Draw.io already allows creating editable PNGs and SVGs: it embeds the diagram definition in the image metadata. You can then import this image like you would import any other .drawio diagram
The VSCode integration is the cherry on top. All files with the correct extension (such as xxx.drawio.png) will automatically open for edit in the draw.io UI embedded in the IDE.
I use this feature often to build on top of the previously made diagrams.
That's very impressive - how do you do this? I also see an IDE screen with the debugger in your other article about telegram - presumably also HTML/CSS
This really depends on the pure strategies that you choose.
The initial set of strategies wasn't very diverse and compensated for the binary search "weaknesses" on the ends of the spectrum by sometimes guessing 1 and 98.
I don't view the original problem this way, but let's think about it!
> the spread on that surely goes over the 0 line.
Do you imagine starting with $1 or $1000? :)
Let's add a condition that Ballmer has infinite money, we start with a specific budget, and we can't continue playing if we exceed budget randomly changes after each game,
In the game where you start with $N, win $1 with probability p > 0.5 and lose $1 otherwise, the chance of eventually losing all your money is (p/(1-p))^N. [1]
So, the ruin chance actually becomes exponentially lower the more money you have at the start.
The steps in the random walk above belong to a simple, Bernoulli-like random distribution. Meanwhile the mixed strategy is a more complex discrete random variable because it can do more steps than just +1 and -1.
However, I believe that the same principle applies for the mixed strategy.
If you zoom out and consider "batches" of steps, you can apply the Central limit theorem and see that all these random walks work roughly the same. The caveat being that you need a large enough starting budget to "zoom out" :)
Granted, the standard deviation for the mixed strategy is ~$1. I would guesstimate that if you start with ~$1000, there's no way you will ever lose your money.
> What would be more interesting is to monte carlo simulate this strategy and look at the win/loss distribution. Presumably the choice is then not so clear cut.
Agree, this would be a nice demonstration! I will think about doing this next time I get a couple of hours of free time.
Exactly. And stretching may lead to the further injuries if your muscles are weak and can't support the safe movement during the full range of motion. Especially if you already have hypermobility.
The author should talk to a knowledgeable physiotherapist, not a chiropractor...