Idiom request for describing a situation in which someone give advantages to their enemy or opponent

I'm looking for an idiom or proverb that can be used for describing a situation in which someone's actions or behaviors are in favor of their opponents or enemies; in other words it seems that they are serving their enemies' or opponents' interests (usually unintentionally).

There is an Iranian proverb that says :

"To provide water for (turning) the enemy's mill"

This proverb mostly is used among politicians when they are accusing each other of giving advantages to the country's enemies, their opponents or the opposite parties.

For example:

It is supposed that a public election be held for choosing the members of the parliament on 26 February in Iran. Regarding the importance of this election, the supreme leader of the country has asked the politicians to stop using discouraging words or showing reactions that would lead people not to participate in the election. Because if the election is not recieved well by the people, it would be considered as a sign of their dissatisfaction from the current leaders and thus "would provide water for the country's enemies' mill".

What do English speakers use in this situation that can convey the same meaning?

I have come across this title " loading the gun of the enemy" in a website, but couldn't find it as a set phrase in available dictionaries.

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Solution 1:

You could say they would be playing into the hands of the enemy.

play into somebody's hands

to do something that gives someone else an advantage over you, although this was not your intention

If we allow terrorists to disrupt our lives to that extent we're just playing into their hands.

_{Cambridge Idioms Dictionary, 2nd ed.. (2006). Retrieved February 24 2016 from http://idioms.thefreedictionary.com/play+into+hands}

According to this source, the expression originated from playing cards, specifically the game bridge. The source gives nice outline of its emergence:

A part of the game’s strategy is to force your opponent to play certain cards. If you manage to do so, then she or he is playing into your hand, giving you an advantage. The expression is often pluralized into playing into someone’s hands. This slight modification has resulted in obscuring the origin of the meaning, making people think of a body part, when actually in card games your hand, refers to the cards you are holding. This meaning goes all the way back to the 16th century as well.

This idiom is very common in the UK, and is also often said with emphasis and pluralised as mentioned above:

played it right into my hands

Searching for the above on Google Books will give you plenty of examples of the use of this phrase in print.

https://www.google.com/search?tbm=bks&q=%22played+right+into+my+hands%22

Solution 2:

give [sb] a stick to beat you with.

Example: If things go badly, you may be giving your opponents a stick to beat you with.

Solution 3:

It may not be so common in AmE, but in BrE you can certainly...

(score) an own goal
something that someone does to try to get an advantage, but which makes a situation worse for them
Usage notes: In sport, an own goal is when someone scores a point for the opposite team by mistake.

Solution 4:

Consider,

give someone all the ammunition they need; give someone ammunition to use against someone/oneself

ammunition: A means of attacking or defending an argument, thesis, or point of view. American Heritage® Dictionary

Google Books

be (all) grist for someone's mill

grist for someone's mill: Something that can be used to advantage. American Heritage® Dictionary

In retirement, Gehlen bitterly complained, “For week after week the [Felfe] affair continued to hold the newspaper headlines: his character, his Nazi past, and his subsequent treachery were all grist for their mill, resulting in exaggerated reports. A Nazi Past

fuel someone's arguments