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> “I know that the fact that the roulette wheel has come up red 10 times in a row tells me NOTHING about spin #11. On the other hand, I know that over time, the
by chx 5y ago
> “I know that the fact that the roulette wheel has come up red 10 times in a row tells me NOTHING about spin #11. On the other hand, I know that over time, there will be just as many black spins as red spins, so at least intuitively, a black spin seems at least a little more likely to come up next in order to push that ratio back towards 50/50. Are these two principles actually in tension with each other? If not, how do we resolve the apparent tension? If yes, isn’t it the case that there must be “some” validity to the gambler’s ‘fallacy’?”
To this my answer would be: if you are doing millions and millions of spins then you should see roughly 50/50 but that just means over a few million spins it will balance out -- and even then it's not usable for predictions because it's not exact. Also, in a similar long sequence you would expect that in 2046 spins you see 10 of a single color in a row. That's not such an outrageously big number...
- zerof1l 5y agoFun fact, the actual roulette wheel in casino has green zero. When betting on any color, you will always have less than 50/50 odds.
- lloydgrossman 5y agoFunner fact, many even have a green double zero as well to tip it even further.
- gexla 5y agoNice points being made here. American roulette has double zero, European roulette has a single zero. The zero(s) represent the house edge and that's what the casino makes its money from. Even funner fact, even if there isn't a zero and you truly get 50/50 odds, you'll still hit ruin over the long run because the house has "unlimited money."
- galaxyLogic 5y agoWhy doesn't competition work here? Shouldn't somebody open a casino in Las Vegas with only a single 0 and thus attract more customers?
- deleted 5y ago[deleted]
- bryanlarsen 5y agoOn the gripping hand, coming up red 10 times in a row is evidence that the odds of red and black aren't even.
- thom 5y agoAlways happy to see this Motie idiom still in use!
- nkurz 5y agoI was familiar with the phrase, but not the origin. Since "motie" is somewhat hard to search for (Ministry of Trade, Industry and Energy?), here's a reference page in case others are interested: In the science fiction classic The Mote in God’s Eye, we are introduced to the Moties, a species that is trapped near a star without interstellar travel, but that has evolved extraordinary abilities. Anatomically, the Moties have two normal hands … and a third one, which gives them the ability to make and manipulate tools with great dexterity. This leads to the idiom of “on the gripping hand,” following “on the one hand or the other,” and suggesting another way, a better alternative. https://ellingtonlab.org/blog/2014/12/1/on-the-gripping-hand https://ellingtonlab.org/blog/2014/12/1/on-the-gripping-hand
- Kranar 5y agoComing up red 10 times in a row is expected to happen once every 2000 rolls. Given 45 spins an hour that means a table will spin red 10 times in a row once a month. Given a casino with 20-30 tables you can expect to see it once a day. Hardly a reason to shake your faith.
- compiler-guy 5y agoStrangely, ten reds in a row is not particularly good evidence of an unfair wheel. For an American wheel, the odds of red in a single spin is 18/38= 0.4737. So ten in a row is 0.4737^10, which is about 0.0005689. So one should expect five or so such sequences in ten thousand spins. Or one in every two thousand spins. If a casino spins its roulette wheel 200 times a day, you would expect to see a sequence of ten reds in a row every ten days. If the casino runs ten roulette wheels, it's an every day occurrence. Low probability events happen regularly with enough samples.
- alan-crowe 5y agoI find it interesting that saying "a black spin is needed to push the ratio back towards 50/50" feels like a sensible thing to say. What role do context and framing play? Consider the first one hundred spins breaking 60 red, 40 black. That is a little odd, but not outrageously so. The ratio is 60/40 = 1.5 Suppose that the next one hundred spins break 50/50. There are no surplus blacks to push the ratio towards 50/50. So what is your intuition? It seems clear enough that the totals are 110 red, 90 black, for a ratio 110/90 = 1.22... Having imagined the next hundred spins vividly, we are comfortable saying "Unless the surplus reds keep coming, the ratio is going to drift back towards 50/50 all by itself.". There is a striking clash between different "things we might say" seeming sensible, depending on the vividness and detail with which we imagine the situation.