Ask Me Anything About Autocross

One of things I like to do in my spare time is write. I am generally not that great at writing. There are plenty of more talented individuals than me out there, but what I do enjoy is sharing my experiences and thoughts through writing.

As this week leads up to the SCCA Pro Solo Finale and Solo Nationals, I thought this space would be a great place for a “Ask Me Anything About Autocross.” I am going to give this Q&A format a try. I would love to field questions from anyone, especially non-racing or non-car people. So… ask away!

Send your questions to me on FB, Instagram, or whatever!

Why are you a shit driver?

K: I don’t push the right pedal all the way down, and I use the middle pedal a way too much.

What is your favorite auto-x element? Least favorite? What do you want to see more/less of at an autox?

K: Most favorite to date would be the “fake walloms” as I would call it. It’s essentially a wallom where only the last cone is relevant. The cones in front don’t do anything at all. Visually deceptive, but lots of fun. Least favorite element would be anything that requires me to slow down to 20 mph to get through. There isn’t any one element I would like to see more or less of. Maybe more creative/unique elements.

Is it more fun/stressful/expensive to auto-x with your daily driver or a car you keep just for racing?

K: Fun – Dedicated race car. The more prepared the car, the more fun it is to drive. Stressful – This kind of depends. More prepared car requires more work to get to get ready. A street car is essentially arrive and drive. Expensive – Definitely the more prepared car. Race tires are not cheap.

Facebooktwittergoogle_plusredditpinterestlinkedinmail

Random Thoughts: Playing Better Pool Players Makes You Better is a Lie.

Back in 2015, a friend and I decided to pick up pool (billiards) again. We both played a lot during our undergraduate days, but since moving back to Fremont and getting real jobs, pool has kind of taken a back seat.

With the opening of California Billiards in Fremont, our desire to shoot was re-ignited. With the opening of a local pool room also came the introduction of pool leagues where there was organized weekly play. Our enthusiasm and desire to become competitive flourished. Playing in a league allowed us more opportunities to be competitive not only at the local level, but also allowed us to “flex our muscles” at the regional and national levels.

Over the last 3 years, as I moved from an APA Skill Level (SL) 4 to Level 7 in 9-Ball, and SL 4 to SL 6 in 8-ball, I’ve noticed several reoccurring themes. The biggest theme is that pool to us average folks is 90% mental. The theme I want to talk about is:

Playing better opponents or in harder leagues or (insert text here) DOES NOT make you a better player.

Anyone that tells you that it does is lying to you.

Yes. Playing better people is a component of becoming better, but itself alone is not enough for you to improve. And this really is true for any other passion or hobby, whether it be sports or autocrossing.

Most of the improvement and growth happens outside of the match. Ask yourself these questions after your match or during practice:

Before my match, did I adequately prepare? Did I warm up? Did I dial in my shot or stroke? Did I practice enough so that I am confident in making common shots? Did I work on my weak spots? What are my goals for this match? (Consistently run 3 balls? Make good decisions for pocketing vs. safeties? Execute key safeties? Minimize the number of mistakes I make?)

During my match, what did I do well? What didn’t I do well? Which shots did I struggle with? Which shots carried me? What were some of the critical mistakes I made? And how could I have avoided them? Or what was a better way to go about the situation? Was I fully invested in my match? And did I give the match the best effort I had?

After my match, what can I take away regardless of winning or losing? Did I practice key shots or safeties that I either struggled with during the match, or completely missed? Did I practice and improve on troubled areas or concepts of my game. Do I understand my mistakes? And did I make an honest effort to do any or all these things?

These are the key questions you really need to ask yourself if you want to improve. More importantly, being disciplined about critically analyzing your game and committing to practice in order to improve is key.

There’s nothing wrong with playing pool at a casual level. You can improve a little bit by playing casually, but modest improvement at most. However, if you wanted to get to that next level, you need to input the work that is needed into becoming a better player.

Facebooktwittergoogle_plusredditpinterestlinkedinmail

2017 Resolutions Recap

Update on my 2017 Resolutions

My goals for 2017 and in no particular order:

  1. Run a 9-ball rack (pool) and improve my billiards game. I’ve actually broke and ran a 9-ball game before, but haven’t done so since my session of APA League Pool. Stretch goal: Top Gun in 9-ball for my local APA league. There were a lot of break and runs this year. No Top Gun, but a strong showing in both 8 and 9 ball.
  2. Stage 0 Weight Reduction (lose some weight) and be a little healthier. Maybe make some time and pick up Aikido again. First milestone is to lose 20 lbs. This didn’t happen. I think that I actually gained a few lbs. This year, I’ve decided to change a few things and am working on making this a reality.
  3. Be a little more selfish and spend MORE time focusing on myself and the things I am passionate about. I think I did this. It’s a work in progress.
  4. Chair at least one autocross event for the 2017 Championship Series and one event for the 2017 Slush series. Done.
  5. Podium at an autocross event in my class with more than 5 entries. Done. This past year has been a huge improvement. After 3 years of owning the car, I finally have a full platform to race on. And this rear wheel drive thing is starting to click.
  6. Fix the Impreza, and then fix the Porsche. Let’s not talk about this. Nothing has changed. Lol.
  7. Be more supportive of my friends in their interests and passions, even if those things are no interest to me. Still trying to do this. I think I’ve gotten better at it, but I still think there is a lot of growth that still needs to take place.
  8. Be relatively debt-free by the end of 2017. I am more debt free, but still a ways to debt-free.
  9. Play more Magic: the Gathering than I did in 2016. I think I played about the same amount of Magic. I am looking to play more in 2018.
Facebooktwittergoogle_plusredditpinterestlinkedinmail

Instant Pot – Vietnamese Yogurt

Sweet Yogurt.

  • 1 can of sweetened condensed milk
  • 1.5 cans (use the can from the condensed milk) of hot water
  • 2 cans of room temp water
  • about 3 spoons full of plain yogurt with active/live cultures

Mix. Mix. Mix.

Instant Pot on Yogurt for 6.5 hrs.

For Sweeter Yogurt Recipe.

  • 1 can of sweetened condensed milk
  • 1.5 cans (use the can from the condensed milk) of hot water
  • 1 cans of room temp water
  • about 3 spoons full of plain yogurt with active/live cultures

For Sweet and a Thicker Yogurt

  • 1 can of sweetened condensed milk
  • 1.5 cans (use the can from the condensed milk) of hot water
  • 1 can of room temp water
  • 1 can of 2% milk
  • about 3 spoons full of plain yogurt with active/live cultures
Facebooktwittergoogle_plusredditpinterestlinkedinmail

Instant Pot – BBQ Pulled Pork

Super easy to do and great for any occasion! Recently made this for our SuperBowl gathering!

BBQ Pulled Pork in the Instant Pot

Ingredients:

Instructions:

  1. Cut up the roast into 1.5″-2″ cubes and put all the pork, water, and marinade packet in the liner of the Instant Pot. I think the pulled pork tastes better if you allow it to marinate overnight.
  2. Close and lock the lid, making sure the sealing knob is on sealing. I set the Instant Pot to manual for 40 minutes.
  3. Once the cooking is done, you can release the pressure by the quick or natural pressure release.
  4. Once the pressure is released, remove the pork chunks and shred. Once shredded, place into a large bowl and add BBQ sauce and mix. Add as much or as little as you want. To help keep the pulled pork moist, I also ladled a little bit of the marinade into the mixing bowl. As I liked my pulled pork with a little sweeter sauce, I added a little brown sugar to the mixture. Feel free to add sriracha if you are looking for a little heat!
  5. Serve with buns and coleslaw or enjoy however you like!
Facebooktwittergoogle_plusredditpinterestlinkedinmail

Understanding Probability in Pandemic Legacy: Season 2 – Part 3

Understanding Probability in Pandemic Legacy: Season 2 is a multi-part series. Links to the other parts can be found here:

Understanding Probability in Pandemic Legacy: Season 2 – Part 1
Probability of Incidents During Set-Up

Understanding Probability in Pandemic Legacy: Season 2 – Part 2
Probability of Incidents During Set-Up and How-To Use the Front 9 Calculator

Understanding Probability in Pandemic Legacy: Season 2 – Part 3
Strategies to Survive Between Set-Up and First Epidemic

Strategies to Survive Between Set-Up and First Epidemic

After the infection stage of set-up, what is the best strategy to hold the disease at bay between Set-Up and the first Epidemic?

Source: ZMan Games

Why only manage until the first Epidemic? Once the first Epidemic occurs, the discard is shuffled and put back at the top of the deck. Once this happens, we’ll generally have the same subset of cards that we’ll be drawing from after each Epidemic. Right after set-up, we are still drawing from the larger unknown Infection Deck. All we can really do is cover all the cities. Once the Epidemic happens, we’ll know the composition of the next 20 or so cards which can help us determine how many cubes, or none at all are needed on each city and the likelihood that a specific city may be drawn.

Since we already know the contents (deck size and composition) of the Infection Deck, what we do between Set-Up and the First Epidemic is largely based on what cards are revealed during Set-Up.

We can use adapt the Front 9 Calculator to better demonstrate the probabilities during the Infection step at the end of each player’s turns.

The Previous Strategy

The strategy will be similar to that of how we distributed the the supply cubes prior to set-up. We want to minimize incidents by addressing the most vulnerable cities. In the case of distribution of set-up, we distributed the cubes like this:

1. Place one supply cube in each city that has 3 cards in the infection deck.
2. Place one supply cube in each city that has 2 cards in the infection deck.
3. Place one supply cube in each city that has 1 card in the infection deck.
4. Place a second supply cube in each city that has 3 cards in the infection deck.
5. Place a second supply cube in each city that has 2 cards in the infection deck.
6. Place a third supply cube in each city that has 3 cards in the infection deck.

We know that regardless of the deck size, the order (of probabilities) of items #1-6 will always stay true, though as the deck starts to thin, the percentages of an event happening increases.

The Adapted Formula

Deck size = N (Remaining number of cards in the Infection Deck)
Total number of cards drawn = R = 2 (Infection Rate prior to Epidemic 1)
Number of New York cards = n = 3
Number of New York Cards drawn = r = [0, 1, or 2]; r can not be 3 as the most cards that can be drawn is 2.

P(X = r) =

C(n, r) * C(N-n, R-r)
——————
C(N, R)

In layman’s terms,

C(n, r) is the number of ways to draw r New York card from n New York cards.

C(N, R) is the number of ways to draw R (R=2) cards, from N (N = # of cards remaining in the Infection Deck).

C(N-n, R-r) refers to the number of ways to draw R-r (Non-New York) from N-n (Non-New York)

The formula is exactly the same as the Front 9. The biggest difference is the N and R values. Here is the adapted calculator.

N=18 (Remaining Deck Size, Cell B3); R=2 (Infection Rate; Cell B4)

A simple substitution of a larger or smaller number in to the Backside Calculator will confirm that the order/priority of the guidelines are still true.

N=16 (Remaining Deck Size, Cell B3); R=2 (Infection Rate, Cell B4)

After the 9 infection cards are revealed during set-up, we can use this information to work backwards to determine what cards are remaining in the Infection Deck. The Infection Deck discard is known information. You may look at its content at any time.

Since the order of probabilities is the same, you won’t need to use the calculator. You only need to base your decision from the remaining Infection Deck subset.

Example 1: If two New York cards are revealed during set-up, then there is one New York card remaining in the Infection Deck. Looking at the N=18 chart, the probability that a New York card will be drawn in the next Infection step is 0.1111. This can be found by looking at Row 8 for 1 remaining card in the Infection Deck, and column D, E, and F. The key cell we are looking at is D8 as E8 and F8 are impossible outcomes. (You can’t draw 2 or more cards when there is a fewer number left in the deck.

Example 2: If no New York cards were revealed during set-up. How many New York cards are left in the Infection Deck at the beginning of the game? What’s the probability of this card coming up during the next Infect step (given there is no Epidemic)?

There are three New York cards left in the Infection Deck. Looking at Row 10, and column D, E, F. (Cells D10, E10, and F10.) F10 isn’t a possible outcome and is 0. The sum of D10 and E10 is the probability. Probability = 0.3137.

Revised Guidelines for Game-play Between Set-Up and Epidemic 1

Here’s the revised guidelines. These guidelines are based on the strategy of keeping the most venerable cities stocked with at least one supply cubes. When all cities have at least one supply cube, then does the city receiving a second supply cube is feasible. According to the table provided by the Backside Calculator, it will be very rare to see back-to-back city cards to come out during the Infection step between set-up and the first Epidemic.

1. If a city has 3 Infection cards remaining in the Infection Deck, and there are no cubes on that city, place 1 supply cube on that city.
2. If a city has 2 Infection cards remaining in the Infection Deck, and there are no cubes on that city, place 1 supply cube on that city.
3. If a city has 1 Infection cards remaining in the Infection Deck, and there are no cubes on that city, place 1 supply cube on that city.
4. If a city has 3 Infection cards remaining in the Infection Deck, and there is 1 cubes on that city, place 1 supply cube on that city.
5. If a city has 2 Infection cards remaining in the Infection Deck, and there is 1 cubes on that city, place 1 supply cube on that city.
6. If a city has 3 Infection cards remaining in the Infection Deck, and there is 2 cubes on that city, place 1 supply cube on that city.

Facebooktwittergoogle_plusredditpinterestlinkedinmail

Understanding Probability in Pandemic Legacy: Season 2 – Part 2

Understanding Probability in Pandemic Legacy: Season 2 is a multi-part series. Links to the other parts can be found here:

Understanding Probability in Pandemic Legacy: Season 2 – Part 1
Probability of Incidents During Set-Up

Understanding Probability in Pandemic Legacy: Season 2 – Part 2
Probability of Incidents During Set-Up and How-To Use the Front 9 Calculator

Understanding Probability in Pandemic Legacy: Season 2 – Part 3
Strategies to Survive Between Set-Up and First Epidemic

Using the Front 9 Calculator

Use this calculator to help determine the best way to distribute supply cubes onto your game board prior to the Infection step of Set-Up.

In Part 1, we calculated the probabilities of drawing 0, 1, 2, or 3 cards of a city (Ex. New York) during the Infection step of Set-Up. In Google Sheets, using the built-in combination function [=combin(n, r)], we are easily able to fill out a table comparing the probabilities of Cities with # of Infection Cards vs. Number of Times a City Infected During Set-Up.

The calculator is provided here. It is write-protected so it won’t provide any spoilers of the game outside of the prologue. You will need to copy it to your own Google Drive to be able to edit it and use it.

The only cell you need to populate is B5 (cell filled green). As your Infection Deck grows or shrinks, update this cell to see the updated probabilities of an event happening.

Understanding the Values in the Front 9 Calculator

The vertical axis (the area shaded in red) represents the cities with 1, 2, or 3 city cards in the infection deck.

The horizontal axis (the shaded in blue) represents the number of times a city is infected during set-up (0, 1, 2, or 3).

The purple area represents probabilities of possible outcomes.

The gray area represents impossible outcomes (0% probability).

The sum of the outcomes of Row 1, Row 2, and Row 3 are 1 (or 100%). This is important as we will used this piece of information to work backwards and to derive context.

Examples

Example 1: What does Cell C11 represent? Infection Deck = 27. The city we are trying to calculate the probability for has only 2 cards in the Infection Deck. What is the probability that we will not draw any infection cards in this city during the Set-Up Infection?

= P(X = 0) or 1 – P(X > 0) or 1 – P(X = 1, 2, or 3)

= C11 = 1 – (D11 + E11 + F11) = 1 – (D11 + E11 + F11)

= 43.59%

In the context of Pandemic Legacy: Season 2: If no supply cubes where placed in this city, what’s the likelihood that this city will have an incident (Infection when no supply cues are present)?

Since there are no supply cubes, both outcomes of P(X = 1) and P(X =2) will cause an incident. Therefore the probability of an incident happening is:

P(X = incident when no supply cubes are present) =  P(X = 1) + P(X = 2)

= 0.4615 + 0.1026 = 0.5641

Example 2: What do Cells C12 to F12 represent? Infection Deck = 27. The city we are trying to calculate the probability for has only 3 cards in the Infection Deck. If we place a single supply cube on this city, what is the probability that we will not have any incidents during the Set-Up Infection?

Since there is a single supply cube in the city, the only way for the city to have an incident is if two or more infection cards are revealed during set-up. There are no incident outcomes if 0 or 1 infection card for this city comes up as the single supply cube negates the effect of the 1 infection card scenario.

= P(X = incident when a city with 3 cards in the infection deck has 1 supply cube on it)

Since we know that X = 0 and X = 1 will not cause an incident; and X > 1 (X = 2 and X = 3) will cause incident, the probability of an incident happening is:

= P(X = 2) + P(X = 3) = E12 + F12

= 0.2215 + 0.0287 = 0.2502

Theory Behind the Distribution Guidelines

Guidelines

1. Place one supply cube in each city that has 3 cards in the infection deck.
2. Place one supply cube in each city that has 2 cards in the infection deck.
3. Place one supply cube in each city that has 1 card in the infection deck.
4. Place a second supply cube in each city that has 3 cards in the infection deck.
5. Place a second supply cube in each city that has 2 cards in the infection deck.
6. Place a third supply cube in each city that has 3 cards in the infection deck.

Understanding the Numbers Behind the Guidelines

We already know this fact: The chance of getting an infection card from a city with 3 cards in the Infection Deck is higher than that of cities with only 2 cards in the Infection Deck. We also know that the probability that a city will be infected is higher for cities with two cards than it is for 1 cards.

Example 3:  There are no available cubes to distribute during set-up. List in order the type of cities (1 card, 2 cards, or 3 cards) that are most-likely to get at least one incident.

This information can be drawn from column C in the Front 9 Calculator. If we put context to these three cells, we would get this:

The probability that a city with 1 card in the infection doesn’t get an incident is 66.67%.
The probability that a city with 2 cards in the infection doesn’t get an incident is 43.59%.
The probability that a city with 3 cards in the infection doesn’t get an incident is 27.90%.

Probabilities that cities with 1, 2, or 3 infection cards in the deck will not be infected.

Most Probable to Have at least One Incident
Cities with 3 Infection Cards in the Infection Deck
Cities with 2 Infection Cards in the Infection Deck
Cities with 1 Infection Card in the Infection Deck
Least Probable

This order of most to least probable will stay true as long the three types of cities have the same number of supply cubes on it. (Except when the number of supply cubes is greater or equal than the number of card cards in the Infection Deck. In that case, the outcomes has zero probability.)

The city with more infection cards in the Infection Deck will have a greater probability if all things else are equal.

Example 5: Place a supply cube in each of the cities that have 3 cities card in the Infection Deck. List in order the type of cities (1 card, 2 cards, or 3 cards) that are most-likely to get at least one incident.

We’ve already determine the probability of this scenario in Example 2 and know the probability is the sum of the outcomes where X > 1 (or cells E12 and F12).

The probability of an incident in a city with one supply cube in it and has 3 cards in the Infection Deck is greater less than the probability of an incident in a city with no supply cubes that has 1 or 2 cards in the Infection Deck.

Most Probable to Have at least One Incident
Cities with 2 cards and has 0 supply cubes. (Cells D11 + E11) = 0.5641
Cities with 1 cards and has 0 supply cubes. (Cell D10) = 0.3333
Cities with 3 cards and has 1 supply cube. (Cell E12 and F12) = 0.2502
Least Probable

Knowing these things, we are now able to order all the scenarios from most to least probable.

Most to Least Probable of All Scenarios

Most Probable to Have at least One Incident
Cities with 3 cards and 0 supply cubes. (Cells D12/E12/F12) = 0.7210
Cities with 2 cards and 0 supply cubes (Cells D11/E11) = 0.5641
Cities with 1 cards and has 0 supply cubes. (Cell D10) = 0.3333
Cities with 3 cards and has 1 supply cube. (Cells E12/F12) = 0.2502
Cities with 2 cards and has 1 supply cubes. (Cells E11) = 0.1026
Cities with 3 cards  and has 2 supply cubes. (Cell F12) = 0.0287
Cities with 1 cards in the Infection Deck and has 1 supply cubes. = 0
Cities with 2 cards in the Infection Deck and has 2 supply cubes. = 0
Cities with 3 cards in the Infection Deck and has 3 supply cubes. = 0
Least Probable

Distributing the Supply Cubes

Using the information above, we can now determine how to best minimize the chance of incidents. In ideal situations where you have unlimited supply cubes, you would just distribute 3 supply cubes to each 3 card city, 2 supply cubes to each 2 card city, and a single supply cube to each 1 card city for a 0% percent chance of incidents.

However, the real-game scenario limits the number of supply cubes that are available during Set-Up. In-game, you would want to prioritize the cities with the highest probability first. As you add cubes one by one to a city, the probability of incidents occurring will decrease.

Cities with 3 cards and 0 supply cubes has the highest probability of incidents. Once  a supply cube is added to the city, the probability of an incident decreases to 0.2502.

The strategy is to address the highest probability incident scenarios, not cities, first. Once that scenario is completely addressed, the next step is address the next highest probable scenario, cities with 2 cards and 0 supply cubes (0.5641). And so on.

When the allotted supply cubes are distributed with the above priority, the board state will have the least probable set-up for incidents. Of course, this is just by the numbers. Higher probability will happen more often. Lower probability will happen less often.

If this method doesn’t work for you, my is disclaimer is this: This method doesn’t take into account luck, misfortune, poor shuffling, and/or Acts of God.

Facebooktwittergoogle_plusredditpinterestlinkedinmail

Understanding Probability in Pandemic Legacy: Season 2 – Part 1

Oh my god. I am actually using my degree.

Before I begin, I just wanted everyone to know that I am going to try my best to not spoil any of the game other than what you might have seen in the Prologue month.

Understanding Probability in Pandemic Legacy: Season 2 is a multi-part series. Links to the other parts can be found here:

Understanding Probability in Pandemic Legacy: Season 2 – Part 1
Probability of Incidents During Set-Up

Understanding Probability in Pandemic Legacy: Season 2 – Part 2
Probability of Incidents During Set-Up and How-To Use the Front 9 Calculator

Understanding Probability in Pandemic Legacy: Season 2 – Part 3
Strategies to Survive Between Set-Up and First Epidemic

Understanding Probability in Pandemic Legacy: Season 2

Pandemic Legacy: Season 2

zmangames.com

Game play of the Prologue month can easily be found on YouTube and the month is often used to introduce the game play, mechanics, and work flow to new players. The prologue has no permanent effects on the game and can be played an unlimited number of times before starting the January month.

For those of you who are in a current game of Pandemic Legacy: Season 2, you might have noticed that the game is quite a bit harder than Season 1. You aren’t alone. It seems like everyone is struggling to meet their monthly objectives. Here are some tips.

Optimize Your Chances of Winning

  1. Review the contents of the Infection Deck. Count the number of cards and see how the city infection cards are distributed. At the beginning of the game, there are 27 cards in the infection deck. 9 cities with 3 card each. This will change as the game progresses. As you are playing the game, keep track of which cards came up. This will help you determine the likelihood of future cards.After each epidemic, before shuffling the infection deck discard and putting it on top of the infection deck, review the played cards and take notes. Again, this will help you prepare for the upcoming infections.
  2. Review the contents of the player deck. Most importantly, get an idea of how often an Epidemic will come up. If the player deck has 60 cards, and there are only 5 Epidemics in the game, you should expect an Epidemic in each 12 card cycle.
  3. Take Notes. Tally the number of players cards that you have gone through. Tally the number of cities that have come up. Tally how many turns/player cards since the last epidemic, or which epidemic cycle you are currently on.

Solving for the Probability of Event (blank)

Now onto the probability. Why is probability so important? A core mechanic of Season 2 is keeping enough supply (gray) cubes in each city on the board to adequately protect the city from incidents, or infection of a city when there are no stockpile cubes left. When a city gets infected, a supply cube is removed. When a city is infected and has no supply cubes left, a disease cube is placed in the city and the incident marker is moved forward. When the game reaches the 8th incident for the game, Pandemic has won and that attempt for that month is over.

Image Source: https://www.polygon.com/2017/8/24/16197080/pandemic-legacy-season-2-preview-release-date-gen-con

How do we determine how many stockpile cubes are adequate? How do we distribute stockpile cubes in such a way that we minimize the number of incidents occurring during the initial infection?

That’s really a great question. To best answer that, we need to make some assumptions as well as simplify the scenario a little bit.

Rules/Context

During the set-up of the game, the players have a limited number of supply cubes to distribute among the cities connected to the grid. For the prologue month, there’s 9 cities and 36 stockpile cubes that need to be distributed. The infection deck has 27 cards. 3 cards for each city connected to the grid. After the cubes are distributed, set-up does an initial infection by drawing 9 cards from the infection deck and infecting the 9 revealed cities.

Solution (Kind of.)

To answer the initial question, let’s simplify even more. Let’s only concentrate on a single city, New York. Of the 27 cards in the infection deck, 3 cards are New York. During the set-up infection (9 infection cards), what’s the likelihood that 0, 1, 2, or 3 New York cards show up? Does it make sense to place 0, 1, 2, or 3 cubes on New York to prevent incidents?

Source: https://www.forthewincafe.com/blogs/news/ftw-staff-picks-pandemic-legacy-season-2

Defining some variables:

Deck size = N = 27
Total number of cards drawn = R = 9
Number of New York cards = n = 3
Number of New York Cards drawn = r = [0, 1, 2, or 3]

If we were only drawing one card, probability would be really easy to determine. P(X = Draw New York) = 3/27.

However, since we are drawing 9 infection cards, we have to factor in that New York cards can fall into any slots. We could draw a New York with the first card, or the last card, or any card in between. In order to account for this, we will use combinations as don’t care about order.

Some other assumptions: Though the remaining 24 cards in the Infection Deck are not all the same, for this problem, we’ll just lump them together and consider them “Non-New York.”

Reference:

More information on Combinations can be found here under “Combinations, Ho!”
https://betterexplained.com/articles/easy-permutations-and-combinations/

For reference:

Combinations = nCr = C(n, r)
Solve in Google Sheets using this function: =combin(n, r)

P(X = r) =

C(n, r) * C(N-n, R-r)
——————
C(N, R)

In layman’s terms,

C(n, r) is the number of ways to draw r New York card from n New York cards.

C(N, R) is the number of ways to draw R (R=9) cards, from N (N=27).

C(N-n, R-r) refers to the number of ways to draw R-r (Non-New York) from N-n (Non-New York)

P(X = Draw 1 New York)

P(X = Draw 1 New York) =

[Combination(of drawing 1 New York from 3 New York cards) x Combination(of drawing 8 Non New York cards from 24 Non-New York Cards)] / [Combination(of drawing 9 cards from 27)]

It should look something like this:

C(3,1) * C(24, 8)
——————
C(27, 9)

P(X = Draw 1 New York) = 0.4708

P(X = Draw 2 New York)

Let’s try for P(X = Draw 2 New York).

C(3,2) * C(24, 7)
——————
C(27, 9)

As you can see, only the numerator changes. C(3,2) refers to drawing 2 New York’s from a total of 3. While C(24,7) refers to the number of ways to draw the 7 remaining cards from the Non New York subset.

P(X = Draw 2 New York) = 0.2215

P(X = Draw 3 New York)

C(3,3) * C(24, 6)
——————
C(27, 9)

P(X = Draw 3 New York) = 0.0287

P(X = Draw 0 New York)

Just for due diligence, let’s also do P(does not draw New York).

C(3,0) * C(24, 9)
——————
C(27, 9)

P(X = 0 New York) = 0.2790

Results

P(X = 0) = 0.2790
P(X = 1) = 0.4708
P(X = 2) = 0.2215
P(X = 3) = 0.0287

Let’s interpret the results.

P(X = 0) = 0.2790 – Probability that New York gets exactly 0 infections
P(X = 1) = 0.4708 – Probability that New York gets exactly 1 infection
P(X = 2) = 0.2215 – Probability that New York gets exactly 2 infections
P(X = 3) = 0.0287 – Probability that New York gets exactly 3 infections

Scenario:

Ex. I put only supply cubes on New York. What’s the risk or likelihood that New York will have an incident during the initial infection set-up? (What’s the probability that New York will be infected 3 times during Set-Up?)

P(X > 2) = 1 – P(X > 2) = P(X = 3) = 0.0287

Ex. I put one supply cube in New York. What’s the risk or likelihood that New York will have an incident during the initial infection set-up? (What’s the probability that New York will be infected 2 or more times?)

P(X > 1) = P(X = 2, 3) = P(X = 2) + P(X = 3) = 0.2215 + 0.0287 = 0.2502

Other Scenarios

Ex. There are only two New York Infection cards in the deck. (2 New York cards and 25 Non-New York cards) What are the probabilities of P(X = 0), P(X = 1), and P(X = 2)?

Deck size = N = 27
Total number of cards drawn = R = 9
Number of New York cards = n = 2
Number of New York Cards drawn = r = [0, 1, or 2]

The set-up of the formula is the same except that we’ll be using the new numbers above to substitute them into the combinations formula.

For P(X = 0), the formula will look like this:

C(2,0) * C(25, 9)
——————
C(27, 9)

P(X = 0) = 0.4359

Furthermore: P(X = 1) = 0.4615 and P(X = 2) = 0.1026.

Set-Up Infection Calculator in Google Docs

I’ve set up this cool little table/calculator to determine the probability that cities will become infected with 0, 1, 2, or 3 infection cubes during set-up. Just update your Infection Deck size in the green box.

Pandemic Legacy: Season 2 – Front 9 Calculator

Conclusion

What’s the best way to distribute supply cubes during set-up? Using the Set-Up Infection Calculator and the combination theories above, the best guidelines are to distribute supply cubes in this order. Continue to the next point if you still have stockpile cubes still available. Proof of this strategy can be found in Part 2.

1. Place one supply cube in each city that has 3 cards in the infection deck.

2. Place one supply cube in each city that has 2 cards in the infection deck.

3. Place one supply cube in each city that has 1 card in the infection deck.

4. Place a supply stockpile cube in each city that has 3 cards in the infection deck.

5. Place a supply stockpile cube in each city that has 2 cards in the infection deck.

Facebooktwittergoogle_plusredditpinterestlinkedinmail

Instant Pot – Tea Eggs Recipe

Details:

Difficulty: Easy
Prep: 60 minutes (most of this time is waiting)
Cooking Time: Most of the time is the eggs soaking.

Ingredients:

  • 3 tea bags of black tea
  • 3 star anise
  • 2 cinnamon sticks (~3 inches each)
  • 1 tablespoon of whole peppercorns
  • 1-2 tablespoon of brown sugar
  • 2 cups of soy sauce
  • 5 cups of water
  • eggs (easily can do a dozen, if not more)

Instructions:

  1. Soft boil eggs.Prior to cooking, leave the eggs out at room temperature for 15 minutes.

    Place the trivet in the Instant Pot and place the eggs on it. Fill water to just under the trivet. Set the Instant Pot to Manual for 4 minutes on High Pressure. Once done, quick release and immediately put the eggs into an ice bath. The ice bath immediately stops them from cooking.

  2. To prepare the eggs, take a spoon and gently evenly crack the shells of the eggs. Emphasis on gently. The Instant Pot has a way of preparing the eggs in such a way that eggs are easily de-shelled. I actually had a whole egg de-shell itself while it was being boiled in the marinade.
  3. Dump out the old water, and lightly clean the Instant Pot liner.
  4. Add 5 cups of water and bring to boil (Saute on High). Cover with a lid to boil water quicker. Add the tea bags and brew for 5 minutes.
  5. Next. add the peppercorn, brown sugar, star anise, and cinnamon and brew for another 5 minutes.
  6. Add soy sauce and bring to boil.
  7. Once at a boil, add the cracked eggs back in and continue to boil for 5 minutes.
  8. Lower the Instant Pot to a simmer. To do this, press the Keep Warm/Cancel button, and then set for Saute on Low (Saute, Pressure [Set to Low by hitting the minus (-) button], wait 10 seconds). Cover 2/3 of the Instant Pot with a lid to keep the marinade at a nice simmer. Simmer for 20 or 30 minutes.
  9. Once done, turn-off and set aside. For best results, leave the eggs in the marinade for 36 hours. This time measurement isn’t exact. Please play with it to get the desired flavor. At a minimum, let it soak over night (9 hours). This provides a more mild taste. A soak of 2-3 days will provide a more prominent flavor.I ended up placing the eggs in Tupperware and covering them with marinade, then storing them in my refrigerator. The remaining marinade, I stored in separate Tupperware and froze it.
  10. Save the marinade for future 1 or 2 tea egg batches!
Facebooktwittergoogle_plusredditpinterestlinkedinmail

Blackstone Labs Used Oil Analysis

9,708 miles on the oil. You read right. Nine thousand, seven hundred, eight miles!

Higher levels of silicon is probably due to the fact that I haven’t changed my air filter in 25,000 miles! No need to worry. I am getting a new one in the mail today!

Facebooktwittergoogle_plusredditpinterestlinkedinmail