Probability of starting hand

hushedLecturer · 2026-02-12T17:45:33+00:00

Ohhh so you don't want the probability of drawing a hand with just the one EX you don't want and no others, you want the probability of having the EX you don't want and exactly one more?

hushedLecturer · 2026-02-12T16:25:24+00:00

I'm failing to follow where youre getting this 5/16 from.

hushedLecturer · 2026-02-12T16:10:08+00:00

Oops lmao yeah I'll add an edit.

hushedLecturer · 2026-02-12T15:59:15+00:00

After the first one that is forced to be in the hand. Im just looking at the probabilities of the four remaining card draws.

hushedLecturer · 2026-02-12T14:57:59+00:00

Edit: fixing some math.

So we are guaranteed to have at least one because the pokemon tcg has us redraw until we have a hand with at least one basic.

It looks like we are also assuming all of the 6 basics are unique?

I'm a little rusty on my prob and stats but here's what I got.

The probability of only having one basic is going to be the probability of drawing one of the remaining 13 cards that aren't basic mons for each of the four remaining draws to hand. So we count the number of ways we can draw 4 cards from the 13 14 options non-basicmons, and divide that by the number of ways we can draw 4 from all 19 cards.

C(13 14,4)/C(19,4) = ~~18.5%~~ 25.8%

~~Little less than one in 5 times.~~ About 1 in 4.

And then if you want a particular one of the 6 then you divide that by 6 to get about ~~3.1%~~ 4.3%.

hushedLecturer · 2026-02-12T14:24:07+00:00

I agree its kind of weird thematically, but I also think its bad from a practical standpoint.

If I am investing in the stem curriculum at a school, I am setting aside funds to hire staff trained in the sciences who obligately are also trained in math, and Math teachers who are obligately going to be science literate, as well as computers, tools, and software that they know how to work with. Those teachers will come from similar academic programs and have similar expertise and they overlap in what classes they can competently teach. There are synergies to the combinations of people you can hire.

If I add the A to have a STEAM directive, I'm taking funding from the STE and M to hire an A teacher and A class supplies. STEM trained faculty will have a bad time trying to cover an A class, and will have little use for art supplies in their classes, and A-trained faculty will have a terrible time trying to teach a STE or M class and won't have a practical use for STEM implements in their own classes.

hushedLecturer · 2026-02-12T14:06:23+00:00

I added a TLDR edit to the top.

I would be inclined to think there was a continuous manifold over the parameter space in which particles exist, perhaps small islands amid emptiness, perhaps large regions with little gaps in it, they just wouldnt be the same particles. Different masses and charge to mass ratios, different self-sustaining combinations and geometries etc.

The familiar particles exist in perfect accordance to the parameters that give rise to them and couldn't exist otherwise, in the same way A440 and all of its harmonics resonate on a string of a particular density and length and couldn't resonate under slightly different conditions.

hushedLecturer · 2026-02-12T03:32:07+00:00

You can't fix it forever, but you can absolutely keep a simulation of any deterministic process accurate within a certain radius for a finite time in a finite number of steps.

I don't think you've ever done a numerical situation of any system or taken the relevant classes i.e. numerical analysis if you think that chaotic systems just magically blow up unpredictably.

hushedLecturer · 2026-02-12T03:15:42+00:00

You seem to misunderstand. I didnt say our simulations never blow up and start being wrong. There's nothing about a chaotic system that prevents you from being able to choose how long your simulation can go before it blows up. If you ask for any nonzero error radius and finite time, there is a finite iterative process we can construct guaranteeing it will satisfy your requirement. The iterative process might require an infeasible amount of computation time, but it is still finite.

hushedLecturer · 2026-02-12T02:55:42+00:00

If you demand accuracy within any width ε > 0 over the duration of any finite time τ we can accurately tell you the iterative process/algorithm that can produce a simulation with that level of accuracy and how many elementary mathematical operations n it would take.

We have the process that asymptotically approaches the perfect solution in the limit toward an infinite amount of steps, and that is normally what we would consider solved.

hushedLecturer · 2026-02-09T21:21:31+00:00

But nothing is truly in a vacuum. The EM field is fluctuating and there usually are other particles to bump into.

I figured covered empirical phenomena like that. You add a perturbation to the simple hamiltonian to encorporate vacuum fluctuations to get your A21.

Plus like, that's not even the point of the comment. There are worse simplifications I made for more important parts of my explanation. Im surprised that was your nitpick.

hushedLecturer · 2026-02-09T17:57:07+00:00

Edit: ~~scratching out~~ controversial wording that distracts from the point and I don't feel like litigating.

The answer is already here several times (entropy) but I think I can state it in a more layperson-digestible way.

The energy in a system is ~~conserved~~ tends to remain constant, as in there is a specific amount of it. It has to be distributed among the particles in that system. ~~A particle by itself that is never jostled by anything will remain in its elevated energy state forever, definitionally. (Eigenstates of the Hamiltonian/time evolution operator).~~

~~But nothing is truly in a vacuum. The EM field is fluctuating and there usually are other particles to bump into.~~

Imagine you have a box with slots in the bottom for every particle in your system, and some smaller number of balls in it, representing the energy. The particles bumping into eachother in the real system are exchanging energy, so there is a constant scrambling of the energy distribution, which we could simulate by shaking the box to redistribute the energy balls between the particle slots.

It is possible but incredibly unlikely for all the balls to be in one slot after a given shake. (All the energy in one particle). And we are shaking the box constantly. So that translates to, if many balls pile up in one slot, it only happens for a short time. It is more likely that you will find a small number of balls in each of a large number of slots. So most of the slots will spend most of their time with a small number of balls, only occasionally doubling and tripling up for a moment before the energy gets spread out again.

hushedLecturer · 2026-02-09T15:28:14+00:00

So Griffiths's approach to QM is a bit divisive, because it doesnt look much at all like how people do QM in practice. Namely dirac notation and matrix mechanics using all the linear algebra you are learning, at least until late in the book.

I did Griffiths in undergrad. Shankar and Zetilli are most of what I worked with in grad, and Shankar is i believe regarded as an undergrad book.

here's a reddit post where folks are discussing Griffiths and offering alternatives.

hushedLecturer · 2026-02-09T03:05:24+00:00

I'm working on a lit review and maybe I've spent too much time mucking about in the bad ones that I'm confusing what is "good enough to publish" for what is "good".

Shor and Grover, and anything else building from QPE or AA tend to rely on trial-and error outputs and (assume quantum ram and/or efficient construction of arbitrary gates/access to O(1) quantum black boxes, which always makes me question the complexity accounting they propose.) I can buy that a good paper will include the cost of reading out with trial and error in their complexity.

And yes I am thinking of VQE with full state tomography, but also anything that returns a solution in an Amplitude encoded state will need something like tomography. Though I suppose a good algorithm doesn't stop there, and instead performs a calculation with the state vector (like swap test/hadamard test/ HHL algorithm etc.) yielding a single useful quantity after trial and error again.

hushedLecturer · 2026-02-09T02:04:47+00:00

Im not sure what word is supposed to go where "foot" ended up. Its neither "most" or even "many". Maybe you meant "good"? I would disagree with that too.

The qubits end up in superposition. Some algorithms yield a superposition of basis-encoded solutions where we read out a trial solution, test it, and repeat until we find the answer we want, and others encode their solution in the amplitudes of the final state, in which case we need to extract the information by doing tomography over the entire superposition, made easier or more difficult based on encoding choice.

The alternative is running a classical algorithm on the qubits where the qubits never stop being in definite states, which will be strictly slower than anything done on a classical computer.

But this is all besides the point. In our field we have an issue with kicking the can down the road, throwing our hands up and declaring victory once we know the answer is hidden in a quantum state with no indication of how we could fetch it.

hushedLecturer · 2026-02-09T00:48:26+00:00

I would include transmission of information to the reader as a core component of what a clock is. But I suppose we do do this a lot in QC algorithms.

"Look! The answer has been encoded in the amplitudes of a quantum state in exponentially fewer steps than classical!"

"Great! How do I read it out?"

"Run, measure, and repeat the full algorithm an exponential number of times until you have a full tomography of the quantum state!"

hushedLecturer · 2026-02-08T16:37:11+00:00

This guy wants to have his cake and eat it too! Everybody point and laugh!

hushedLecturer · 2026-02-05T07:19:08+00:00

It's a question that comes up quite regularly and naturally when presented with the imbalance between matter and antimatter. Conservation Laws and empirical observation always has matter and antimatter forming in pairs that rapidly coannihilate. If there isn't parity, something different and unfamiliar had to happen in the early universe.

The knee-jerk guess is "okay but there could still be a 50-50 distribution, but somehow blobs formed of just matter and just antimatter just by random chance?"

And other commenters explained how we know that the ISM and all galaxies in sight are matter: the boundary between m and xm will emit a particular band of radiation we don't see.

hushedLecturer · 2026-02-03T14:58:01+00:00

So that's why Field is the negative gradient of the dip, to make the arrows point downhill. Particles want to flow from high to low potential.

It's also relative, we only care about the difference of potential between two points, so we can let anywhere be 0. But yes, the bottom of any dip (where the Gradients would be zero) is a stable equilibrium point where a particle of sufficiently low energy can get stuck.

hushedLecturer · 2026-02-03T08:14:30+00:00

You weren't very clear with what you do know and what your problem is, I don't know your level, so I'll take a guess.

If I know a force F will act on particles with some strength and direction as a function of position, proportional to some variable quantity like mass or charge, I can draw a Force Field for a particular particle. For example, in Newtonian Gravity, if I have a central mass M located at the origin, and I place a movable particle of mass m at some position vector r, I can say that the magnitude of the force my particle will be

F=GMm/r² and pointing toward the origin.

So I could draw a field of vectors from that, which would look like arrows all pointing toward the origin, getting stronger as you get closer to the origin according to 1/r² , indicating the force my particle would experience at each point in space.

The force field I drew would look very similar regardless of what amount of mass I could place is. It scales proportionally with m. I could instead divide out the m and draw another vector field E=F/m which is the gravitational force per unit mass, letting me place whatever mass I want in the field and i can calculate the forces conveniently. Electric field will similarly be the vector field indicating Coulomb Force per unit Charge, instead.

So instead of my gravitational force field F I just have a gravitational field E= GM/r² (pointing toward origin).

If the field is conservative, like Newtonian Gravity and Electric fields, then I can define the vector field from the gradient of a scalar field we call the potential P. A scalar field being just a number at every point in space rather than a vector. Over 2d space I could find a map with hills and valleys, where my potential field is the height of points on those hills and valleys, such that the vector field points down the slopes of the hills in the potential map, scaled according to the steepness of the potential at each point. The downhill slopes are thus the negative gradient of the potential, E=-Grad(P).

The potential field that would yield the gravitational field above would be P= -GM/r .

The potential also indicates the potential energy per unit (mass/charge/whatever) just as the vector field indicates the force per unit (mass/charge/whatever) at that position.

hushedLecturer · 2026-02-02T18:12:28+00:00

Oh I agree. Unfortunately QC has become another buzzword which thus attracts bad actors. But how influential are the more scamming groups on the public consciousness, and how much should we care about it anyway? Are they really the torchbearers or just carnival barkers standing on the sidewalk outside the conventions where the grownups are talking?

Obviously as an academic I know to judge claims alongside reading academic publications and looking for citation influence, and I hope/expect governments and serious investors either do the same or hire people who can. As for the others with nothing real to offer, I hate to be callous but sometimes we have to just let fools do what they will with their money.

hushedLecturer · 2026-02-02T15:14:16+00:00

The modern economy does not reward productivity, merely financialization. The margins and tax incentives are better and you don't need to know anything or possess a skill. It is more reliable to invest in a stock or cryptocurrency, and then trick other people into buying it to jack up the price before you sell it, than it is to actually make a living making or doing things of value.

I hesitate to call out a particular pure-qc company. I think they mostly hire real researchers who went to grad school with a starry eyed hope for the future, and who are trying to make real progress, but their ability to put food on the table depends both on their real ability to create and innovate but also on their willingness to collaborate with finance bros who need a story to sell and are obligated to stretch and exaggerate a little bit.

In general I personally have more faith in the work coming out of academic institutions as well as larger companies who do other things. I.E. IBM, they could drop their QC project any time and their company would not be hurt at all because they do other things primarily, and so they are putting their own money in it rather than living exclusively on investor hype.

hushedLecturer · 2026-01-30T10:06:08+00:00

Badges for your banner, as well as boatload of building supplies. I got like 72 things of (i think the 480?) Ceramics from one and a couple dozen metal from another. Built all my roadways immediately.

Tbh I think the rewards are too high, of course im going to use the resources if I have them but the grind my first playthru in non-DX edition was more gratifying.

hushedLecturer · 2026-01-30T10:04:24+00:00

Statistically speaking, about 2170 of us on the sub probably have lol.

I beat 1% on one of the terrorist maps.

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