>Hi Christophe!
>
>I think it would be more fair to compare a single CPU machine with the same CPU
>in a dual.
That's what I have done in the first paragraph.
However it is not really useful because in real life you don't have simply the
choice between single CPU X and dual CPU X, but generally it's single CPU X or
dual CPU Y, where Y is significantly slower than X.
> A dual Athlon motherboard is almost impossible to buy anyway.
You see what I mean. In real life, you have to make a compromise.
My intention was to show that after you have done your compromise, what you get
with a dual is hardly better than what you get with a fast, single processor,
PC.
> If you
>look at the most common dual system, a dual P3, things look very interesting.
>For a reasonably small extra cost (mainly an additional CPU) you get a system
>that will run about 75 percent faster for dual capable programs. For now the
>highest speed of a P3 is 1 GHz but soon (sic!) there will be a 1133 MHz which
>will compare very favorably with an Athlon 1200.
And at that time you'll be able to buy a faster Athlon.
Let's compare what is available right NOW.
>I have done some testing myself on an old dual Celeron 466@560 MHz. I mainly
>used Crafty and DeepJunior. I got almost exactly the performance increase that I
>expected. Crafty ran three times faster on my dual compared to the Crafty on
>SSDF's list (K6-2/450).
Maybe I'm missing something, but three times faster isn't what is expected...
> The testgames indicated a performance around 2580-2590,
>ie 100 points higher than on the K6.
>
>
>>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.
>>
>
>I think this is unclear. Some tests need to be done to see if points are lost or
>not.
>It is probably best to avoid IDE drives when using a program with very
>aggressive tablebase access. By using SCSI drives you could perhaps reduce the
>problems to a minimum.
>
>
>Paul
And by using a SCSI drive you would also increase the rating of a single
processor CPU, so the problem remains.
Christophe
>>****************************************************************************
>>** 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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