FUN WITH NUMBERS! (Musings for Probabilists and All Who Enjoy Gaming)

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As any probabilist worth half his salt would tell you, there are very few perfect answers; only tradeoffs.

That's certainly true in the world of investments. It's impossible to earn well-above-market returns, like clockwork and over an extended period of time, unless you were a long-time client of Bernie Madoff's. (Well, up until late 2008, anyway.)

Many people suffer from something of a case of innumeracy and have a bit of trouble thinking critically about media reports on health matters and other issues. Very often facts are presented out of context or in such fashion as to attempt to mislead or bamboozle readers with little understanding of probability.

On that topic, a very fun read is A Mathematician Reads the Newspaper, by John Allen Paulos.

https://www.maa.org/press/maa-review...-the-newspaper

A good example of how someone who doesn't understand such things as risk variables and cohort skewness (let alone Simpson's Paradox!) occurred in this forum just a couple of days ago:

https://eccie.net/showpost.php?p=106...0&postcount=38

Therein was included a concise explanation of how something that seems so counterintuitive to the uninitiated can nevertheless be quite true.

One fun little tidbit probability students are introduced to early in a typical introductory course is the so-called "birthday paradox." Many are surprised to learn that you only need to assemble 23 people for the probability to reach 0.5 that at least two of them will have the same birthday (month and date, not necessarily year).

To me, though, the following little exercise is significantly more counterintuitive than the birthday paradox.

Consider the case of a man who is a terrible hypochondriac and continually gets himself tested for various genetic markers or other health status issues, even though he has no reason to believe that he is at even the slightest elevated risk of being affected by any of them.

Suppose that there is a condition that occurs in 0.01% (1 in 10,00) of the general population. There is a test that is "99% accurate," both for positive and negative status.

He takes the test and it comes back positive. What is the probability that he is actually affected by the condition?

(Note: It might be fun for the people who everyone knows could supply the answer almost instantly to refrain from doing so for now, so that those whose mathematical educational status is unknown can take a shot at it! Although very likely none will.)

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I am looking for the answer to a probability challenge that I'm having trouble with, since I have no knowledge of a most critical risk variable. (No idea how bad covid outbreaks are in Latin American countries right now.)

Suppose that a man who is not quite so young anymore (a bit north of 70) is weak of flesh and succumbs to various temptations on a quite regular basis.

In particular, he occasional hungers like a half-starved wolf for hot young Latina women.

One of this forum's frequent posters suggested recently that he might be the go-to guy for information on south-of-the-border hooker bars.

Suppose further that this hypothetical gentleman (who shall remain nameless in order to avoid personal embarrassment) might consider a short trip to a venue where he could boink three, maybe four hot women over a 2-day period. (Without masks. of course, as he wants to fully immerse himself into the experience!)

Our Latina consultant is a gamesman and a fine probabilist, so I'd like to see what other variables or risk profile info he may need in order to estimate the guy's risk of expiring from covid-19 as a direct consequence of this excursion.

"Asking for a friend"

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For non-mathematicians - I trust you will post an answer discussion
CM - thank You.

I've heard that question before, but I forgot how to solve it. I think you're suppose to use Bayes Theorem, but I've no idea. I could look it up, but that would be cheating. I studied a little bit of that stuff but I never actually used any of it, so consequently I forgot.

Does a problem like that ever actually come up on the job, in the real world?

I guess it would if your job was to develop tests for diseases.

I gave up and looked up the answer. I won't post it here, but it's a common textbook question that anyone can Google and find the answer to LOL. It is definitely counter intuitive.

I failed at actually solving it, though.

O well. You know what they say? No sense in reinventing the wheel.

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I am looking for the answer to a probability challenge that I'm having trouble with, since I have no knowledge of a most critical risk variable. (No idea how bad covid outbreaks are in Latin American countries right now.)

Suppose that a man who is not quite so young anymore (a bit north of 70) is weak of flesh and succumbs to various temptations on a quite regular basis.

In particular, he occasional hungers like a half-starved wolf for hot young Latina women.

One of this forum's frequent posters suggested recently that he might be the go-to guy for information on south-of-the-border hooker bars.

Suppose further that this hypothetical gentleman (who shall remain nameless in order to avoid personal embarrassment) might consider a short trip to a venue where he could boink three, maybe four hot women over a 2-day period. (Without masks. of course, as he wants to fully immerse himself into the experience!)

Our Latina consultant is a gamesman and a fine probabilist, so I'd like to see what other variables or risk profile info he may need in order to estimate the guy's risk of expiring from covid-19 as a direct consequence of this excursion.

"Asking for a friend"

. Originally Posted by CaptainMidnight

Damn it Midnight, why do you have to tie my hands behind my back? The obvious answer is strap on an N95 mask and aviator goggles (more stylish than a face shield). Carry along a more comfortable KN95 mask for your date, along with a home COVID test kit, available for $25 from CVS. Don't feel uncomfortable asking her to use it. Remember, if she won't let you stick a cotton swab up her nose she's sure as hell not going to allow DFK. Then insist on reverse cowgirl and go to town. You can use this strategy in any cathouse in the world, no matter the level of COVID.

The two most obvious locations to pull Latin hookers in the time of COVID are the Cocal Hotel Bar in Jaco, Costa Rica, and the Clock Tower in Cartagena, Colombia. Both are open air venues, which cuts down greatly on the risk of infection. Both have lots of hot women. There are open air restaurants in both places where you can eat.

For what your friend wants, banging 4 or more women over a two day period, the Cocal is clearly superior. It's quicker and easier to get to, and it's so easy to shuttle them in and out of your room from the open air bar. Hell, if you've got the money and an endless supply of Viagra you could do six a day, easy.

Cartagena on the other hand is a great place to wife up. Most of the hookers are from Venezuela and other cities in Colombia, so don't have to be worried about friends or families seeing them around town with gringos old enough to be their fathers. And Cartagena is one of the most romantic cities in the world. The problem is getting there. You're probably going to have to make an extra connection through Panama City or Miami. So a lot of travel time for a short trip.

So should it be Costa Rica? This is where we have to put on our thinking caps. First Google "Costa Rica Covid." You'll see a chart of new cases, running about 2300 a day. Costa Rica has a population of 5 million, so that's 455 new cases per million per day. Now Google "Colombia Atlantico Province Covid." Atlantico province, where Cartagena is located, has 170 cases a day and a population of 2.5 million people, that's only 68 new cases per million per day.

So what are your chances of dying from COVID if you decide to go boinking in one of these places? I've actually worked that out for climbing a particular mountain. This has many more moving parts, and depends on specifics of your friend and where he plans to go. But these are some of the considerations,

1. What is his age? Does he have co-morbidities? From this you can estimate an appropriate infection fatality ratio (IFR), if he comes down with the disease, assuming he's unvaccinated. There are papers in the literature and also information on the CDC web site that will help. Take into account he's male, as IFR's for men are higher than for women.

2. What vaccine did he receive? How long has it been since the second dose, or third dose if he got the booster? For example, data from Israel might indicate if he received his 2nd Pfizer shot 6 months ago, his probability of coming down with severe disease are 15% of what they would be if he were unvaccinated. Make the simplifying assumption that the 15% would also apply to death. You can adjust the IFR determined from "1" downwards by 85% then.

3. The IFR for the USA before vaccines was about 0.8%, based on antibody studies and death statistics. Take your friend's IFR and divide by 0.8%. We'll call this the Death Ratio, and it's how much more or less likely your friend is to die from COVID then the unvaccinated population as a whole, if he's infected.

4. Remember the curve we got from Googling "Covid Atlantico Province Colombia"? Well, not only is there a "new cases" curve, but there's also a "deaths curve." For Atlantico Province, there are currently about 4 deaths a day from COVID. You may want to adjust this upwards for undercounting. I can provide suggestions on that depending just how deep you want to get into this. (I don't know how good of a friend this is.) Anyway, for Cartagena, you've got 4 deaths per day per 2.5 million people. If your friend were representative of the population of Cartagena as a whole, then maybe he'd have a probability of .00016% of dying from a COVID infection he caught in Cartagena if he were there one day, or .00032% if he's in Cartagena for two days. Take this number and multiply it by the Death Ratio determined in step "3" above. This is your friend's probability of death from COVID for his Cartagena trip.

Now, on one hand, we didn't take account that your friend's probability of actually coming down with COVID may be less than your average Cartagena resident, because he got the Pfizer vaccine 6 months ago. But then on the other hand, we didn't take into account that 30% of the population of Colombia is fully vaccinated, with crappy ass Chinese vaccines, and that will reduce their chances of dying if they contract COVID, and is reflected in the 4 deaths per day statistic. Maybe those two simplifying assumptions will balance out. Also, how likely is your friend to wear a mask and social distance while in Cartagena, including boinking time, compared to your average resident? Another big unknown. Finally, we took a "Death Ratio" for the USA and applied it to Colombia, which has a different demography, differences in the percentage of overweight residents, and differences in the prevailing COVID variants.

If you want to take a simpler approach, note that the 655 per million per day reported cases in Texas is 9X the number in Cartagena. Even though Cartagena must be undertesting more than Texas, I say go for it. He's probably more likely to get COVID here than Colombia.

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As any probabilist worth half his salt would tell you, there are very few perfect answers; only tradeoffs.

That's certainly true in the world of investments. It's impossible to earn well-above-market returns, like clockwork and over an extended period of time, unless you were a long-time client of Bernie Madoff's. (Well, up until late 2008, anyway.)

Many people suffer from something of a case of innumeracy and have a bit of trouble thinking critically about media reports on health matters and other issues. Very often facts are presented out of context or in such fashion as to attempt to mislead or bamboozle readers with little understanding of probability.

On that topic, a very fun read is A Mathematician Reads the Newspaper, by John Allen Paulos.

https://www.maa.org/press/maa-review...-the-newspaper

A good example of how someone who doesn't understand such things as risk variables and cohort skewness (let alone Simpson's Paradox!) occurred in this forum just a couple of days ago:

https://eccie.net/showpost.php?p=106...0&postcount=38

Therein was included a concise explanation of how something that seems so counterintuitive to the uninitiated can nevertheless be quite true.

One fun little tidbit probability students are introduced to early in a typical introductory course is the so-called "birthday paradox." Many are surprised to learn that you only need to assemble 23 people for the probability to reach 0.5 that at least two of them will have the same birthday (month and date, not necessarily year).

To me, though, the following little exercise is significantly more counterintuitive than the birthday paradox.

Consider the case of a man who is a terrible hypochondriac and continually gets himself tested for various genetic markers or other health status issues, even though he has no reason to believe that he is at even the slightest elevated risk of being affected by any of them.

Suppose that there is a condition that occurs in 0.01% (1 in 10,00) of the general population. There is a test that is "99% accurate," both for positive and negative status.

He takes the test and it comes back positive. What is the probability that he is actually affected by the condition?

(Note: It might be fun for the people who everyone knows could supply the answer almost instantly to refrain from doing so for now, so that those whose mathematical educational status is unknown can take a shot at it! Although very likely none will.)

. Originally Posted by CaptainMidnight

Just checking. You do use Bayes Theorem? Like McDingDong suggested in post #4.

I’ll leave math to the smart guys. I’d suggest playing in the Dominican Republic. They have several sex resorts which would likely lower the overall risk. I suspect they have a Covid testing policy and Dominican woman are hot as all get out.

I’ll leave math to the smart guys. I’d suggest playing in the Dominican Republic. They have several sex resorts which would likely lower the overall risk. I suspect they have a Covid testing policy and Dominican woman are hot as all get out. Originally Posted by 1blackman1

Current COVID infection rates look to be low too. I didn’t bring it up because I’ve never been there. Would you go to Sosua, Santo Domingo or puerto plata?

Impersonally I prefer Punta Cana but I did enjoy going over to Puerto Plata.

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Impersonally I prefer Punta Cana but I did enjoy going over to Puerto Plata. Originally Posted by 1blackman1

Interesting. I read something about this a couple of years ago in the Dallas or Austin Men's Lounge. (Or maybe it was in the national section; not sure.)

If I understand the concept correctly, these are resorts wherein there are all sorts of things to do, right? Getting therapeutic massages, hot tubs, beaches, various forms of entertainment?

How hot are the girls? Do you mingle in a bar-like setting and pick one? Is there generally a pretty good choice at any given time?

Got to get a few things done, but will get to the other issues and more stuff later or tomorrow. (Just wanted to get these key questions posted up at an early time!)

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It’s like being at any all inclusive resort - drinks food etc. you get to pick a girl or two based on your package to spend the days with from a portfolio. You can also add or switch girls as well If you get bored with the one you’ve chosen or you don’t click. They also tend to have free roaming gals that you can pick up or add or switch to.

I found 90% of the girls to be very hot. The other 10 weren’t unattractive just were t my type. All the ones I saw or spoke with were Dominican but I’ve had friends state there were other Nationalities such as Argentines and Mexicans. Considering the range of hues amongst the Dominicans they coulda just been trying to seem more exotic.

I suggest learning a little Spanish because theirs generally isn’t very good (though they understand enough English to suck fuck etc). Also, my experience was that It was best to keep your options open and not get tied to one chick for the whole time (I never did more than 3 days), I get bored easily and after 12-24 hours how much more fucking can you do with the same chick that you’re not in a relationship with.

Plus you’re walking around looking at a lot of hot ass and we all know the best pussy is the next pussy.

I also understand that there is an option to just mingle and pick a gal for hours, not sure exactly how that works but I know it’s an option hence the roaming gals.

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As requested, I'll try to fill in the blanks for the "hypothetical gentleman," who will be referred to as "HG." (Comments in red):

Damn it Midnight, why do you have to tie my hands behind my back? The obvious answer is strap on an N95 mask and aviator goggles (more stylish than a face shield). Carry along a more comfortable KN95 mask for your date, along with a home COVID test kit, available for $25 from CVS. Don't feel uncomfortable asking her to use it. Remember, if she won't let you stick a cotton swab up her nose she's sure as hell not going to allow DFK. Then insist on reverse cowgirl and go to town. You can use this strategy in any cathouse in the world, no matter the level of COVID.

Yes, understood. But HG is the sort who enjoys the ultimate in an erotic experience, and fears that all that stuff would dull the senses a bit. Besides, earlier this week he took the plunge and really decided to push the risk envelope (according to his QAnon friends)and got the booster (3rd dose Pfizer).

The two most obvious locations to pull Latin hookers in the time of COVID are the Cocal Hotel Bar in Jaco, Costa Rica, and the Clock Tower in Cartagena, Colombia. Both are open air venues, which cuts down greatly on the risk of infection. Both have lots of hot women. There are open air restaurants in both places where you can eat.

Sounds great!

For what your friend wants, banging 4 or more women over a two day period, the Cocal is clearly superior. It's quicker and easier to get to, and it's so easy to shuttle them in and out of your room from the open air bar. Hell, if you've got the money and an endless supply of Viagra you could do six a day, easy.

Cartagena on the other hand is a great place to wife up. Most of the hookers are from Venezuela and other cities in Colombia, so don't have to be worried about friends or families seeing them around town with gringos old enough to be their fathers. And Cartagena is one of the most romantic cities in the world. The problem is getting there. You're probably going to have to make an extra connection through Panama City or Miami. So a lot of travel time for a short trip.

Maybe a charter can get in and out of there quickly and easily?

So should it be Costa Rica? This is where we have to put on our thinking caps. First Google "Costa Rica Covid." You'll see a chart of new cases, running about 2300 a day. Costa Rica has a population of 5 million, so that's 455 new cases per million per day. Now Google "Colombia Atlantico Province Covid." Atlantico province, where Cartagena is located, has 170 cases a day and a population of 2.5 million people, that's only 68 new cases per million per day.

So what are your chances of dying from COVID if you decide to go boinking in one of these places? I've actually worked that out for climbing a particular mountain. This has many more moving parts, and depends on specifics of your friend and where he plans to go. But these are some of the considerations,

1. What is his age? Does he have co-morbidities? From this you can estimate an appropriate infection fatality ratio (IFR), if he comes down with the disease, assuming he's unvaccinated. There are papers in the literature and also information on the CDC web site that will help. Take into account he's male, as IFR's for men are higher than for women.

Age is early 70s, so that creates a bit of a risk. Another small (perhaps) risk factor is a history of significant grass and pollen allergies which precipitated (possibly) a pretty unpleasant case of bronchitis a few years ago. I have been taking (desensitization) allergy shots once every four weeks.

But weighed against this are some plusses: Low body fat (13.2% according to recent hydrostatic measurement at the Cooper Center in Dallas), BP hangs out well into sub-120/80 territory, resting HR 48. Very healthy diet (well, on most days!), some strength training, endurance work most days, high-intensity interval training 2-3X/week.

2. What vaccine did he receive? How long has it been since the second dose, or third dose if he got the booster? For example, data from Israel might indicate if he received his 2nd Pfizer shot 6 months ago, his probability of coming down with severe disease are 15% of what they would be if he were unvaccinated. Make the simplifying assumption that the 15% would also apply to death. You can adjust the IFR determined from "1" downwards by 85% then.

Cool info, thanks! 2nd dose Pfizer 3/1, 3rd 9/7.

3. The IFR for the USA before vaccines was about 0.8%, based on antibody studies and death statistics. Take your friend's IFR and divide by 0.8%. We'll call this the Death Ratio, and it's how much more or less likely your friend is to die from COVID then the unvaccinated population as a whole, if he's infected.

4. Remember the curve we got from Googling "Covid Atlantico Province Colombia"? Well, not only is there a "new cases" curve, but there's also a "deaths curve." For Atlantico Province, there are currently about 4 deaths a day from COVID. You may want to adjust this upwards for undercounting. I can provide suggestions on that depending just how deep you want to get into this. (I don't know how good of a friend this is.) Anyway, for Cartagena, you've got 4 deaths per day per 2.5 million people. If your friend were representative of the population of Cartagena as a whole, then maybe he'd have a probability of .00016% of dying from a COVID infection he caught in Cartagena if he were there one day, or .00032% if he's in Cartagena for two days. Take this number and multiply it by the Death Ratio determined in step "3" above. This is your friend's probability of death from COVID for his Cartagena trip.

Now, on one hand, we didn't take account that your friend's probability of actually coming down with COVID may be less than your average Cartagena resident, because he got the Pfizer vaccine 6 months ago. But then on the other hand, we didn't take into account that 30% of the population of Colombia is fully vaccinated, with crappy ass Chinese vaccines, and that will reduce their chances of dying if they contract COVID, and is reflected in the 4 deaths per day statistic. Maybe those two simplifying assumptions will balance out. Also, how likely is your friend to wear a mask and social distance while in Cartagena, including boinking time, compared to your average resident? Another big unknown. Finally, we took a "Death Ratio" for the USA and applied it to Colombia, which has a different demography, differences in the percentage of overweight residents, and differences in the prevailing COVID variants.

I think that after I tell him all this, he will be feeling better! (Maybe so good that he'll feel like warming up by paying a couple of Dallas SBs a quick visit!

If you want to take a simpler approach, note that the 655 per million per day reported cases in Texas is 9X the number in Cartagena. Even though Cartagena must be undertesting more than Texas, I say go for it. He's probably more likely to get COVID here than Colombia. Originally Posted by Tiny

Good info! Although the mind boggles, I'll start calculating!

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Although many may not think of it this way, we all have to be practical probabilists at times, as we have to weigh risks and decide whether something is a chance worth taking.

During registration week of HG's first semester as a freshman at UT-Austin in the 1960s, he ran into a friend from high school who mentioned that two or three guys were planning on riding with him to Nuevo Laredo that night, since they all had finished the registration process. So had HG, and he figured "why the hell not," although he was not quite sure what this would entail or what it would cost. After checking his wallet to be sure there was more than just perhaps a single $5 bill in there, he stupidly said, "OK, I'm in!"

Being 18 and naive, he wasn't even sure that any of the "girls" would be remotely young, as he envisioned a bunch of fat, aging old hags.

Most were, actually, but HG spotted a pretty young babe who had great legs and couldn't have been much over 18. As she realized that she had caught his eye -- big time -- she moved right in for some dealmaking.

"10 dollars!," she said. HG fished through his nearly bare wallet and acted like he couldn't quite make it. Maybe he could borrow a couple of bucks from one of his nearby friends!

Perhaps realizing that patience was part and parcel of good dealmaking, but more likely because he was just nervous as hell, he paused and seemingly hesitated.

"Eight dollars!," said the cute Latina. As HG was fishing through his wallet and counting, she said, "Seven dollars."
And then after about a 5-second pause said, "Because you handsome!" (Yes, thought HG. Surely that's got to be the first time she's told a guy that this week. Or at least within the first hundred.)

The two of them head quickly to a room, where HG assumed that she'd have a "cover."

Nope! Apparently not the thing at that time. So HG plunged in bare, without a care in the world (for now). Of course, there may have been a little alcohol involved.

The next day, he started worrying. What if he'd caught something? It was Wednesday and he was looking forward to a Saturday night date with a girl he'd seen twice and things seemed to be moving in a positive direction, although so far he'd only been able to cop a feel. (But maybe only because she had to be in early because of the dorm curfews enforced at the time.)

Maybe it would be a good idea to find a family doc in Austin and go by for a visit, HG thought.

So he did, nervously mumbling and bumbling something like:

Doctor, I went to a border town and ... uh, well ... you know ... something like ...

The doc interrupted and said, "So you fucked a Mexican whore without a rubber."

HG: "Uh, yeah, I think that's kinda how it went down."

Doc: "Any pain or burning during urination?"

HG: "No! Well, not yet. Doesn't that take two or three days?"

Doc: "Yeah, come back if you develop any of those symptoms."

HG: "Wait! What about the possibility of taking a shot as a sort of prophylactic? I mean, wouldn't that prevent getting anything? I have a big date soon, and although I'm not sure anything will happen, I don't want to fuck things up for good by giving her the clap!"

Doc: "Sure! We can shoot you up with 1.5 million units of penicillin and whatever you might be growing in there will be killed stone dead!"

HG: "OK!"

HG asked the doc what the probability of catching gonorrhea from that one contact might be and he said, "Oh, maybe 10% up to 25%."

Holy shit! Did he really want to take up to a 25% risk of torpedoing a possibly budding good thing? (Marsha was fucking hot!)

As with so many probability problems there are conditionals, of course.

Can you imagine a phone conversation like this, though?

"Hey Marsha! Sorry about that case of the clap; I'll be more careful from now on. That new movie you mentioned last week opens Friday. Wanna go catch the movie Saturday night? I'll even pay for your penicillin shot. I mean, even if I have to go mow a couple of lawns or something. I'll round up the money. Don't worry about a thing."

Pretty sure that the probability would be at least 0.999 that the reply would be something like, "Catch a movie? No, you fucking asshole! I don't want to catch anything from you!"

So it appears that HG made the proper decision in view of the judgment that the new dating opportunity offered significant utility (to use the term an economist might use.)

This is a true story. HG's friends got a kick out of it for years, although some said they handled their trip to Mexico in considerably dumber fashion. (In fact, my own father did so many years ago, well into adulthood. Yep, a raging case of the clap. Way to go there, dad.)

Well ... I hope someone got a chuckle out of this. I got a bit of amusement reminiscing about it.

As well as some much needed typing practice, as I've mostly been vacationing and need to get back up to speed on my "real" keyboard.

Weigh the risks and place your bets appropriately, gentlemen!

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Lol. Same shit happens today and will happen tomorrow.