Not more eggs....

Skeeter said:
The chance of the game ending RRB is 1, but your missing that the chance of the game ending at all is still only 1/2. The game cannot end RBR, but what your missing is the probability the game never ends, which takes the place of the RBR result (and its 1/2 probability) as soon as RR is spun.

The chance of throwing infinate Rs is not zero, and is actually irrelevant. What your after is the chance of the NEXT spin being R.
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I think you've got yourself in a complete muddle... the game will end, in most cases fairly rapidly... you can simulate it yourself if you don't believe me...

The probability that the game never ends is not 1/2

As for 'RBR' well you've got one 'R' towards either combination... though RRB is the more likely one...
 
Here is a revised version of the Penney's Game odds using Red and Black (One in Yellow is one in OP)

2h2gnyt.jpg
 
This is a clever puzzle because simplistically your immediate thought is 'There are only 8 combinations, so they must all be 1 in 8', which would be true for a total set of 3 spins only and no more.

Then when you think about it with just two combinations 'in play' and continuous spinning, for some combinations to appear, others must have appeared one move prior, for example to get RRB, beforehand either RRR or BRR will have to have been a combination. When you thrash out all the permutations you can see that actually, each combination is more and less likely than some of the others, meaning when you pick two of them, one of them will inherently be more likely to appear first.
 
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wiki said:
Many readers of vos Savant's column refused to believe switching is beneficial despite her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong (Tierney 1991). Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy (vos Savant 1991a). Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation confirming the predicted result (Vazsonyi 1999).
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I enjoy the idea of 1,000 PhD types getting together in a really large, terrible room and group writing a badly worded and ill-thought through refutation to something which they are very wrong about :)
 
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