Per Player X Golfer(S: Fill & Download for Free

I have good news and bad news for you. The bad news is that your solution is already optimal. The good news is that we can prove it, using really cool technology!Instead of feeding the problem to the big hammer of simulated annealing like I did last time, let’s feed it to the even bigger hammer of pseudo-boolean constraint solvers. A PB solver is a generalization of a SAT solver; it takes a set of Boolean variables (say [math]x_1, x_2, x_3 \in \{0, 1\}[/math]) and a linear system in these variables with integer coefficients (say [math]x_1 - x_3 \ge 0[/math], [math]x_2 - x_3 \ge 0[/math], [math]x_1 + x_2 - x_3 \le 1[/math]), and attempts to optimize a given linear function of the variables (say [math]2\cdot x_1 - x_3[/math]) given these constraints.We’re going to use clasp, a free and open source PB solver:http://www.cs.uni-potsdam.de/clasp/(This code should work with any PB solver that accepts the standard OPB format; another one is MiniSat+.)Here’s a Python script that generates the variables and constraints representing this golf scheduling problem, runs clasp to compute the optimal schedule, and interprets the output in a format we can read. It runs for about 8 seconds and computes the following optimal schedule, in which 27 of the 36 pairs of opposing players get to play together (like your first solution):AB12 CD34 EF56AC26 DE13 BF45AE35 BC16 DF24#!/usr/bin/python from subprocess import Popen, PIPE from tempfile import NamedTemporaryFile  # Define the variables we're going to use. num_vars = 0 def new_var():  global num_vars  num_vars += 1  return 'x' + str(num_vars)  plays = {(p, r, g): new_var()  for p in xrange(12) for r in xrange(3) for g in xrange(3)}  constraints = []  # together_game[p1, p2, r, g] = plays[p1, r, g] AND plays[p2, r, g]. together_game = {} for p1 in xrange(12):  for p2 in xrange(p1 + 1, 12):  for r in xrange(3):  for g in xrange(3):  together_game[p1, p2, r, g] = new_var()  constraints += [  ([[1, plays[p1, r, g]], [-1, together_game[p1, p2, r, g]]], '>=', 0),  ([[1, plays[p2, r, g]], [-1, together_game[p1, p2, r, g]]], '>=', 0),  ([[-1, plays[p1, r, g]], [-1, plays[p2, r, g]], [1, together_game[p1, p2, r, g]]], '>=', -1),  ]  # together[p1, p2] = exists r, g: together_game[p1, p2, r, g]. together = {} for p1 in xrange(6):  for p2 in xrange(6, 12):  together[p1, p2] = new_var()  for r in xrange(3):  for g in xrange(3):  constraints.append(  ([[1, together[p1, p2]],  [-1, together_game[p1, p2, r, g]]], '>=', 0))  constraints.append(  ([[1, together_game[p1, p2, r, g]] for r in xrange(3) for g in xrange(3)] +  [[-1, together[p1, p2]]], '>=', 0))  # Each player plays in one game per round. for r in xrange(3):  for p in xrange(12):  constraints.append(  ([[1, plays[p, r, g]] for g in xrange(3)], '=', 1))  # Assume each game has two players from each team. for r in xrange(3):  for g in xrange(3):  for t in xrange(2):  constraints.append(  ([[1, plays[p, r, g]] for p in xrange(t*6, (t + 1)*6)], '=', 2))  # Team members shouldn't play with each other more than once. for t in xrange(2):  for p1 in xrange(t*6, (t + 1)*6):  for p2 in xrange(p1 + 1, (t + 1)*6):  constraints.append(  ([[-1, together_game[p1, p2, r, g]] for r in xrange(3) for g in xrange(3)], '>=', -1))  # No one should play anyone else in all three rounds. for p1 in xrange(6):  for p2 in xrange(6, 12):  constraints.append(  ([[-1, together_game[p1, p2, r, g]] for r in xrange(3) for g in xrange(3)], '>=', -2))  # Without loss of generality, round 1 is AB12 CD34 EF56. for g in xrange(3):  for t in xrange(2):  for p in xrange(t*6 + g*2, t*6 + (g + 1)*2):  constraints.append(  ([[1, plays[p, 0, g]]], '=', 1))  # Maximize the number of pairs of opposing players that play with each other. opt = [[-1, together[p1, p2]] for p1 in xrange(6) for p2 in xrange(6, 12)]  # Run PB solver. f = NamedTemporaryFile() print >>f, '* #variable=', num_vars, '#constraint=', len(constraints) print >>f, 'min:', ' '.join(' '.join(str(s) for s in c) for c in opt), ';' for lhs, op, rhs in constraints:  print >>f, ' '.join(' '.join(str(s) for s in c) for c in lhs), op, rhs, ';' f.flush()  pr = Popen(['clasp', f.name], stdout=PIPE)  # Interpret the output. s = set() for l in iter(pr.stdout.readline, ''):  print l,  if l.startswith('v '):  s.update(l.split()[1:]) pr.wait()  for r in xrange(3):  for g in xrange(3):  print ''.join("ABCDEF123456"[p]  for p in xrange(12)  if plays[p, r, g] in s),  print 

Callaway normally makes good strides between their club generations, so I think it is safe to say that the X-22s are better clubs.That said, depending on the level of golfer you are, it might not make a difference at all. A person who plays non-competitively and plays once or twice per week with friends isn't going to notice the difference between the clubs.Callaway's X series of irons are meant for those who have a fairly okay understanding of what they're doing. They have a slightly smaller sweet spot and are thus slightly harder to hit. But if you connect properly, the ball will go further. If you are confident in your game, the X series and the RAZR series Callaway replaced them with, will help you become a better golfer by going further and potentially straighter.Callaway's Big Bertha series (now replaced with the Diablo series) is much more forgiving in terms of sweet spot hitting. You can get bad contact and the ball will still fly well, but you sacrifice distance for the advantage of being able to play a sloppier game.I myself still use X-16s, and it fits my game and budget perfectly. The clubs do help a bit, but good golfing comes down to the player more than the equipment.

Flexibility -Hold no attachment to trades-Endeavour to have no emotional attachment to an idea. When a trade is wrong he will just cut it, move on and do something else.Change opinions on a dime-When people ask me for my opinion about the markets I always tell them, “what I think the market should do today may not be the same view I hold tomorrow.” As traders, it’s not our job to be right; it’s our job to make money.Focus on the here and now-Quick decisive decision making is crucial. We base our decisions on the information in front of us at the time of the trade.You have to stop trying to will things to happen in order to prove that you’re right. Listen only to what the market is telling you NOW. Forget what you thought it was telling you five minutes ago. Remember the objective is not to prove you’re right, but to hear the cash register ring.Intuition is gained from experience-Whether you consider yourself a discretionary trader or mechanical trader there’s a level of intuition and feel that develops from observations and experience.In addition to live trading and reviewing charts, the quickest way I’ve found for developing a sound trading intuition is to keep a log of market behavior.Write down what is happening in the market. Then write down what you think will or should happen as a result. Once the outcome is revealed, compare your initial hypothesis. This is a great way to build a solid macro understanding and strong intuition.The Importance of Implementation -Right strategy for the idea-With so many markets and instruments out there to trade there are many ways to express your ideas. It begins with an observation or hypothesis. Sometimes buying the underlying is the best trade. Other times, a derivative or currency makes for a better play.When looking to express an idea in the markets, seek out the trade with the least risk, greatest reward potential.Draw a line in the sand-Know where you are to be proven wrong before even entering a trade. Start by deciding where the market would have to go, that is at what level your idea would be invalidated. This is where you place your stop. Colm O’Shea stressed this idea in his trading.Execute consistently-Even though I place my trades manually, I try to be as mechanical as possible. This means, if I see a setup that meets my criteria, I take it. The mechanics of trading should not be left up to the judgment of the trader. To be a winner you have to be able to toe the line and pull the trigger.Embrace uncertainty and risk-I accept that a trade will be a loser even before I enter the position. That is, I’m accepting the worse possible scenario and I’m okay with it. This keeps me focused and objective during the entire trading process.Belief is in the Numbers -Think like a “Turtle”-The turtle trader experiment resulted from a dispute between commodity speculator(this I was told by a long time friend over the idea of whether great traders were born or made). Some believe that they could teach people to become great traders and some think that genetics and aptitude were the determining factors.I suggest you recruit and train yourself to be a better trader, giving yourself actual account to trade and see if you can be correct.You can be the one to make the most profit ever made by a trader..The rules instructed are easy to follow because sometimes they are not only very precise, but provided answers for each of the decisions they were to make while trading. This can also make it easier to trade consistently because there was a set of rules which defined exactly what should be done.Ignore individual trade outcomes-The best way to gauge our trading performance is not to look at the result from our last 1 or 2 trades; it’s to look collectively at a group of say our last 20 trades. In this way, the outcome of each individual trade is masked. This also helps dilute any “recency bias” that we may encounter and prevents past trades from influencing future decisions.Calculate your expectancy-Expectancy is simply you projected return over a longer period of time. Expressed (Avg $ W x Win %) – (Avg $ L x Loss %) – commission per trade.(Parker Joas taught me well on this and I think this is key to the whole process)HE says, “If you know that your system makes money over the long run, it is easier to take the signals and trade according to the system during periods of losses. If you are relying on your own judgment during trading, you may find that you are fearful just when you should be bold and courageous just when you should be cautious.” you can add him on Skype with the name4. Accept Mistakes -Mistakes lead to improvement-Check your ego at the door and accept that you will be wrong. Mistakes provide the path to improvement and ultimate success. Each mistake offers an opportunity to learn from the error and to modify one’s approach based on this new information.Whenever you make a significant mistake in trading, write it down, both to reinforce the lesson and to serve as a future reminder. Then change your trading process based on this new experience. In this way, mistakes can become the essential ingredient for continual improvement as a trader (or any endeavor for that matter).Be bold, embrace disagreement-Parker joas employs a culture encouraging independent thinking and innovation. he believes there must be thoughtful disagreement and non-ego impaired exploration of mistakes and weaknesses to achieve goals.Imagine how much better decision making would be if people who disagree were more open to trying to get at the truth through thoughtful discourse. It is a process that produces discovery.Collaborate on ideas-Something you may not know about me is that I studied architectural design in college. One of the things I loved about design studio was the ability for collaboration. When an idea first pops into your head it seems fantastic, but as you begin to discuss your idea with others, questions arise that you may not have thought about at first. Thinking through all these facets leads to the development of a structurally sound idea.Seek out opposing views-The better we understand the opposition, the better we can understand who is on the other side of our trades and how they might react.The great thing about being a trader is that you can always do a much better job, no matter how successful you are. Most people are busy trying to cover up their mistakes. As a trader, you are forced to confront your mistakes because the numbers don’t lie.Find what works for YOU-Do as others do NOT-In order to achieve greatness we must get uncomfortable. As a trader, you can’t be afraid of going against the grain.If you do the same as others do, you can expect to be average. Going against the grain is tough. There can be a lot of social pressures and questioning from family and friends. In order to live your life the way YOU want, you need to put yourself in opportunistic situations. Surround yourself with the people you want to be like who share your same moral beliefs.Think about the opposite-Look at things from all angles and think about the opposite action. When a lawyer prepares a case they will often prepare the opposing arguments first. In this way they know what to expect and have all their bases covered. In trading, think about who is on the other side of your trades and if you were that person, how you would react.Just because everyone is buying gold, doesn’t mean you should too. The media and the talking heads are often on the wrong side of the trade.Learn by doing-There’s no substitute for experience. Go out and try something. If it doesn’t work for you, learn from it and move on.Isolate yourself from negativity-Surround yourself with people who have a positive impact on your life. Learn from those who’ve come before you, taking bits and pieces, making them your own.Get uncomfortable, don’t be afraid to be different!Over Prepare-Follow your passion-Winners don’t just work harder than everybody else. At some point they fall in love with their craft to the point where they want to do little else, it becomes their life.Luck favors the prepared mind-No one is perfect, especially in trading, but preparation pays. It’s essential to know more than the other players in the game. You’ve heard the saying the rich get richer, well the lucky also get luckier. To increase your luck, you must adequately prepare for the day ahead. The trader who shows up better prepared will be the one with the greatest chance of coming out ahead.Think like a chess player-Always be thinking 2 steps ahead. Don’t think about what the market’s going to do; you have absolutely no control over that. Think about what you’re going to do if it gets there. In particular, you should spend no time at all thinking about those rosy scenarios in which the market goes your way, since in those situations, there’s nothing more for you to do. Focus instead on those things you want least to happen and on what your response will be.Never stop learning-The worst thing we can do is to stop learning. We get settled with our lives and become complacent, stuck in our comfort zone. In order to evolve as a consistently profitable trader you must constantly be on the lookout for opportunities. I find myself always thinking about the markets and new ways to implement my ideas. Life is an iterative learning process.Visualize-Believe in yourself-Greatness starts from within. You must believe in yourself and your ability to become successful.Attitude influences behavior-Jesse Livermore made and lost his fortune a number of times over. Donald Trump is another example. These individuals share the same mindset; they believe that they can build back up from scratch. Their mental attitude and belief in themselves gave them the confidence to achieve greatness.Mental practice-One reason Tiger Woods was such a great golfer is not necessarily the hours spent at the range, but time spent off the course using a combination of visualization techniques and internal biofeedback.Envision your ideal self-Before you fall asleep each night, take moment to envision your ideal self. Close your eyes for a moment…What does your ideal self look like?What are you wearing?How do you carry yourself down the street?Approach others?Make decisions?What things surround you?What people surround you?When repeated and practiced with deep though these visualization exercises go a long way towards turning ourselves into the person and trader we want to be.Evaluate Yourself Based on Your Goals -Don’t compare yourself to others-This principle goes far beyond trading. There is absolutely no reason to compare your situation to that of others.What is your unfair advantage?-Everyone has something that is unique to them and no one else.a trader quoted saying if a betting game among a certain number of participants is played long enough, eventually one player will have all the money. If there is any skill involved, it will accelerate the process.Something like this happens in the market. There is a persistent tendency for equity to flow from the many to the few. In the long run, the majority loses. To win you have to act like the MINORITY. If you bring normal human habits and tendencies to trading, you’ll gravitate toward the majority and inevitably lose.Draw your own conclusions-“The average man doesn’t wish to be told that it is a bull or a bear market. What he desires is to be told specifically which particular stock to buy or sell. He wants to get something for nothing. He does not wish to work. He doesn’t even wish to have to think.”Set personalized metrics-We each live in our own reality with our own beliefs. Winners compare themselves to their own goals, not to the achievements of others.Establish a Routine -Create a solid foundation-Dedication and discipline are the foundation of success, hands down. A consistent routine develops habits that transform into subconscious behaviors.For a period of time I used to run a split sleep schedule, sleeping for a few hours waking up to trade the Euro open and then returning to bed before the NYSE open. Over time it took its toll on the body, especially with racing mountain bikes. What it did teach me however, is the importance of adhering to a routine, day in and day out.Focus on what you CAN control-You have more power over your trade outcomes than you might think. While no one can control the market itself, you can control your actions and reactions. You can control how well you prepare and plan for the given trading day, and most importantly you can control your risk exposure associated with a position.Schedule meditation, walks, and exercise-I’m a big believer in having balance in life. Think time is incredibly powerful. When you’re in a rhythm you feel great. Taking walks, listening to podcasts, getting outside, exercising, playing sports, sitting quietly, meditating, these are all things that help bring a healthy balance to a person’s life and have a great impact on a person’s long-term success.Be Humble -Always question yourself-“don’t be a hero. Don’t have an ego. Always questions yourself and your ability. Don’t ever feel that you are very good. The second you do, you are dead.”Feeling invincible is a death trap-If you’re not careful the market will take from you in an instant that which you worked longest and hardest to obtain. When you’re experiencing a string of winners and feel like you are untouchable that’s precisely when you should be the most cautious.Use positive self talk-Studies show positive self talk has a strong impact on your actions so it’s important to talk to yourself in a positive way. Responding positively to situations helps keep a clear head and reinforces a good attitude. As I said before it is our attitudes that influence our behavior.Give back-I’m not alone when I say that it is better to give than to receive. I’ve had the privilege to learn from some exceptionally great traders who were doing their part to give back what they had learned. I’m a strong believer in giving back anyway I can.Action Plan for you to consider:Commit (commit to doing what you love)Be flexible (do not become attached to your trades)Focus on execution (trade the right strategy for the idea)Calculate your expectancy (the #s need to make sense)Hold yourself accountable for your mistakes (this is the path to improvement)Do what works for YOU (don’t be concerned with what others are doing, go against the grain)Establish a routine (it’s always best to over prepare)Determine your unfair advantage (we all have one, what’s yours?)Remain humbleVisualize what you want, then make it happen!Put some thought into these principles and incorporate them into as many aspects of your life as you can. Trading is a fantastic teacher of life’s greatest lessons. Allow the trading journey to shape you into the person you want to become.I wish you the best of luck in your trading!