Daren Liang

Examining Parlays in Prediction Markets

Mon, 11 Aug 2025 00:00:00 +0000

It’s been a while since my last post.

I’d like to share a quick post on something I’ve been noticing on prediction markets like Polymarket regarding parlay contracts.

Overview of Prediction Markets

For those who don’t know, here’s a quick primer on how prediction markets work:

A Prediction Market is an “Information Market”

A prediction market, similar to an option market, is a platform where participants buy and sell contracts that pay out based on the outcome of future events. Rather than paying out based on the price of an underlying asset, like a stock option, these contracts pay out based on specific events, such as the outcome of an election or a sports game. Beyond financial incentives, prediction markets aggregate information from many participants to produce a consensus probability for future events.

Solving Dice Problems with Markov Chains

Sat, 28 Sep 2024 00:00:00 +0000

A colleague asked me an interesting probability problem involving dice. If you roll a die continuously, are you more likely to roll two consecutive 5’s or a 5 immediately followed by a 6? On average how many rolls are required to roll two consecutive 5’s? How about rolling 5 immediately followed by a 6?

Interactive Example

Solution

Reveal the Solution

The state machine diagram for rolling two consecutive 5’s:

A New Way to Write Microservice Code

Sun, 28 Jan 2024 00:00:00 +0000

Microservices are getting really popular, but have we reached the pinnacle of microservice design? I’ve been imagining a new way to write microservice code where you can annotate functions you want to be microservices. That way, you get the microservice architecture directly baked into the code.

Sounds a bit like the new hit buzzword “Infrastructure as code” that everyone is using.

Selling the idea

The concept is simple. You can decorate functions that you want to be highly available, highly durable, highly reliable, highly resilient, highly fault-tolerant, or anything else scalability preachers might want.

Dealer Router Pattern in NNG

Fri, 12 Jan 2024 00:00:00 +0000

NNG is a broker-less message queue that is a lightweight alternative to ZeroMQ and supersedes the older nanomsg project. It offers a more “orthogonal” API and does a few things better than ZeroMQ.

Thread-safe sockets
Websocket transport support
POSIX-compliant sockets API
True zero-copy messaging

A common messaging pattern is Dealer-Router which can be easily implemented using ZeroMQ’s DEALER and ROUTER sockets. Unfortunately, NNG does not have such sockets and implementing the pattern is not trivial. Fortunately, using NNG’s raw mode sockets we can emulate Dealer-Router.

Problems with Proxying Images

Sat, 27 Aug 2022 00:00:00 +0000

Let’s face it. Serving images on the web sucks. You have to manage endless formats, dimensions, variants, and more. What are some of the solutions we have at the moment?

Let’s discuss some flaws that affect each of these services.

imgproxy is a self-hosted solution for proxying images. The core is open source but advanced features are paid. One major downside is that you must pay for concurrency, making it not suitable for real-time image transformations. Moreover, it can be expensive to self-host multiple image proxies, making it hard to deploy image proxies to the edge, increasing latency to your users.

The Basketball Tryout

Fri, 13 May 2022 00:00:00 +0000

Here’s another interesting probability question that I’ve found in Adrian Torchiana’s Probability Math Puzzles app.

You’re trying out for a basketball team, and the coach gives you two options: you can take six shots, or you can take four. In both cases you have to make at least half of the shots, or you’ll be cut from the team.

Each shot you take has a fixed probability of succeeding. What is the probability of making a successful shot, in which it makes no difference what option you choose?

FUSEing for Fun

Sat, 26 Mar 2022 00:00:00 +0000

Something that I find absolutely fascinating are Filesystems in USErspace (FUSE).

What is FUSE?

FUSE, to put it simply, allows people to implement filesystems in userspace. Filesystems are traditionally implemented in the kernel, but when using FUSE, non-privileged programs can be used to create custom filesystems.

Why is it cool?

Filesystems don’t need to be concrete! You can implement virtual filesystems with little or no limitations.

Don’t want files to write to disk? Implement a “ramdisk” in FUSE.
Want to use Amazon S3 as if it is a hard drive on your computer? Use s3fs-fuse.
Want to be evil 😈 and store files on Google sheets? Use spreadsheetfs.

Introducing dsfs

Dsfs is an experimental filesystem written in Go and backed by Discord attachments.

Generating Images with Serverless

Fri, 18 Feb 2022 00:00:00 +0000

One thing I’ve always wanted to do was write a serverless function that could generate CS:GO crosshair images. The serverless platform that I chose is Cloudflare Workers which utilizes a vast edge network and supports 0 ms cold starts.

Writing a serverless function for this task didn’t seem too difficult, but I quickly ran into some issues.

Using node-canvas

Modern browsers are equipped with the Canvas API which makes it extremely easy to create 2D graphics. Although this API is meant to be used in the browser, Automattic (the maker of WordPress) has an implementation of Canvas for Node.js called node-canvas.

The Gambler's Ruin

Wed, 26 Jan 2022 00:00:00 +0000

Here’s an interesting probability question that I’ve found in Adrian Torchiana’s Probability Math Puzzles app (highly recommended!) back in high school.

You find $2 in your pocket and decide to go gambling. Fortunately, the game you’re playing has very favorable odds: each time you play, you gain $1 with probability 3/4 and lose $1 with probability 1/4.

Suppose you continue playing so long as you have money in your pocket. If you lose your first two bets, you go broke and go home after only two rounds; but if you win forever, you’ll play forever.

Secret Sharing by Example

Thu, 20 Jan 2022 00:00:00 +0000

1. The Scenario

You are haphazardly appointed as the group in charge of authorizing the launch of your country’s nuclear weapons. No idea how you got appointed, maybe you were just unlucky 🤷‍♂️.

Knowing that you are tasked with managing the launch code, you’ve decided that the only way to ensure no one abuses this code is to share the code in such a way that you and your friends must come together to reveal the secret code.

Algorithms in Javagony

Tue, 08 Oct 2019 00:00:00 +0000

The Javagony

First coined by flawr, Javagony is Java with a few statements made not available.

Here are the statements that are not available:

for (){}
if (){} else if (){} else {}
while (){}
do {} while ()
switch (){}
?:

These statements can be substituted for try catch statements and recursion.

Although Javagony is not the least bit fun to write, it makes you think about clever tricks that utilize many of Java’s obscure features.

PolymarketGPT: Event Oracle

Sat, 01 Jan 0011 00:00:00 +0000

Ask a question about current or past events! This demo is powered by Polymarket and Qdrant.

Example questions:

(Ctrl/Cmd+Enter)

Query Financial Statements

Fri, 01 Jan 0010 00:00:00 +0000

All queries are executed in the browser using DuckDB WASM on all 10-Qs since January 2009.

Loading dataset

Get financials for a period

Ticker: Period:

Graph financials over time

Example queries:

(Ctrl/Cmd+Enter)

In-browser SQL using DuckDB

Thu, 01 Jan 0009 00:00:00 +0000

All queries are executed in the browser using DuckDB WASM. P.S. I mainly use this tool when I’m too lazy to set up a proper database to test SQL queries

Feel free to come up with your own SQL queries, as everything is running at your own expense!

Example queries:

(Ctrl/Cmd+Enter)

Real-time Ethereum Rollups Info

Tue, 01 Jan 0008 00:00:00 +0000

Real-time information provided by public RPC APIs.

Yellow indicates that the chain has yet to report two blocks.
Red indicates that the chain has not reported blocks for a while.

Many more chains are missing, you can comment below to have them added.

Real-time Prices with Pyth Network

Mon, 01 Jan 0007 00:00:00 +0000

Real-time prices for the MarketVector Coinbase 50 Index (COIN50) provided by the Pyth Network.

FFmpeg Wasm YouTube Downloader

Sun, 01 Jan 0006 00:00:00 +0000

Note: The demo currently doesn’t work due to recent changes to YouTube’s API. If you have any ideas on how to fix it in a browser setting, please open an issue on GitHub

This is a simple browser-based app (using ffmpeg.wasm and node-ytdl-core) that allows you to download YouTube videos without the need to use youtube-dl locally.

There are four options in this demo:

Get formats: Manually select formats to merge. If video is selected, the output will be a video. If only audio is selected, the output will be an audio file.
Get best video: Encode the highest quality video file with audio. The best video and audio files are merged into a single file.
Get best audio: Encode the highest quality audio file.

The source code can be found here.

Imglabs.io Image Proxy Demo

Sat, 01 Jan 0005 00:00:00 +0000

Imglabs.io is an image proxy that caches and transforms images on the network edge. The image proxy core is written from the ground up in Rust and compiled to WebAssembly and deployed to hundreds of edge locations around the world to achieve industry-leading image proxying latency and performance.

Want to give a try on your website or project? You can sign up and proxy images for free at Imglabs.io.

Image URL:

This Is Your Weather Forecast

Thu, 01 Jan 0004 00:00:00 +0000

3D Shapes Using the 2D Canvas API

Wed, 01 Jan 0003 00:00:00 +0000

This is a JavaScript reimplementation of pygame3Dtest, which is a simple pygame demo I wrote to show how to draw 3D shapes using the pygame API.

Press the arrow keys ⬆️ ⬇️ ⬅️ ➡️ or drag on mobile to rotate the shape!

CS:GO Crosshair Preview

Tue, 01 Jan 0002 00:00:00 +0000

This is a simple demo which utilizes Cloudflare Workers to generate CS:GO crosshair images.

To learn more about how this demo: Generating Images with Serverless

Loaded image in: - ms

Note: you can sometimes get super low image loading values, this is caused by fetching the image previously saved in cache.

About me

Mon, 01 Jan 0001 00:00:00 +0000

Hi there!

I am Daren Liang, a graduate of the University of Toronto and currently a software engineer in risk management at Citi based in NYC.

In my free time, I work on Imglabs.io, a cloud-based image proxy service, and other programming projects. You can find me on GitHub @darenliang.

Additionally, I like exploring the beauty of mathematics and probability. Feel free to email me any interesting problems at daren@darenliang.com. I’ll take a shot at them!

Here is my public key

Mon, 01 Jan 0001 00:00:00 +0000

Kelly Criterion

Mon, 01 Jan 0001 00:00:00 +0000

The Kelly Criterion is a formula that determines the optimal theoretical size for a bet.¹

General formula:

\[ f^* = p - \frac{q}{b} = p + \frac{p-1}{b} \]

where:

$ f^* $: is the fraction of the current bankroll to wager
$ p $: is the probability of a win
$ q $: is the probability of a loss $ (q = 1 - p) $
$ b $: is the proportion of the bet gained with a win ($ 1 $ means you will gain the same amount you bet)

Projects

Mon, 01 Jan 0001 00:00:00 +0000

Imglabs.io

Proxy, cache, and transform images at the network edge

Website

🃏

The Gang

Cooperative Poker Game by John Cooper and Kory Heath

Website

MikuBot

Modular anime Discord bot built for weebs

MikuBot

Nikel API

Data API for the University of Toronto

nikel