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How many bets until a 1% house edge is visible? The (k·σ/e)^2 rule, with the numbers

A 1% house edge is the headline number on every casino game, and it is a number no player ever sees. Not because it is hidden, but because it is small next to the thing it sits inside. Here is the arithmetic, with the numbers for a coin-flip bet. Take a bet that wins with probability p and pays m times the stake (profit m − 1), otherwise loses the stake. Per unit staked: expected return: p · m, so the edge is e = 1 − p·m standard deviation: σ = sqrt(p · m² − (p·m)²) For a roll-under-50 dice

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ExternalSoftware Engineering
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#Python Functions: Parameters, Arguments, Default Arguments, and Keyword Arguments

As part of my Python learning journey, today I explored different concepts related to functions. I learned how parameters and arguments work, how default values are assigned, and the difference between positional and keyword arguments. Let's look at what I learned with simple examples. A function is a reusable block of code that performs a particular task. We define a function using the def keyword. def greet(): print("Hello World") greet() Output: Hello World Here: def is the keyword use

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ExternalSoftware Engineering
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Instatools for Instagram Posts

I built instatools, an open-source tool for creating Instagram graphics without AI. It comes with customizable layouts, typography, colors, and design elements, so you can create polished posts without starting from scratch or spending time learning a full design suite. The project has been tested and used over the past year across multiple Instagram accounts, including: Underground New Mexico: https://www.instagram.com/undergroundnewmexofficial/ https://www.instagram.com/southwestbaddiesofficia

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ExternalSoftware Engineering
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Building trail cams that aim themselves: a heat grid from wildlife sightings

WildFeed (wildfeed.live) streams hunting and fishing live from the field. Most hours, no human is live, so we run PTZ trail cams in South Carolina to keep the woods on screen. A fixed camera keeps pointing at sky, though, after wind, a bump, or someone driving it during a session. So we built an "aim director": Phase A: snap-back. Every ~2 minutes, if the cam is already live, idle (nobody in the control queue), PTZ-ready, and battery is ≥40% or on external power, it issues return-to-home and log

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ExternalSoftware Engineering
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# 230,756 Requests/Second. And Breeze Is Much More Than a Fast Go Framework. 🚀

What if your Go web framework could deliver exceptional performance while providing an entire ecosystem for building, operating, and scaling modern applications? Meet Breeze v2.2. Built on gnet. Engineered for throughput. Designed for production. Breeze v2.2 (Go 1.27) has achieved: Concurrent Connections Requests / Second 64 230,756 256 207,333 512 198,196 Nearly 200K requests per second, even at 512 concurrent connections. And how does it compare with other Go frameworks on The Be

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ExternalSoftware Engineering
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ElevenLabs vs Murf AI for a Script-to-Voiceover Pipeline: How I'd Choose in 2026

ad #ElevenAgentsPartner Disclosure: I'm an ElevenLabs affiliate partner, and my site also uses affiliate links for Murf AI. If you buy through links on my site I may earn a commission at no extra cost to you. There are no affiliate links in this post; the only link goes to the original article on my own site. ElevenLabs and Murf AI get compared as if they were two versions of the same product. They aren't, and if you're wiring text-to-speech into a video or content pipeline, that difference ma

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ExternalSoftware Engineering
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What Becomes Scarce When AI Flows Like Water and Electricity? | AI普惠时代，什么最稀缺？

AI普惠时代，什么最稀缺？ Start Question： ** 很多人问‘llm ai让智能像自来水、电力一样 打开‘龙头/电闸’ 就能流过来’，就是很快普及，那么之后什么是稀缺的呢 最又价值的呢？ ‘执行力？’， 具身智能？ ** 先把前面三条脉络收在一起，再回答这个问题，这个类比才不会飘： 铁路：物质的运输能力变成普惠底座之后，稀缺的不是“运东西”，而是值得被运输的标准化商品、品牌、分销合约、需求理解 电网：能量的供给能力变成普惠底座之后，稀缺的不是“有电”，而是懂得用电的设备、工艺、产品、内容、组织流程 光纤互联网：信息传输能力普惠之后，稀缺的不是“带宽”，而是可信信息、注意力、服务、交易履约 LLM 作为“智能自来水”：通用语言推理、知识调用、基础生成能力变成按流量计费、随开随用的公用基础设施；稀缺的不再是“能不能聊天、能不能写文案、能不能做基础推理”。 一句话结论： 智能本身，而是把智能锚定到真实世界、并承担后果的闭环能力。 下面分层拆开，并且区分【短期（3–5年）】、【中长期（5–15年）】，再单独辨析：执行力、具身智能到底处在什么位置。

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ExternalSoftware Engineering
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Simulate Your Cloud Architecture with an MCP Server Before You Deploy

Most capacity questions I get asked boil down to "what happens if traffic triples?" Usually the honest answer is "we'll find out in production." I build Cloud World Model (CWM), a simulator you can call over MCP, so an AI assistant can work through that question before deploying or changing infrastructure. This post walks through one real run: connecting, describing a small AWS stack, running it at a baseline, spiking the traffic, and reading the results. Every number below came straight from th

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