Ethereum’s Ether (eth)the second largest cryptocurrency is spot exchange trading funds, looking at the profits of renewed investors (ETF) The US records one of the strongest momentum in its one of the most in its one-year history.

iShares Ethereum Trust in BlackRock on Thursday (Eta) Data compiled by Farsise Investors booked the largest daily inflow ever, pushing its managed total assets to $5.6 billion, up over $300 million.

This is part of a broader revival of ether-supported investment products.

Nine US-listed ETFSs collected a net inflow of $703 million this week, according to Crypto data provider SosoValue. Data for Friday is still pending, but it has already marked the third strongest weekly haul since the product launched last July.

Investor demand has recently been featured, despite Ether prices falling behind Bitcoin this year, according to a new report from asset manager FineQia.

AUM for exchange products backed by ETH (ETPS) In the first half of 2025, we grew 61% faster than the market capitalization of our underlying assets. This is a sign of a stable inflow into the product, the report says.

The report notes that demand for ETP began to recover by late April and continues until June, surpassing ETH price rise.

The capital flood helped fuel the ETH rebound to $3,000. This is the best price for over 4 months.

Read more: The Ethereum Foundation sells 10,000 ETH and sells it to Sharplink.

Assume S I want to send it 3 Sit down R. You can assume that further S Each local channel has sufficient liquidity 3 soil. It also assumes channel fluidity (A,R), (B,R) and (C,R) It is distributed evenly.

One optimally reliable payment flow in this diagram looks like this:

1 sat: S --> A --> R   probability: 2/3
2 sats: S --> B --> R  probability: 3/5

This flow has a total probability 2/3*3/5 = 2/5 = 0.4 = 40%

question:

How to calculate the expected value of the arrival of Satoshu R if S send 3?

Option a

(I already know I’m wrong, but I think some people have similar initial thoughts, so I’ll write it down)

At first I thought this was just right 3 sats * 2/5 = 6/5 sats = 1.2 sats This is obtained by multiplying the amount of transmission with the probability of flow. This seems strange when sending two SATs S-->B-->R There is a chance of 3/5 And with the above reasoning 2 sats * 3/5 = 6/5 sats = 1.2 sats. The expected value of 1 is sitting along S-->A-->B The path is bigger 0 This is inconsistent with the expected additive.

Option b

Starting with the above reasoning, we add the expected value to the broken path.

E(3 sats) = 1 sat * 2/3 + 2 sat * 3/5 = 10/15 sats + 18/15 sats = 28/15 sats

Option c

Of course, two Satoshi Passes S-->B-->R You don’t need to send it as a single onion as an onion, but you can send it as two onions each with one soil.

The first is the probability 4/5 The second is a conditional probability 3/4 This is widely explained in this issue. You should be able to add these expectations using the logic in option B. Therefore S--> B --> R It is calculated as follows:

E(2 sats) = 1 sat * 4/5 + 1 sat * 3/4 = 31/20 sats 

Add one Saturday onion S-->A-->R That was 2/3 soil

We expect to have

E(3 sats) = 31/20 sats + 2/3 sats = 93/60 sats + 40/60 sats = 132/60 sats = 33/15 sats

This is 5/15 sats = 1/3 sats More than the answer to option b

Option d

Worse, I’m confused if there’s a chance that the expectation of analyzing two SAT onions in option C into two SAT onions could be linearly added, as the second onion is conditional to have two SAT onions in the channel. If the first onion fails, the second onion certainly fails. Therefore, in order to send such two Saturday onions, you need to calculate the expected value.

E(2 sats) = 1 sat * 4/5 + 1 sat * 3/5 = 7/5 sats

This gives you the following total expected value:

E(3 sats) = 2/3 sats + 7/5 sats = 10/30 sats + 21/15 sats = 31/15 sats

thought

There are results just for comparison

• Option a: 18/15
• Option b: 28/15
• Option c: 33/15
• Option d: 31/15

Option B certainly seems correct, but it makes sense to further analyze the two SATS onions. In the simulation, option D appears to be correct. This is a bit surprising to me. Using the formalism of probability theory, the difference between the 2 SAT paths is as follows:

• Option c: E(2 sats) = 1 sat * P(X>=1) + 1 sat * P(X>=2 | X >= 1)
• Option d: E(2 sats) = 1 sat * P(X>=1) + 1 sat * P(X>=2)

As mentioned earlier, the simulated setting indicates that option D is correct, but that is very surprising to me as I expect the second term to be a conditional probability.

BitMEX co-founder Arthur Hayes believes the Federal Reserve is primed to inject massive liquidity into the US economy.

In an interview on the David Lin Report, Hayes says that between now and 2028, liquidity in the “realm of $9 trillion” will be injected into the US economy, initially flowing into the traditional economic sectors before trickling down to risk assets such as Bitcoin (BTC).

“…And I think the banks are going to free, because they now don’t have to hold all this equity capital against their treasury book, they can lend more into the real American economy. And so you’re going to see the amount of loans going to manufacturing firms increase, which is again… that’s an increase in credit. And that will make its way into crypto as well.”

The BitMEX co-founder says Bitcoin could skyrocket by around 139% from the current price by the end of the year. By 2028, Hayes Bitcoin could go up nearly tenfold.

“So I think that we get to $250,000 by the end of the year. It will be bumpy along the way, obviously. But that’s sort of my end-of-year price target. And then a $1 million Bitcoin.”

On why Bitcoin could outperform other risk assets amid the expected injection of liquidity, Hayes says,

“So Bitcoin has a fixed supply. It’s obviously a much smaller market in terms of market cap. And so you have a lot of things chasing a very small door, then the price goes up on the margin. And so that’s why Bitcoin has been the best performing financial asset in the last 15 years.”

Bitcoin is trading at $104,462 at time of writing.

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Generated Image: Midjourney

It was quite the coincidence that the cryptocurrency market jolted back to life after Easter Sunday, with Bitcoin leading the way with more than a double-digit gain. While the price of BTC continues to hold above the critical $94,000 level, the premier cryptocurrency seems to be losing some momentum.

Unsurprisingly, investors appear to be increasingly confident in the promise of this recent rally, as significant amounts of BTC continue to make their way off major centralized exchanges over the past few days. Here’s how much investors have moved in the past few days.

Over 35,000 BTC Move Out Of Coinbase And Binance

In a Quicktake post on the CryptoQuant platform, crypto analyst João Wedson revealed that Binance, the world’s largest cryptocurrency exchange by trading volume, has seen increased activity over the past few days. The exchange netflow data shows that huge amounts of Bitcoin have been withdrawn from the platform in recent days.

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According to CryptoQuant data, a total of 27,750 BTC (worth $2.63 billion at current price) was moved out of Binance on Friday, April 25. This latest round of withdrawals represents the third-largest net outflow in the centralized exchange’s history.

The movement of significant crypto amounts from exchanges, which offer services like selling to non-custodial wallets, suggests a potential shift in investor sentiment and strategy. Large exchange outflows often signal increased confidence of holders in the long-term potential of an asset.

Wedson noted that the recent outflows do not guarantee a price rally for Bitcoin, but they do signal strong institutional activity, which is often a precursor for major volatility. Citing China’s crypto ban in 2021, the crypto analyst highlighted how massive exchange outflows didn’t prevent the dump.

At the same time, Wedson mentioned that the continuous Bitcoin outflows over several days, like during the FTX collapse, preceded a price bottom and the eventual market recovery. Ultimately, the online pundit hinted at paying close attention to the overall trend of the exchange netflow rather than a single-day activity.

Similarly, more than 7,000 BTC (worth approximately $66.5 million) have made their way out of the Coinbase exchange. According to the CryptoQuant analyst Amr Taha, this negative exchange netflow could be an indicator of increased institutional activity, as Coinbase is known as the primary crypto vendor for US-based institutions.

Taha said:

These large outflows typically suggest accumulation by institutions or large investors, potentially signaling bullish sentiment.

The analyst outlined that if the dwindling exchange reserves correlate with an increased spot demand or ETF inflows, a supply squeeze could be on the horizon, potentially pushing the price to the upside.

Bitcoin Price At A Glance

As of this writing, the price of BTC sits just beneath $95,200, reflecting an almost 2% increase in the past 24 hours.

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Featured image from iStock, chart from TradingView