Why is "go" spelled with the same vowel as "do" and "to" since it is pronounced differently?

How do we decide pronunciation for english words?

Pronunciation of many (probably all) English words has varied over time and from place to place.

As you have noted, spelling is not a foolproof guide to current pronunciation in any specific place. This is particularly true as spelling currently varies from place to place (e.g. color and colour).

We decide how to pronounce a written word in any of the following ways.

• By hearing how people around us pronounce the word.
• By looking in a dictionary that provides a guide to pronunciation.
• By guessing based on how we most often pronounce other words with a similar spelling.

The result may be judged correct in some places at some times yet be judged incorrect elsewhere or elsewhen.

Why 'go' pronounce as 'go' and not 'goo' [as in 'do']?

The idea of standardised spelling is a relatively modern one. Shakespeare quite happily wrote his name using many different spellings. It was only with the advent of dictionaries that spelling gradually became frozen in whatever choice of letters the dictionary compilers selected. The early compilers do not appear to have been especially concerned about consistency between spelling and pronunciation. Noah Webster was a bit of an exception.

Words that today have similar spellings may have, in the past, had spellings that differed more widely and which reflected different pronunciations. Such words may have originated in different languages and have spellings adopted from those differing languages - which may have had different rules of pronunciation.

So the contradictions you identify might arise from an unfortunate convergence of spelling changes or from a difference in source language or even from an arbitrary change in pronunciation (e.g. in "the great vowel shift").

Because the English language has co-opted words from many languages, and then corrupted/changed them over time we have a variety of pronunciation and spelling rules...which are not inflexible (compare the pronunciation of words by an Essex native with that of a Geordie, for example)

There are general guidelines which do broadly work - as long as you know or can guess the origin of a word. Did it come from a Latin root, or one of the Germanic languages, or Norse etc.?

There are many, many more vowel sounds in English than the five traditional Latin vowels. So it is inevitable that the same letter will represent different sounds in different words.

At best, English spelling reflects Middle English pronunciation, not Modern English pronunciation. That means it was locked in before the Great Vowel Shift.

These two simple observations go most of the way towards explaining your mystery.

Do and to come from Dutch doe and toe. (Those familiar with Dutch are aware that oe is ooh as in shoe). Then later, as e's were dropped, doe became do and toe became to.

As Reg Dwight said in a comment, they have different historical pronunciations:

the "o" in go was originally an /ɑː/, while the "o" in do and to was originally an /oː/. So they were always different to begin with, and even the Great Vowel Shift could do nothing about it, because different vowels shifted into different directions.

Go and do happen to be spelled the same because in Middle English, the time period when much of the current English spelling system was formed, their vowels were fairly similar (/ɔː/ and /oː/ respectively), and there are not as many vowel letters in the alphabet as there are vowel sounds in English. But they have never been pronounced the same.

The original pronunciation of the word go was "goo", so that it rhymed with "too".

The following text is from the book "A wife for a month" printed in London in 1717:

Since I am not an expert in the history of the English language, I cannot tell you why the pronunciation has changed from "goo" to "go".

I'm not sure, but I think "to" and "do" are spelled that way because they are function words. According to Wiktionary, the Middle English ancestors of "do" and "go" were pronounced with /ɔː/ and /oː/, the vowels that became /oʊ̯/ as in "goat" and /uː/ as in "goose". So based on modern English spelling conventions, we could expect "go" to be spelled as is, and "do" to be spelled "doo". Why the shift? I suspect scribes truncated it based on the general notion that function words should be one or two letters long while content words should be three or more (this is also why "are" is spelled with a silent "e" even though it's pronounced like "start" and not like "square").

While it would be naive to believe English spelling represents English pronunciation, there are well enforced rules that govern their relationship, and ambiguities almost always have reasons behind them. I assume it was about these reasons that the OP wanted to learn when they asked the question.