Yao (pin yin first tone) is a common way to say "one" in northern china when reciting multiple digits and basically the only way Beijing locals say 1 in a phone number or a string of numbers. for going to a market and asking for 1 of something, "yi" is the preferred way.

Pretty uncommon among southern Chinese people and Taiwanese (many American mandarin speakers are of Taiwanese descent).

The Yao pronunciation was introduced to me as the "military" one in Taiwan. Kind of like you would use "foxtrot" to spell out F on the phone.

yi-ga when asking for one of something

1 is pronounced "yoh"/"yao" in the context of phone numbers.

Which I find very frustrating as it sounds much more similar to liu (6) when pronounced in my crappy Chinese than yi does.

chinese speakers like yao often because it sounds LESS like other numbers and is harder to miss.

yao1 (1) and liu4 (6) should be pretty distinct. but if the way you pronounce them is similar for whatever reason, you can always use yi and chinese listeners won't flinch. in fact, taiwanese americans will be confused by yao, but zero people will be confused by yi so it's arguably better to use that if you don't know the background of your counterparty.

Perhaps I'm mishearing but it sounds to me more like they are pronouncing it "yo" (English) or "you" (Chinese) here in Beijing, which does sound more like 6. yi/qi are slightly similar but I never have the same issue. I've given up on trying to be correct and use yi most of the time.

if there's question about pronunciation, i find that putonghua (mandarin) educational material is very good and there are lots of references with clear pictures of what your mouth and tongue should be doing when pronouncing that make it just about impossible to make the wrong sounds (it won't fix your tones though).

it's difficult to describe and people pronounce english words differently so this isn't definitive, but

yao1 is like "yao ming", like if you stub your toe and say "owww!" in pain, or "yowzers!" -- those vowel sounds are all the same for me, so if they are for you too, that's probably the standard sound for "yao" in chinese.

liu4 is much more closed mouth. rather than opening your mouth wide, your mouth will be closed as if you are pronouncing the english name of the letter "e". the vowel sounds are roughly like taking the words "he" and "who", stripping the "h" sounds, and ramming the vowel sounds together. this (for me) sounds similar to the sound a child makes when he/she sees something disgusting and says "Ewwww!" or the english word "few" (the opposite of many). hopefully those 3 also sound the same to you.

It's the tone. yao sounds very different from liu because of the tone. yi also sounds different from liu because of the tone. yi does not sound very different from qi, and yi is hard to disambiguate with multiple yi in a row.

you use yao because it's easier to understand

qi yao yao yao ba san

than

qi yi yi yi ba san

It's mostly the qi yi yi / yi yi yi that gets hard to disambiguate.

What is likely happening is that you don't yet have the ear for the tone.