The pots of gold — a thought experiment about 1. c4 Na6

The pots of gold — a thought experiment about 1. c4 Na6


Today is your lucky day — your audience with the King.

The herald announces your arrival into the throne room. Before you are seated King Harold, his queen and their beautiful daughter, Fortuna. Standing next to them are their bishops, knights and soldiers. All are dressed in white. As is traditional, you are dressed in black.

You recognize King Harold's favorite bishop, Bernat de Fenollar, who long ago traveled to the king's court whom the king fondly calls the Catalan bishop. Bishop Bernat greets you:

On behalf of the King, welcome!

As thanks for your service to the kingdom, the king invites you to play the game of the pots of gold.

Before you stand twenty pots. 

Each pot contains both gold coins and lead coins in various ratios.

Our generous king grants you three wishes.

For each wish, you shall pick a pot. Princess Fortuna will be blindfolded and will pick a coin randomly from that pot, be it gold or lead.

For each wish, you can choose any pot. You can change pots or you may stay with the same pot.

Whether gold or lead, you get to keep the three coins as tokens of the king's gratitude.

If Fortuna selects three gold coins for you, you not only will be wealthy but also will win a special prize.

Choose wisely and good luck!

As is traditional, to assist you with your choices, you brought along as your second Father Ruy Lopez from Spain, who has studied this game for decades.

The first pot that Ruy Lopez points out to you is the pot called the Anglo-Indian pot, named after a renowned Indian player who was the first to pick the pot. You learn that it is by far the most popular pot. On average, 42% of the coins randomly picked from this pot are gold coins.

The second pot that Ruy Lopez shows you is called the King's English pot. It is the next most popular pot. On average, 46% of the coins picked from this pot are gold.

The third pot that Ruy Lopez shows you is called Agincourt, named after a famous battle that the king's ancestor King Henry fought against the French. It is the third most popular pot to pick. On average, 43% of the coins are gold.

After showing you a few more pots, Ruy Lopez tells you to not bother with the rest because they either have too few gold coins or are unpopular and rarely picked.

Yet as you are walking back to announce your first wish, Princess Fortuna catches your eye. She winks at you and glances at a dusty pot in the far corner. Curious, you ask Ruy Lopez about this pot. He tells you that is it called the pot of salt because the king's insane alchemist, who believed he could turn salt into gold, was the first to choose the pot.

Ruy Lopez tells you that the salt pot is extremely unpopular. It is virtually never picked. He proudly reminds you that he is a national master in this game and sternly tells you that the idea of picking the salt pot is "silly" and that he would NEVER pick it himself.

To warn you away from the salt pot, Ruy Lopez shares with you the story of a poor player who years ago who picked another unpopular pot. Although he won two gold coins, which is quite good, the king and his court laughed at him for his choice. The king exclaimed "This is not a game of skittles!" and made the player wear a dunce cap for a year.

Even so, you ask Ruy Lopez about how lucky the salt pot has been. He tells you that while only 10 coins have ever been picked from the pot, at least five or six of them have been gold, which is the highest ratio of all the pots.

Because you have written a paper on the new science of probability, you quickly do the math in your head. Assume you have a pot containing 1000 coins — 420 gold and 580 lead. Assume that you randomly pick 10 coins out of that pot. The chance of picking five or more gold coins is only about 40%. Since at least half of the coins picked from the salt pot have been gold, that suggests to you that the salt pot might possibly contain a higher ratio of gold coins than the Anglo-English pot. Even though you don't trust the small sample size, you tell yourself that the salt pot at least may not be significantly worse than the 42% odds that you'd get with the most popular pot.

It is now time to announce your three wishes.

Are you going to follow wise Ruy Lopez's advice and pick only from the popular pots where 42 to 46% of the coins have been gold?

Or are you going to trust Fortuna and pick at least once or maybe more from the extremely unpopular salt pot, where half or more of the coins have been gold?



And so this is the thought experiment I promised in my last post, Introducing the Sodium defense to the English opening, where I suggested that the seemingly insane 1...Na6 might actually be a playable defense to 1. c4. 

It is true that over the last century thousands of chess masters have played millions of English opening games.

It is also true that out of those millions of game, those masters have ventured 1... Na6 in only about ten games, which is essentially 0.00% of the time.

Yet, as's Opening Explorer reports, in the extremely few games beginning with 1. c4 Na6, White has won 20%, 40% are draws and Black has won 40% for an expected value to Black of 0.6.

While the sample size is absurdly small, the expected value to Black of 1... Na6 — what I'm calling the Sodium defense — is greater than that for the Anglo-English, the King's English and the Agincourt defenses.

Unlike the hero in our thought experiment who got only three wishes, you can play as many games on as you wish so you get an unlimited number of chances to try out any defense you wish, even including the Sodium defense, 1... Na6. If you wish, you can even play unrated games so that you can give a move like 1... Na6 a shot without it hurting your rating.

So why not give the Sodium defense a try sometime?

And if you're crazy enough to play this silly defense, please let me know how you fared in the comments. 



As a postscript, I should note that if you're an inexperienced player, you should start with the basics. Pick a favorite opening, either 1. e4 or 1. d4. Pick a favorite defense to 1. d4 and a favorite defense to 1. e4. You're probably doing to play lots and lots of games before you ever see an opponent open with 1. c4 against you and when that happens, the symmetric English is a good defense to try out. 

Playing 1. c4 Na6 isn't anything I recommend for beginners. Even if you're intermediate or advanced, I view it as a fun experiment.