Skip to main content

Probability and Cumulative Dice Sums

Post a Comment

Building a Personal Supercomputer

It's time for a workstation upgrade; here's what I've assembled.

The massive case has plenty of space for additional drives to store the extreme amount of data that nearly every sport is now collecting together with the associated video footage. The case, power supply and motherboard allow up to 3 additional video cards to use as GPU units as your analytical needs demand (and budget can handle).
  1. Cooler Master Cosmos II - Ultra Full Tower Computer Case


    An absolutely massive case - plenty of room for an E-ATX motherboard, large power supply, multiple video cards and hard drives.

  2. PC Power & Cooling 1200W Silencer MK III Series Modular Power Supply


    An exceptionally large power supply, but platinum rated and plenty of room to spare allows it to operate nearly silenty, plus it'll handle any additional video cards you'll add later for GPU computing.

  3. ASUS Rampage IV Black Edition LGA 2011 Extended ATX Intel Motherboard


    Space for 4 video cards, 8 memory sticks (up to 64GB), superb quality and extreme tweakability.

  4. Intel i7-4930K LGA 2011 64 Technology Extended Memory CPU


    Ivy Bridge, 6 cores, exceptional ability to overclock. My day-to-day overclock is 4.5 GHz.

  5. Corsair Hydro Series H90 140 mm High Performance Liquid CPU Cooler


    Fits well in the Cosmos II case. Whisper quiet and keeps the CPU at comfortable temperatures even when overclocked to 4.5 GHz.

  6. (2) Corsair Dominator Platinum 32GB (4x8GB) DDR3 2133 MHz


    Total of 64GB. Top-quality, you'll need your RAM in matched sets of 4 to enable quad-channel.

  7. EVGA GeForce GTX TITAN SuperClocked 6GB GDDR5 384bit


     Top-of-the-line NVIDIA Kepler card for GPU computing. 2688 CUDA cores that reach 4800 TFLOPS single-precision and 1600 TFLOPS double-precision.

  8. (2) Seagate NAS HDD 2TB SATA 6GB NCQ 64 MB Cache Bare Drive

    Solid hard drive; you'll need 2 or more drives for a RAID 10 array.

  9. Samsung Electronics 840 Pro Series 2.5-Inch 256 GB SATA 6GB/s Solid State Drive

    Small, fast SSD for quick booting and anything bottlenecked by drive read/write times.

  10. Silverstone Tek 3.5-inch to 2 x 2.5-Inch Bay Converter

    Needed to adapt the SSD to the Cosmos II case.

  11. Ubuntu Linux


     Ubuntu Linux - what else?

Comments

Post a Comment

Popular posts from this blog

Probability and Cumulative Dice Sums

Let a die be labeled with increasing positive integers \(a_1,\ldots , a_n\), and let the probability of getting \(a_i\) be \(p_i>0\). We start at 0 and roll the die, adding whatever number we get to the current total. If \({\rm Pr}(N)\) is the probability that at some point we achieve the sum \(N\), then \(\lim_{N \to \infty} {\rm Pr}(N)\) exists and equals \(1/\rm{E}(X)\) iff \((a_1, \ldots, a_n) = 1\). The direction \(\implies\) is obvious. Now, if the limit exists it must equal \(1/{\rm E}(X)\) by Chebyshev's inequality, so we only need to show that the limit exists assuming that \((a_1, \ldots, a_n) = 1\). We have the recursive relationship \[{\rm Pr}(N) = p_1 {\rm Pr}(N-a_1) + \ldots + p_n {\rm Pr}(N-a_n);\] the characteristic polynomial is therefore \[f(x) = x^{a_n} - \left(p_1 x^{(a_n-a_1)} + \ldots + p_n\right).\] This clearly has the root \(x=1\). Next note \[ f'(1) = a_n - \sum_{i=1}^{n} p_i a_n + \sum_{i=1}^{n} p_i a_i = \rm{E}(X) > 0 ,\] hence this root is als...
Post a Comment
Read more

Simplified Multinomial Kelly

Here's a simplified version for optimal Kelly bets when you have multiple outcomes (e.g. horse races). The Smoczynski & Tomkins algorithm, which is explained here (or in the original paper): https://en.wikipedia.org/wiki/Kelly_criterion#Multiple_horses Let's say there's a wager that, for every $1 you bet, will return a profit of $b if you win. Let the probability of winning be \(p\), and losing be \(q=1-p\). The original Kelly criterion says to wager only if \(b\cdot p-q > 0\) (the expected value is positive), and in this case to wager a fraction \( \frac{b\cdot p-q}{b} \) of your bankroll. But in a horse race, how do you decide which set of outcomes are favorable to bet on? It's tricky, because these wagers are mutually exclusive i.e. you can win at most one. It turns out there's a simple and intuitive method to find which bets are favorable: 1) Look at \( b\cdot p-q\) for every horse. 2) Pick any horse for which \( b\cdot p-q > 0\) and mar...
Post a Comment
Read more

Mixed Models in R - Bigger, Faster, Stronger

When you start doing more advanced sports analytics you'll eventually starting working with what are known as hierarchical, nested or mixed effects models . These are models that contain both fixed and random effects . There are multiple ways of defining fixed vs random random effects , but one way I find particularly useful is that random effects are being "predicted" rather than "estimated", and this in turn involves some "shrinkage" towards the mean. Here's some R code for NCAA ice hockey power rankings using a nested Poisson model (which can be found in my hockey GitHub repository ): model The fixed effects are year , field (home/away/neutral), d_div (NCAA division of the defense), o_div (NCAA division of the offense) and game_length (number of overtime periods); offense (strength of offense), defense (strength of defense) and game_id are all random effects. The reason for modeling team offenses and defenses as random vs fixed effec...
3 comments
Read more