http://www.brainpop.com/math/probability/basicprobability/

http://www.brainpop.com/math/dataanalysis/statistics/

**Concept map**

**Teaching prompts**

**Statistics**

**Probability**

**Percentage**

**Population**

**Sample**

Standard Deviations

by Gary Smith

How stats are used poorly to create data

Sampling

Biases

**Observation**

**Causality**

Mean

Median

Mode

**Misleading**

Stats

Stats

**Analyze**

Possible Outcomes of Rolling Die

More trials means better odds of rolling any number

Shark Attacks!

Rare

Fewer than 50 per year

Chances are 1 in 10 million

More unlikely than...

all these things

Shark attacks have risen...

Why?

Maybe there's just more people in the water

How do I not get bit?

Don't splash

swim in groups

don't wear flashy jewelry

http://www.brainpop.com/science/earthsystem/sharkattacks/

**Outcomes**

(results)

(results)

Probabilities

in real world

weather

rain

storms

lightning

hitting something

Lottery/

gambling

Biology

movement of water

not exactly random, but chaotic enough to appear random

Blackjack probability tables

Health

cancer development or recovery

genetic drift

mutations

Predation

Actually the question of how something finds food isn't totally probabilistic, but it's often hard enough to predict that we treat it that way

Langrangian vs. eulerian perspectives- eulerian approaches try to predict a systems response as a whole, and always involve probability

Pox (game)

Not taking a random sample of the population

Physics

Quarks

Position of electrons

Poker probability tables

Conditional probability

Distributions

Independent and Dependent Events

A BrainPOP movie

http://www.brainpop.com/math/probability/independentanddependentevents/

the probability of one event has no effect on the probability of another event

independent

ex. Dice

The chance of rolling a six on one roll has no effect on the chance of rolling a six on the next

dependent

the probability of an event changes the probability of a second event

in the brainpop movie, the probability of Tim choosing an apple affected the probability of Moby choosing an apple

ex. choosing without replacement

Compound Events

http://www.brainpop.com/math/probability/compoundevents/

the combined probability of two or more events

mutually exclusive events

the probability of both events having at the same time is zero

also, p(A or B) = p(A) + p(B)

inclusive events

it is possible for these events to happen in conjunction

also, p(A or B) = p(A) + p(B) - p(A and B)

**Game Theory**

http://www.brainpop.com/science/ecologyandbehavior/gametheory/

Mean, Median, Mode, Range

Range

A BrainPOP movie

http://www.brainpop.com/math/probability/meanmedianmodeandrange/

also, P(A or B) = P(A)

Deduce diseases from symptoms

Expectations/

Average of

outcome * probability

Network

depictions

Computer networks/

hacking

Stock markets, etc

Thermodynamics/

Properties of gases

(chaos?)

Clinical trials for medicines

twisting my ankle once makes it more likely that my ankle will be twisted in the future

Increased probability

Once I get sick with the flu, my body has built up resistance that makes it less likely to get the flu in the immediate future

Decreased probability

Autocorrelations

A statistic test that determines if an event is correlated with itself, in a sense measures the length of time in which future events are likely to follow the initial event. Also can find periodic patterns.

contains multiple choices

different areas have different infection rates

central limit theorem

Infections

**Predict**

**Manipulate (distributions, initial states, objects, etc.)**

Combinations

Permutations

**likely game mechanics**

http://www.spark101.org/video/using-expected-value-to-determine-life-insurance-p/

Dominant and recessive genes lead to ratio of traits being expressed in offspring

Distribution for a mixture of 2 different traits

"In asexual organisms, genes are inherited together, or linked, as they cannot mix with genes of other organisms during reproduction. In contrast, the offspring of sexual organisms contain random mixtures of their parents' chromosomes that are produced through independent assortment."

: Dependent and Independent Events

"Genetic drift is the change in allele frequency from one generation to the next that occurs because alleles are subject to sampling error."

: Stats concept

Use non-mendelian/blended inheritance, caused due to incomplete dominance or influence by multiple alleles, to represent continuous distributions, or change of values in future generations.

http://en.wikipedia.org/wiki/Genetics#Multiple_gene_interactions

reduced by large population sizes

isolated populations

bottleneck

founder effect

funny video about genetic drift, bottle necking and founder effect

Hardy-Weinberg Principle

Mendelian Genetics

1866, Mendel discovers heritable factors in generations of peas

true-breeding: when self-fertilization produces offspring that are all identical to the parent

hybrids: the offspring of two different varieties

cross: the cross-fertilization of two individuals

Epidemic Models

SIS/SIRS (deterministic models)

Random assignment of initial infections, some probability of contact with neighbours and spread.

People are susceptible, immune, infected.

Population changes are modeled, immunity after infection can be included, […]

Speciation

Pandemic (board game)

Pandemic (digital game)

http://www.theguardian.com/news/datablog/2013/mar/15/john-snow-cholera-map#

John Snow maps spread of cholera visually, convinces people that it's spreading from some point source in the middle of town.

showing infectious disease rates by size of country

http://en.wikipedia.org/wiki/Epidemic_model

population bottleneck

founders effect

http://www.genetics.org/content/148/4/1667.full

neutral mutation- changes in base pairs which do not affect protein coding regions, and therefore organism fitness

non-neutral mutation are about 1/300 per cell division (i.e. 1 in every 300 cell divisions is a change that effects fitness)

In genetics, a mutation is a change of the nucleotide sequence of the genome of an organism, virus, or extrachromosomal genetic element. Mutations result from unrepaired damage to DNA or to RNA genomes (typically caused by radiation or chemical mutagens), errors in the process of replication, or from the insertion or deletion of segments of DNA by mobile genetic elements.[1][2][3] Mutations may or may not produce discernible changes in the observable characteristics (phenotype) of an organism. Mutations play a part in both normal and abnormal biological processes including: evolution, cancer, and the development of the immune system.

https://www.khanacademy.org/math/probability/independent-dependent-probability/dependent_probability/v/introduction-to-dependent-probability

Two events are dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed.

drawing from a set without replacement is ALWAYS a dependent probability event.

http://www.mathsisfun.com/data/probability-events-conditional.html

Drawing a hand of cards from a deck- once I draw my initial cards, I am unable to draw those cards again

Nicotine is addictive- smoking once increases the probability that I will smoke more in the future

Once my dog poops, he is unlikely to poop again in the near future because it is out of his system

Examples of Inclusive events

Let's say you have to pick a dog at random. The probability of finding a black-haired dog and a long-haired dog is a mutually inclusive event, long-haired black dogs exist. On the other hand, the probability of finding a chihuahua and a respectably-sized dog are not inclusive events- chihuahuas are never respectably sized

Founder Effect Videos

Possible Human

Evolution

Hybrid Man

Illustrative on a very simple level...

Differences among

New area

Natural disasters

http://en.wikipedia.org/wiki/Non-Mendelian_inheritance

Positive

Genetic

Infections?

mutations affect resistance which affect

infection which affect mutation, and on

spatially dependent events

Sentinels of the

Multiverse

http://sentinelsofthemultiverse.com/multiverse/heroes/legacy

**How might we teach that infections are spatially dependent probabilities?**

who's this guy?

Legacy

and his daughter

Legacy

how might we teach that genetic drift, founder effect, and bottleneck effect differ?

how might we teach that genetic drift is a sampling error? +1

**How might we teach that trait inheritance is a set of compound events?**

**How might we teach that the outcome of one event affects the probability of later events?**

how might we teach that the probability of an "and" compound event is the multiplication rather that addition of those events probabilities? +1

Like in the Monty Hall Problem, every move should be precluded by some additional bit of information. So the person has to think if this influences his move’s likelihood of success or not, and how.

a la Pox – layout and interaction. Disease is spreading, there are probabilities of infections, and probabilities of vaccine/inoculation working. Each move select some people to try inoculating.

Somehow, the probability of infections spreading changes in different places? Or greater infected area/number of people increases strength of infection and probable places of next infection; calls for player to change path of action in response.

Risk (/Pandemic) – map of the world, infection is spreading. Like Risk, greater infected areas gives the infection more reinforcements. Some interesting probability fights to conquer territories, that are not dice-based?

Can a dice based interaction be made to exhibit or participate in non-trivial probability calculations?

General thought: Making this into a board game, or non automated game, especially in terms of effect of actions, would be much better I think.

// In dice games like Risk, does one think about the expected win chances of 3 dice and their army vs. 2 dice and the defending army? I know I haven’t, and even if I did, I remember having lost terribly ‘unfairly’, so to say, at times. ‘lies, damned lies, and statistics’.

Then the players themselves can be expected to manually figure out the composition of the outputs, and results of their actions, and sooner or later engage in prediction of their actions’ success as well. Because in solving for compound events, the general rule of finding different permutations, and so on, I think a significant factor is in understanding the scenario correctly and multiplying the right sets of numbers.

Move character around to avoid infection which has different probabilities at different places. (and at different times?) While trying to do tasks that require going to risky (wrt infection) places frequently.

A task like obtaining a specified population configuration 2-3/more generations in the future. Distribute traits in today’s population in a specific manner for this task (given properties like dominance/recessiveness about trait). Some other element? What ways could this be dynamic?

One of the factors that could influence infection spreading rates could be the connectivity of the node in which the infection is (imagining a graph of vertices and edges). If it connects to 5 other nodes, it is more likely somebody'll get infected soon, rather than a node with lesser connections. Or vice versa

Totally agree! I feel like that is the challenge. I don't think it is enough to just say that we are in a game that involves dice, QED there is probability here. How can we reinvent the game a it so that the probability gets brought to the forefront, strategy-wise?

What if the disease is spreading around a map, and your job is to allocate where your people should hide until the disease ends. The disease starts in one or two squares, and it's probability of spreading to adjacent squares depends on the type of disease (airborne, via rats, etc) and the types of terrain it's spreading over. You need to basically predict the spread of the disease and which spaces will be safest in 28 turns (28 days later). The earlier you place your people, the more points you gain if they stay safe

I kind of like the idea of having control over a population rather than a person. Reduced the cost to failure, which I think needs to happen in a probability game

I like the idea of having infections depend on population density, creates a nice push-pull. Group a lot of people in one are that might be safe, but because there are a lot of people the disease will spread fast if it gets there.

Or have a population with traits already distributed, and choose which members to move to an island, like in the lego video

I think we'd need to get two different traits to co-occur together- maybe there's a bunch of dogs of different colors and different hair length. If you need a long and yellow-haired, you have to figure out which ways to breed the dogs to get that-

I think the breeding would have to be constrained somewhat- maybe instead of being able to select only two dogs to interbreed, you have to select 3 males and 3 females, which we randomly mate and create a new population. You'll have like 3 cycles to produce at least 5 yellow-long-haired dogs.

Would be interesting to have some kind of game where the inheritance could switch from being totally exclusive (one gene does not effect the other) to a dominant/recessive genepool (one gene somewhat effects the other) to a linked set of genes (one trait always includes some other trait). And maybe the player strategies would have to change as a result of this difference. This would span the range from exclusive to inclusive events.

Thought of something like ticket to ride, where you have to follow one goal to completion, but by spending resources building towards one goal, you limit your opportunities to pursue future later goals.

Could be like dominion, you have a deck of cards, and you are trying to get certain combinations of cards each round, as you draw 5 cards. Each round, you also have the option to sub out certain cards for different ones.

Thinking about an ever morphing monster (like the AIDS virus, but that's a bad theme for a game). As you throw one type of attack at a monster you are able to weaken it, but then it will build up resistance, making that action less successful in the future.

In general, having actions change the state of the game that effects the effectiveness of later actions.

http://en.wikipedia.org/wiki/Monty_Hall_problem

http://store.steampowered.com/app/292200/

Spore

In the first level you play

as a featureless amoeba-like

creature. You pick up parts

from other creatures that have

died around you. You can

begin to use these traits to

adapt your creature (i.e., claws

for fighting, proboscises for

omnivores) according to

how you prefer

Crazy Plant Shop

**Ecodefenders**

https://www.filamentgames.com/fws2/projects/eco-defenders

**External**

**Internal**

**Who is our audience?**

Spore didn't really allow for environmental influences that players could/would react to

Perhaps we could develop a

game where there are natural,

random occurring events and

the player would choose how

to adapt according to their

knowledge of events that

would occur in the future

based on probability

I'm not sure what the game is but there are some very interesting interacting probabilities here.

mutating immunity to vaccine

probability of offspring spread of immunity

Apparently, different kinds of viruses have varying rates of mutation (mutation per round of replication)

probability of infection

Starcraft

Micromanagement of populations. You can

divide your units to move

to different areas of a

map and engage in

different tasks

The tasks could be

to respond to certain environmental events with decisions based on which evolved species is best suited to deal with the issue

mutating advantages against immune cells (much less likely)

Rapid Forced

Evolution

There's a probability that pest develop resistance to pesticides but a much smaller chance that they'll evolve traits that make them immune to their natural predators.

Pokemon

You raise creatures

that battle for you

with different types

that are better suited

for fighting other creatures

http://nautil.us/issue/17/big-bangs/how-world-of-warcraft-might-help-head-off-the-next-pandemic

**WoW and**

Pandemic

Simulations

Pandemic

Simulations

http://bulbapedia.bulbagarden.net/wiki/Effort_values

http://bulbapedia.bulbagarden.net/wiki/Individual_values

EVs are traits that Pokemon

develop from exposure to other

Pokemon. Can be intentionally

developed at trainer's discretion.

IVs are traits that Pokemon are found with or inherit from parents. These can

be intentionally bred for.

Mega Evolution

allows you to force

evolve your creature

in situations to gain

increased attributes

Mechanic that can allow

the player to forcibly

evolve their population

in response to or in preparation for situations

**'Pre'/User-Research**

**What is the 'context' for use?**

Does the teacher have a say in the choice of when/which game is played? (

Will

)

Does the teacher have a say in the choice of when/which game is played? (

Will

)

Throw some number of viruses against a disease, some die, some survive and develop resistance. The more you send, the more you lose, but the more probability of getting resistance.

This does not

seem to be only

external events (i.e. volcanoes

etc). Could be in relation

tp one genomic event

Mean gene slot machine

need a high number of individuals, or a high number of events on a single individual

Multiplayer, one player controls viruses and tries to spread, one player tries controls people and tries to keep them way from viruses

If you are trying to

gain one trait

a dice or a probability

element will determine

what commonly

associated traits you

might acquire

20 traits, every time the game starts the traits are linked in a uniquely different way

Have players map the traits visually

**Goal-**

Rules-

Pieces-

Theme-

Strategies-

CC elements-

Rules-

Pieces-

Theme-

Strategies-

CC elements-

**Extremes of not doing stats right in a games**

Take a game like minecraft

The oppositional stats- in this case the stats really mostly function to oppose your desired goal. To produce grinding, in random. For instance in Minecraft, 1 in 10 blocks of gravel produces a flint. If you want flint, you have to mine a whole bunch of gravel. The implementation of stats just leads to grinding, not to strategic thinking about stats

The linear relationship- One way to get rid of the oppositional stats is to just increase probability to 100%- every time you mine stone, you get cobblestone. You are now better able to achieve your desires in the state of the game- but the stats have disappeared, in favor of deterministic relationships.

I think we want a game that avoids either of these states, i.e. one that involves stats and requires strategic thinking about those stats.

**Thus, who all are the users and stakeholders whose opinions/needs influence the design of the game and the choices we make?**

**What prove-able need or problem is being solved?**

What is needed – by teachers; for students wrt probability? (possible information from brainpop as to what videos are commonly used, or what things teachers have asked for or remarked about?)

What is needed – by teachers; for students wrt probability? (possible information from brainpop as to what videos are commonly used, or what things teachers have asked for or remarked about?)

**What 'features' are expected in the target product? How do we plan to incorporate them?**

Players play cards or moves that damage a common enemy (success of attack associated with probabilities). This changes the state of the common enemy. And make the consequent players recalibrate planned attacks. For instance, if player 1's attack removes the dragon's arm, player 2's attack on the arms has a lesser chance of succeeding. Something more complex so that checking depended of events requires thought.

To reconsider: (what's mentioned in the right on things that could be done wrong)

Probabilities in moves for individual play is still a matter of luck; somehow the person should be playing [for] the probabilities themselves (rather than, as earlier said, "against the probabilities", hoping they work out)

The Bean Machine – configure the bars above in different manners to get different distributions beneath. analogous to the, distribute trait amongst population for a final desired configuration.

More clearly reflective of statistics, it feels?

Also, appropriate representative of what playing *for* probabilities should be like. Where the desired output requires a certain probability of occurrence, which needs to be made to happen.

Yes, I think the phrases not wanting to play "against the probabilities", but play the probabilities themselves is desirable, was discussed.

I imagine one way of doing this would be: that actions should not function like they normally do – i.e. players want to conduct attacks as is traditional, and they're hoping against probabilities it works. Instead, an attack's (or move's) requirement itself should be a certain probabilistic scenario (say only 60% of the artillery should fall on the enemy for it to work correctly). And the player has to manipulate things to make that happen.

**Literature research about teacher's or students' needs wrt understanding probability – what are common difficulties, etc. (**

Vishesh

)

Vishesh

)

**Will this be for class room use? General distribution?**

I agree. You should use stats

to make informed decisions

about the best actions to take out

of a set of actions i.e., which adaptations

given a table of info or something etc.

http://www.teacherlink.org/content/math/interactive/probability/numbersense/misconceptions/home.html

http://www.corestandards.org/Math/Content/6/SP/A/2/

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

http://www.corestandards.org/Math/Content/7/SP/C/7/

Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

http://www.corestandards.org/Math/Content/7/SP/C/8/c/

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

http://www.corestandards.org/Math/Content/7/SP/A/1/

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

http://www.corestandards.org/Math/Content/7/SP/A/2/

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

http://www.corestandards.org/Math/Content/HSS/CP/A/2/

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

http://www.corestandards.org/Math/Content/HSS/CP/A/5/

Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.

http://www.corestandards.org/Math/Content/HSS/MD/B/5/b/

Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.

http://www.corestandards.org/Math/Content/HSS/MD/B/5/a/

(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

http://www.corestandards.org/Math/Content/HSS/MD/B/7/

**It should be fun to play**

The concept should be embedded implicitly in the gameplay (i.e. the game should be designed such that effective play strategies require understanding and manipulation of statistics concepts)

The concept should be embedded implicitly in the gameplay (i.e. the game should be designed such that effective play strategies require understanding and manipulation of statistics concepts)

The E-coli breeder game

Goal- You are a breeder trying to generate a brand of bacteria with a particular pesticide resistance ratio, to protect people from getting sick.

Rules- On each turn of the game, you are told how common 3 species of diseases are each game. You have a limited number of turns to breed an E-coli with the exact resistance ratio that matches the disease prevalence in the population. You spread the E-coli to 3 petri dishes. Each round, you can insert a certain amount of a certain kind of disease. That disease will both kill a certain percentage of the E-coli, and grant the surviving E-coli some resistance to that particular disease (according to some probability distribution), and reduce an E-coli's resistance to all diseases not encountered that round. All E-coli then triple their numbers, and the process repeats itself. After a certain number of turns, you need to pick one E-coli that matches the desired disease ratio.

In later more difficult levels, we can add conditional probability, such that being infected with disease A will make more more likely to die to disease B, or more likely to develop resistance to disease C.

Pieces- 3 petri dishes. A population of E-coli. 3 kinds of infectious diseases.

Theme- It's the future, and E-coli are all the craze. You are a geneticist, breeding Ecoli in your lab all day. E-coli can fight the most common diseases on the planet, but only if they are bred right. You are given the desired profile of E-coli to create, and limited time to do it. The health of the world depends on you!

Makes me think of forest fires potentially, fires are more likely to spread down different paths than others, spatially dependant probability events

I'm starting to think that spatially dependent probabilities are too subtle- yes they are dependent event, and their probability depends on their spatial configuration, but I think the dependancy between the events is too subtle, too nature to players. Usually the thing next to something gets effected by it. Teaching dependant probabilities in a non-spatial way might be better, education-wise

Host vs Parasite

Perhaps we can do interplanetary worlds to provide for a host of different environments to adapt to

Events:

E. coli goes rogue; need to counter

Resistances developed against certain strains

Expected negative abilities when trying reach for higher tier abilities

**yes**

**via BrainPOP's GameUp**

**if we hit common core, we are reaching the needs of teachers**

3 use cases on GameUP, work for all 3

-outside school on own

-inschool, part of lesson

-inschool, free time

**outside school**

In-school – teacher assigned and like-homework

Extra time in school

In-school – teacher assigned and like-homework

Extra time in school

**Alignment with content (wrt curriculum), and other site content**

**www.brainpop.com/games**

way to visually represent how traits in the next population are related to the current one

like a final fantasy tactics job tree. Or games where using a weapon more an more makes ou an expert in that weapon, opening up later job trees

job tree adaption design circle

(note for Kevin to flesh out later)

**Make the game fun!**

http://www.brainpop.com/educators/community/bp-game/the-sports-network-2/

Be able to manipulate

your probabilities

statistical

specialization

Cost-Benefit

Analysis

What are real life

"microbial-jobs"?

High risk-high reward

Rogue-like breeder game

i.e. Rogue Legacy, FTL, Don't Starve

i.e. Rogue Legacy, FTL, Don't Starve

Playtesting

Had three petria dishes with populations of bacteria, each had to survive being hit with a disease. when hit with a disease, each individual would gain one of three possibilities: survive and reproduce (double in number), gain resistance and not reproduce, or die. Probability of each of each occurring was determined by the disease, each disease was given difference ratios as shown below.

Had a some interesting play dynamics, and visually it felt very cool to have the resistances of each individual displayed visually. Treating resistance as a bit of a binary state, individual by individual, didn't feel like the greatest dynamic, not did it embed stats the most-effective way. Since new resistances just overwrote old resistances, the conditional probability didn't feel totally with it.

Also, I talked it over with my girlfriend a bit post-testing, and it did not in fact treat genetics and evolution in the correct way. Exposure to a disease doesn't create genetic resistance, it simply makes those in the population that have resistance more prevalent in the population. Generally, variation needs to exist, for natural selection to have something to act on. Which meas we need to be starting with populations that contain some resistance to each disease.

mid-game

end-game

Version 2, we thought of after playtesting. I think more biologically accurate, and will treat the statistics in a more interesting way. Not each petridish doesn't contain individuals, but one giant population. That population has 4 statistics: number of individuals, and % of the population that is resistance to disease A, B, and C. By exposing the population to one of the three diseases, you generally lower the total number of individuals, but increase the percentage that are resistant to a particular disease. In general though, individuals with resistance grow slower than those without resistance (having the genes to grant resistance creates a metabolic cost), such that the % of the population that is resistant will tend to go down with time. The goal of the game is the same, to hit certain benchmark numbers of % resistance by exposing petri-dishes to certain diseases before the time limit runs out.

Evolve(r)

Main interaction – select groups of people (/beings) and make them procreate with each other, for certain problems coming up a few generations later

You’re controlling a village of people who are grouped by traits. Reorganization, or selection of a certain trait according to which people aren’t grouped, requires specifying desired traits, and an option to select people with that trait.

The aim is to move people around into these sub-villages where they'll procreate and exchange spread across their traits according to the numbers they're distributed in.

The target traits they have to evolve could/should change with respect to how they evolved. In that if some mutation is required to be spread across 1/3 of the population (which solves some problem) - the new problems are in response to the new mutations the population has. (similar to the different worlds and people one obtains in Spore?)

<Just moving people around might be overly simple? Is there a better interaction or more complex system to work on?>

---I think allowing for an initial movement, and then allowing for other movements at elect times, or a limited number of times, would be ideal- moving people around should feel like a limited resource and thus require strategic thought

What if there are a few things to respond to- disease, predators, and heat. Each population is in a different environment, and so has a different survival requirement based on those three traits.

What would time scales be like

for this game? Millions of years

to accommodate for the changes

that would take place in a population?

Perhaps they could be a space faring race

to include more exotic environments; perhaps a look into future possibilities of human evolution if they moved around the

universe. grandiose, but a thought.

Time moves in years/decades. After rearranging people, you can start(/resume) time, and see the population composition in terms of traits change live. You'll have quests of composition, and challenges to face. Possibly in parallel. // The challenges could have rewards of different mutations you can distribute across your population.

And you can rearrange people while time is moving as well. And certainly change tracks (substantial rearrangement of people/beings) when a new challenge or quest comes up.

More information:

Apart from the composition of the people, there could also be some measurement of the population's traits' feature ratings: values on immunity, agility, diet/metabolism etc. (this appears like it could become overcomplex) but some of the components could also influence the rate of growth of population, being able to face challenges like predators or diseases, and different characteristics/abilities.

(Tentative) Rules

Although the game is about statistics that involves strategy,

can we include chance/random probobility to change game

dynamic for a game?

Is this multiplayer?

Is the game beatable after few plays? (is there a probability pattern that can be used eveytime to beat the game?) or does the difficulty adapt or/and change?

I see this game featuring the

job tree mechanic the most out

of any of the three

It seems like a tower defense kind

of game where you upgrade your

units every round

How does this/can this incorporate

statistics though? What are cellular level

statistics? Population proportion die-offs

given before each action is taken so you

can do a cost-benefit analysis

Will it be possible to play multiplayer?

job tree for the parasites, the host, or both?

Is there a way to include conditional events in this? Connect this with the teaching prompt on the left, that new information intermediately could lead to different chances of the final results?

I like the idea of a tower defense feel a little more, the current game feels a bit like you'd be investing a lot of time in micromanaging the spatial position of your units, and not leave enough time for thinking about stats strategy. If attack paths and defense points are predefined, that can free things up a bit.

i would say both. if multiplayer, then both players

would have trees, and knowledge of other's trees.

if single player, then player can foresee and adapt. the game can indicate percent chance the opponent will choose next 3 or so traits and player can plan accordingly

yeah i'm imagining more

static turn-based type

of tower defense if anything

Building off of netrunner, what if the host can build a bunch of defenses, but those are not initially known to the parasite until they attack the host and have to encounter the defense. Then you have to weigh statistic unknowns in planning your attack.

Suddenly, a certain village is affected by some weird storm that possibly affects their traits, or how it is passed on – is it preferable to change configuration or not?

turn-based or real-time?

build out tech tree, define core mechanics, and define potential actions for both sides

going back on job tree at a cost but to adapt; set action points

Christian

http://www.ologames.com/Free_Games/Who-Wants-To-Live-A-Million-Years

**Benchmarking**

**Listing other probability games;**

their features and shortcomings;

and comparing our plans or imagination with respect to them

their features and shortcomings;

and comparing our plans or imagination with respect to them

This whole idea of playing with ecosystems of microbes is fascinating.

Host v Parasite Playtest

The parasite started on the right side of the board with three 20 sided die. Each die represented a swarm of 20 viruses.

Orange rectangles were immune cells. They ate 5 viruses per encounter. It was not possible to develop immunity to them.

The host started on the left with three cells and 3 Mutation Points. Each turn, he got 1 MP per cell.

The

objective of the game

for the

host

was to keep at least one cell alive for 30 turns. The objective for the

parasite

was to destroy all three cells.

Green/blue squares were antibiotics. They had kill percentages of 50 and 40 percent, respectively. Anything not killed in an encounter became immune to that color. The square moved under the die to denote its immunity.

Each side took turns moving their pieces. Each piece could move 2 spaces.

Parasites reproduce by getting 5 viruses

to a cell. The cell becomes infected for two

turns. At this point, it is destroyed and

produces two new swarms, which inherit

immunities of their forefathers.

In three turns, a new cell emerges.

When viruses and antiobiotics collide, we rolled a die for each member of the swarm. All that didn't die, became immune.

Results

Compelling gameplay. I think it's the start of a very interesting system. I knew next steps would be increasing the number of choices that were based on careful consideration of not just single probability but nested probability.

Yellow squares were cells.

Host uses MP to buy immune cells (3 MP), blue antiobiotics (1 MP), and green (2 MP).

Host vs Parasite v2

Mostly redesigned the upgrade and resistance-developing system to be more in players' control.

Playtest 2

Based on version 2 of the game, as described above- it felt more tedious to keep track of percentages, and a less interesting game overall. The tediousness would be totally alleviated if a machine were to do the calculations for you. With only two things to track percentages on (death rates with and without a resistant gene), the play mechanics felt a bit static. To get to the desired percentages, you have to know what are the resistant percentages in your population. And then you simply add more of the type of disease which is furthest from the required percentages, to kill a bit more of everything else while leaving that gene intact. Very uninteresting strategy.

A more interesting game might be one where you are instead trying to eradicate a population of bacteria using antibiotics. Maybe you are a doctor and you have to prescribe a sequence of antibiotics that can cure the disease, given a patients prognosis (which includes a description of the resistance percentages). After each treatment, the bacteria randomly mate and double the population in size.

To add complexity, maybe the population can be given a 3-4 gene signature, which the genes not each corresponding directly to an antibiotic. There can also be 3-4 antibiotics, which each have a differing effect based on the genes present. For example, antibiotic 1 might be really effective against bacteria with genes A and B, but really terrible against C and D. Antibiotic 2 might be extremely effective against C, and mildly ineffective against A, B and D. Each round of the game would present you with different available antibiotics.

This is the setup I chose from understanding the rule description.

3 petri dishes; 30 E.Coli are given to begin with; Diseases A, B, and C such that A - kills 50% of who it attacks and gives resistance to the rest; B kills 25% and C kills 70%; and both give resistance to the rest.

And then I chose that all E.Coli have 2 units of resistance against A, B, and C each to begin with. And gaining resistance on fighting any one disease, implies those E.Coli get a +1 resistance unit against who they fought, and -0.5 against the others. And the target resistance ratio was 3:2:1.

This was interesting to try, but I felt harrowed after one-two moves due to excessive data keeping and not being able to keep track of all the things that I probably should be aware of.

After trying one-two moves itself, I was pretty confused and found it hard to keep track of all the information. One of the primary points of confusion was, what did the target resistance ratio mean? Do we need any strands of E. Coli, even one or two individuals, to have that resistance ratio, or is the 'average' resistance ration of all the surviving E. Coli supposed to be 3:2:1 (or chosen target).

Also, as problem setters, is any combination of the diseases' kill ratio and desired target ratio achievable, or not?

Here, I simply put all the E. Coli into one petri dish, and 'inundated' them with the different diseases one by one, just to see what sort of resultant resistance ratios emerge.

Multiple villages and traits seemed again, slightly overwhelming to compute and keep track of manually. So I simply tried to see what can be achieved in one village, with two [pairs of] traits: in 64/60 people, I assigned everybody to be 'purebreds' as in both alleles of their genes are the same, and we're considering two genes – concerning eye color, and height; and distributed the 4 kinds of people in equal numbers.

I tried to figure out ways to reduce the population of the tall people (assuming the tall allele is dominant), and it's interesting to see that it takes three generations for this to be manageable, assuming previous generations go away. This was so far the only observation of an achievable task I could make.

Playtest

100 B (Black eyed) - T (Tall)

& 100 B-s (short)

100 B (Black eyed) - T (Tall)

& 100 G (Green eyes)-T

So I got a friend to move people around, and tried to work on the calculations, and sadly couldn't move beyond three moves because the calculations became overwhelmingly tedious.

In that limited an experience, my friend said that she couldn't form much of a clear picture about what is happening, or the possible impact of a move. Also, she tried to attempt some of the calculations herself, and those seemed pretty daunting too, and she said that as a player, she wouldn't want to deal with that kind of math.

So this wasn't a fun experience in practice, this time. I think mostly because of how I took 15-20 minutes of computation between moves to report the next status.

I feel like it might be possible to generate a vague intuition as the player practices on the game, but I'm not sure what else can be done to make this more fun.

Predicting traits

People in different 'localities'/villages/regions are moving around, and you have to predict after some movements, the likely composition of a trait.

I'm doubtful about the fun-ness in this game, but essentially reversing the above game, seemed like a possibly interesting concept – in that it makes the calculation and thinking about probabilities more explicit.

Making the Punnett square for different sets of traits/gene pairs in the population, and finding out the resultant genes and their compositions, although largely tedious, was moderately challenging, and felt like something that *might* be an engaging task in itself, in some form.

In retrospect right now, and looking at the other playtests, this game might be more playtestable, as well as playable/approachable if I didn't work with large populations in hundreds, but very small ones, say less than 10.

The demerit here, of course, is that the random event is probably a random number or a die throw, and not being sampled a lot, leading it becoming less predictable in terms of scale, I think (as we discussed with respect to the other dice games).

But I'll try to do this tomorrow to see what I can get.

This, for me, raised the repeated earlier question, of the extent of explicit or formal calculation we want the player to engage in, if ever. If yes, how does this work in comparison to the related trade-off with fun (can this computation ever be fun, somehow?).

Or is a primary focus more for this to be a fun game, such that the underlying concepts of probability can be formally described and taught later, and this only works as a representation to help prime a player?

Couldn't think of a good way to do the calculations easily, so didn't actually playtest the game, but I did draw out a potential gameboard. The idea was that the game would involve a series of levels, and each level would have a different arrangement of islands, and number of traits. Player moves involve opening and closing migration routes between islands.

^What the player was told

^Background information and calculations I (/the computer) worked on

nice, math!

Next Generation

Population calculator

https://docs.google.com/spreadsheets/d/1qWsGB5rhD8GuRpFdlzRMS_5qhfkFk49aFFUeVjt1MoY/edit?usp=sharing

is ^here.

Enter the populations of specific allele pairs in the top row, and the resultant population (though often in decimals), shall be given in the bottom row

Calculations from the computer

Level 1, a simple island configuration

Mid level difficulty island configuration

Playtesting v2

New eradication game- end of round view from playtesting

This game felt very puzzle-like. There didn't feel like there was enough complexity in the game to feel interesting. There was also the suggestion of tieing this more directly into antibiotic treatments- so instead of multiple diseases, only one disease, and needed multiple treatments, enough to cure the disease, but not so many that you exhaust your limited resource pile

http://www.carolina.com/teacher-resources/Interactive/online-game-cell-structure-cellcraft-biology/tr11062.tr

Cellcraft

hero academy

Wave attacks a la Tower Defence – After some generations, village 2 is going to be attacked by a composition of 40% archers and 80% militia.

The aim is to maximise survival, knowing that you can procreate mages and knights which are good against militia and archers, respectively.

Calculator V2

https://docs.google.com/spreadsheets/d/1XvdqL6lrRdKHoxRjZpSD6EcKJlXLHVlB4SSRT2RA-So/edit?usp=sharing

or https://drive.google.com/file/d/0ByEKm4TLSaMuajlUTzZlak1rSUk/view?usp=sharing

When you start the game, you need to enter values in row 6. After that, you simply need to enter changes (how many people of this trait set moved away from or into this population). The resultant values will be printed in row 22.

Copy row 22 into row 6, and the values to be reported to the player, will be updated in row 2.

Where is the stats in the strategy? Needs to be clearly elaborated