That efficiency allowed Burch and his colleagues to try solving the full game of heads-up limit Texas hold’em, rather than just a simplified version. By applying compression, they reduced the memory requirements to less than 11 terabytes for storing the counterfactual values and just 6 terabytes for computing the main strategy. http://spectrum.ieee.org/tech-talk/computing/software/computers-conquer-texas-holdem-poker-for-first-time
At this time there might not be an accepted understanding of the importance or role of playing cards or any types of random number generators nonetheless the author would like to walk through a short observation on a possible explanation of the evolution of the 52 Card deck. However in order to make sense of any kind of history of evolution of such an “object” we must first define a plausible utility or in other words motivation (or gravitation) for such an evolution. What is the purpose of the evolution of cards, and what might be the “force” behind such an evolution and the direction of it. The importance of course is if we can understand the history and present day facilitators of games (especially of the effectively skilled kind) we might then have a chance at understanding the future of them. Who knows what interesting uses and breakthroughs this might have and lead to!
The author would like to make a small proposal or conjecture which comes from a seemingly new realization about the relation of currencies to the institutions of their respective times as pointed out by Nick Szabo in Shelling Out. By understanding currencies and institutions in relation to their economic environment we are able to take a possible perspective that currencies are much like a (favorable?) bi-product of an inefficient trade. That is, when trade cannot happen without facilitation, currencies might then naturally arise. This is the significant premise we will use with respect to the evolution of the 52 card deck, that such an “object” has naturally arisen as a bi product for the need of some useful probabilistic transactions in our society (aka games)!
Now we might trace the history back and ask ourselves what is the importance of such subsets or inferior rng objects in relation to respective times of creation/existence. For this purpose we must/should call on another important observation that unsolvable games have a chance at being viewed and played as “skill” games in our society and that solved games (or well understood games) essentially are games of chance. In other words if all players exhibit the same perfect strategy in an otherwise fair game, the outcome of the winner is going to be based on the “chance” associated with the game. This allows for the observation of two types of game throughout the history of man-effectively skilled or chance.
It is quite easy to see for example that a coin, which has a 50/50 chance generator will not function as an effective skill game creating object as it’s nature is generally quite understood by both parties. This isn’t quite so with a 52 card deck as many games have arisen from such a configuration that are not very solved and seemingly not very well understood. Although this in itself may not be a revelation or evidence of one it might be helpful to delve into the concept a little further.
Lets think of a 10 card poker deck, which is not necessarily something uncommon in the recent history of man. It may have been at some time between 2 or 3 players a type of game similar to poker could be played. For some this would be a game of chance with little skill, but no doubt some of the fore-thinkers of their respective time were able to play the game as an effectively skilled game vs those that were not knowledgeable about the overall solutions to it.
Somewhere between such a time and now its seemingly reasonable to suggest that such a game was effectively solved and rendered not very worthy of an “effective skill game” title. There might be many reasons for such a change which could include popularity (as well as obvious advances in math, and less obvious advances of societies overall understanding of strategy,game theory, and gambling). So seemingly such a deck evolved by adding cards, possibly suits, colors, etc. This evolution arises the possibility to keep a skilled game in the reach of the population as well as adding other useful traits such as scalability to a larger amount of players (ie how to deal 2 cards to 6 players with a 10 card deck).
But why would such an evolution occur, or what is the significance of an effectively skilled game?
To understand this we must understand today’s result of such evolutions of the history of gaming and cards and see the popularity and effect poker and its variants has on society today. Although it is not quite time to suggest how and what drives such a movement it can be shown today that poker in its moral/ideal sense ultimately facilitates a favorable intelligent and capitalistic society we should all hope and dream for. Only a skilled game is capable of training and attracting the brilliant, motivated, and creative minds as well as “donating” the funding needed for such peoples to pursue their non poker objectives/ventures. We might then (mistakenly perhaps because our lack of strong probability theory!) see it as luck that such as phenomenon has arisen, but it is hard to deny it is not prevalent. The author would like to further suggest in the near future poker will play a more significant and respected role in society than generally thought possible.
In this light the evolution of cards might make sense. With a deck of say 10 cards only certain game variants can arise. Eventually though, this deck evolved until the deck we use today came about. With it came many different types of game variants and possibilities for new variants. It’s possible we have found the significant variants, yet socially and “politically” it seems relevant to point out that Texas Hold ’em (of the no limit kind) which replaced limit as the primarily effectively skill game, is sometimes believed to be soon or already replaced by PLO, which interestingly enough has the addition of 2 hole cards making the game slightly more difficult in the effectively skilled sense (or possibly more difficult to solve at least by the general public).
Now it is difficult to trace, suggest, and prove that such a phenomenon has arisen specifically from an economic race to create and keep a skilled game just so that the intelligent peoples might profit from the unsuspecting, however it is only the author’s suggestion (at least) that such a movement has arisen only with humanity’s transition into a civilized society. As we became intelligent and our financial institutions have grown more evolved, out of this came a natural social tendency to want to have a prominent game of effective skill.
So the authors conjecture then is this: The 52 card deck has arisen out of a naturally progressive evolution of man in order to fuel our want of an effectively skill game. If poker was solved (or better said well understood tomorrow) the population would move on to a game of effective skill or a deck that facilitates such a game.
And now we have outlined an area for great study and restudy. Not only must we re look at the history of game, cards, and other rng objects, but we must also understand the importance and ramifications of solving poker. But this also gives rise to an important likely missing link in all of this, namely that in order to solve poker we should likely think beyond poker in relation to the many variations of it that have arisen from a 52 card deck. In other words it is the 52 card deck we need to solve as it is a perfect byproduct of our misunderstanding of the game theory and probabilistic principles it represents.
In conclusion, like Szabo and Nash point out that our weak understanding of currency has fostered mythical beliefs about our economy, the author here would like to suggest our misunderstanding of the role of playing cards, poker, effectively skilled games, games in general, and probabilities, has fostered mythical beliefs in those sciences directly related to and relatable to probabilistic functions.