An emergency fund should be completely liquid.

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An emergency fund needs to be stable and liquid. Unless your emergency fund is peanuts, Bitcoin is the better emergency fund. However, if your funds are so low that 20-30% dips would put you at serious risk (meaning you have an emergency which you cannot pay for because the fiat value is now too low), then fiat is the better emergency fund.

I think most people would profit more from having a BTC emergency fund, as in the next few years we can expect a Bitcoin price of >$100k.

Anyone betting against Bitcoin at this point has not realized the reality of Bitcoin.