1. Any estimate is likely to be very inaccurate. Also there are fat tails. There might be one very infectious person there such that you actually have a very high risk of infection in this case. A single point estimate of risk throws away a lot of information. What would be better would be a Bayesian type probability density.
2. This may be the wrong question. Given in Iceland for example half the infected showed no symptoms, it is important to consider the risk that you may infect other people.
3. (total) Risk (across the crowd) goes up approximately with the square of the number of people in the crowd.
4. This is somewhat analogous to the situation with STDs. It is not just the number of people you interact with, but the number of people they have interacted with, and the number they have interacted with. The rather disconcerting image with STDs is that you are actually in bed with maybe 1,000 people; similarly here you are actually in a room with who knows how many people.
5. Also take into account that in many situations at present, there is a bias to the people you are going to interact with. In any given bar or conference, the risk averse, careful people will be staying at home. The risk-blind careless reckless people will be over-represented. E.g. the people who attended Chinese New Year gatherings in NYC.
6. You need to update the calculation on a daily basis.
7. I think that with viral diseases the initial viral load is important because it greatly affects how long your body has to mount a defense against the disease. No idea how to model this. There are also differences in individual vulnerability etc.
8. You might also take into account the flow on effects. If you get infected, how many people will ultimately get infected as a result, similarly if you infect someone, how many people will ultimately be infected.
Here is my attempt
IR: Reported infections in NY 20k, I assume that the true number is 2X, 10X or 20X that. So the rate is about 20k/9M = 0.002 (reported) 0.004 2X, 0.020 10X, 0.04 20X
B: Bias for people attending a gathering, maybe 2X 5X or 10X more risk-loving than the average.
PT: Chance of transmission 1% 2% or 5% if you come into contact with people
If a gathering has X people that you come into contact with then the risk of infection is
1 - (1 - IR*B*PT)^X
and the risk of infecting someone else would be similar.
I sum across all combinations of the estimates. Note do the formula above for each combination and then average the results. Do not average then do the formula - this is wrong because of the nonlinearity.
Plugging this into a simple spreadsheet (Guaranteed to be wrong - use at your own risk https://drive.google.com/file/d/15Qdwqcjg-4g3Kn4r7hFH-BlRGrq80Wpt/view?usp=sharing) I get
#People => Risk to me
10 => 5%
100 => 27%
1000 => 66%
10000 => 95%
This is most sensitive to the higher factors above and to the numbers of people. But even with low factors, with large numbers it is bad.