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The metaphor with the elephant and the goldfish had absolutely nothing to offer either, it was just a rehash of the previous sentence.
Watch the embedded video, it's a great illustration of the article. :-)
Sadly, I suspect everyone would then copy that strategy and much like everyone choosing the letters R, S, T, L, N, and E in Wheel of Fortune, it would quickly become a formula and would ruin the suspense the show hopes to create.
Did anyone else find that article meandering? The description of the game, in particular, struck me as especially pompous wiring. The metaphor with the elephant and the goldfish had absolutely nothing to offer either, it was just a rehash of the previous sentence.
In this case it does have something to "offer": it offers the insight that the only value that looking at past states can offer is a sort of "strategy tomography" to tell you what the other person's conditional probabilities actually are, but that once you know this, your strategy is first-order Markov, just because their strategy is first-order Markov. (This term, nth-order Markov, just means "depends only on the last n game states.")
It's true, however, that this leads to a very interesting consequence which is not discussed in this context, something quite convoluted: "I will commit to a first-order Markov strategy in order to prevent my opponent from using a higher-order Markov strategy, so that my own analysis of their strategy simplifies." It is a curious statement that your own ignorance forces someone else to be ignorant, which you can then exploit.
This is proven in appendix A of their paper. To state the conclusion in their words, "In iterated play of a fixed game, one might have thought that a player Y with longer memory of past outcomes has the advantage over a more forgetful player X. For example, one might have thought that player Y could devise an intricate strategy that uses X’s last 1,000 plays as input data in a decision algorithm, and that can then beat X’s strategy, conditioned on only the last one iteration. However, that is not the case when the same game (same allowed moves and same payoff matrices) is indefinitely repeated. In fact, for any strategy of the longer-memory player Y, X’s score is exactly the same as if Y had played a certain shorter-memory strategy (roughly, the marginalization of Y’s long-memory strategy), disregarding any history in excess of that shared with X."
If I were playing Split or Steal, my strategy would be exactly this: tell the other player that I'm going to choose "steal" and if they choose "split", I'll give them half of the winnings. We would shake on it on national television which forms a nice contract: an offer, consideration for both parties, and acceptance. The beauty of this is that if they're not an idiot they'll choose "split" and we each walk away with…
If I were playing Split or Steal, my strategy would be exactly this: tell the other player that I'm going to choose "steal" and if they choose "split", I'll give them half of the winnings. We would shake on it on national television which forms a nice contract: an offer, consideration for both parties, and acceptance. The beauty of this is that if they're not an idiot they'll choose "split" and we each walk away with…
I've seen people immediately regret doing it when they see that their opponent shared. They seem more upset about it than the loser and tend to cite an expectation that the other person would steal as their reason for stealing, even though this makes no logical sense. It was a fascinating but horrible ending to sixty minutes of otherwise tedious viewing.
If I were playing Split or Steal, my strategy would be exactly this: tell the other player that I'm going to choose "steal" and if they choose "split", I'll give them half of the winnings. We would shake on it on national television which forms a nice contract: an offer, consideration for both parties, and acceptance. The beauty of this is that if they're not an idiot they'll choose "split" and we each walk away with…
The thing that always bugged me about Golden Balls (aside from the terrible name) was the way stealers would act like it was just a game when they had in fact taken thousands of pounds from another person through deception. Certainly it was legal and even encouraged by the format of the show but it was never the right thing to do. I've seen people immediately regret doing it when they see that their opponent shared.…
If I were playing Split or Steal, my strategy would be exactly this: tell the other player that I'm going to choose "steal" and if they choose "split", I'll give them half of the winnings. We would shake on it on national television which forms a nice contract: an offer, consideration for both parties, and acceptance. The beauty of this is that if they're not an idiot they'll choose "split" and we each walk away with…
If I were playing Split or Steal, my strategy would be exactly this: tell the other player that I'm going to choose "steal" and if they choose "split", I'll give them half of the winnings. We would shake on it on national television which forms a nice contract: an offer, consideration for both parties, and acceptance. The beauty of this is that if they're not an idiot they'll choose "split" and we each walk away with…
Here is the video of this happening on the tv show. http://www.youtube.com/watch?v=S0qjK3TWZE8 . It worth a watch, I recommend it.
If I were playing Split or Steal, my strategy would be exactly this: tell the other player that I'm going to choose "steal" and if they choose "split", I'll give them half of the winnings. We would shake on it on national television which forms a nice contract: an offer, consideration for both parties, and acceptance. The beauty of this is that if they're not an idiot they'll choose "split" and we each walk away with…