I know it's just geeky fun, but consider: 1. Do you think there's a problem with you knowing it's always an A/B choice? That is: do you think the results would be different if you were ever given two same Pepsi? 2. What would happen if you added N cans of M brands? That is, let's say you get 7 extra cans and 2 will be RC Cola and the other ones will be some store brands or whatever. 3. Would it be a good test of caffeine hypothesis to tamper with a number of cans by adding a predetermined caffeine solution? If so, should you only tamper with one brand? 4. Can any of scenarios 1-3 be combined in a way that'd, to say intuitively, add information while reducing noise? Since apparently two is enough to even mention confidence: I bet that if we were playing Russian Roulette, you'd absolutely insist on letting you re-spin when going second despite the difference being noticeably less than 25%.with confidence of 75% (barely better than a 50% guess)
1. If I could distinguish labeled Coke and Pepsi, it would be interesting to pull one or two wrapped cans from the fridge and see if I could identify them. The two were so similar to me I am sure I could not identify a single can, and if I got two of the same soda I wouldn't be sure if they were different. 2. I don't remember what RC Cola tastes like. I tried to find a Tab but was too late. I am pretty happy with an occasional Diet Coke (or Pepsi), and not looking for something better, just curious to see if I should really prefer getting one or the other. 3. I think the caffeine might have a small effect on loyalty over time, but the 27% higher drug content in Diet Coke could be compensated by drinking more Diet Pepsi. I don't think of myself as impressionable to advertising, but I don't have a better explanation for my preference for Coca-Cola than a lifetime of exposure to better marketing. 4. Complicating the experiment seems likely to add both information and noise. The "first trace" of the Russian roulette concept appeared in the 1840 story "The Fatalist" in which a loaded pistol was used to demonstrate predestination (with twenty gold pieces gambled) based on whether it misfired on the first trigger pull. In the 1937 short story "Russian Roulette" "things were cracking up, so that their officers felt that they were not only losing prestige, money, family and country, but were also being dishonored before their colleagues of the Allied armies, some officer would suddenly pull out his revolver, anywhere, at the table, in a café, at a gathering of friends, remove a cartridge from the cylinder, spin the cylinder, snap it back in place, put it to his head and pull the trigger. There were five chances to one that the hammer would set off a live cartridge and blow his brains all over the place. Sometimes it happened, sometimes not." A sergeant survives this version at least seven times, before "he took out five cartridges and left one, reversing the order of chances" and staked two thousand francs (and his life) on the outcome. My preference would be to decline to play. If it is given that I must play, and I will be in second place, should I prefer the variant in which the cylinder is spun only once at the start, or re-spun after each trigger pull? We can model the choice with two rows of six chairs each. In the re-spin row, there is a revolver on each chair with one cartridge in a random unique position. In the one-spin row, five chairs have empty revolvers, and one chair chosen at random has a revolver fully loaded. I can choose between the second chair in the re-spin row or the second chair in the one-spin row. In this perspective it looks like every chair has a 1/6 chance of disaster, so what difference does the choice make? Tradition is that the game is concluded as soon as the revolver fires, so chair #2 in the re-spin row gives a 1/6 chance that I'll not have to participate at all because chair #1 was fatal. If I do have to take my turn, it's a (5/6)(1/6) chance of disaster. With these high stakes, yes, I would pay a lot to improve my chances by 16⅔%.
