I was about to write a bunch of dribble on tire chains but realized
@BlueOx was kind enough to find something I wrote in the past.
In truth if you are just carrying a set of chains for the "just in case" (such as R3 chain control or glazed ice off roading) any chains will do: either diamond pattern or ladder. DO NOT however get cable "chains", they just flat out suck. In fact last week I just drove past a truck in the ditch with these cables. Some notoriously icy roadway sections around here do not allow cables to pass for chains. In deep snow they are OK but on ice they will just spin. The cable cross links are covered with a series of small steel rollers. Their intended purpose is to 1-increase the diameter of the cross links as the cables are very thin and would provide little paddling resistance in the snow. 2-if the cables were to catch on a piece of course asphalt aggregate it will likely snap at the end swaged connection.
About a month ago we were out cutting our Christmas tree. Turns out all the flat landers were up here cutting that weekend too. It had been cold and no new snow for weeks. The snow that was on the ground was slicked ice. You should have seen the number of bro-dozers sideways on the trails (dirt roads). Mudders and 3 peak snow flaked AT tires were NOT cutting it. When we had to back down a trail due to one of these sideways tards, my father in-law almost slide off the road as he was sliding backwards on the ice. He had some Falken's AT with the 3PMS rating. Myself and other locals (in their subarus) with true winter snow tires (I run Blizzak DM-V2) were all driving around like it was dry pavement. This would have been a good situation to have a set of tire chains.
I have recently acquired a VW Eurovan for our winter Ski Rig. As ski lodges are closed, this has become our parking lot Ski lodge on wheels. The van however is FWD. I put on a set of Goodyear Winter Command Ultras. Though I have a set of chains for it, I have yet to have to use it. Those sticky tires have been unstoppable. Here is the road to and from the ski resort. It gains about 1150 feet in 3.3 miles. So far this season I have seen 3 cars crashed on the road as a result of snow/ice, all occurring on the downhill slope; can't stop can't turn.
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My final bit of advice is to buy chains used. If you look on ebay or craigslist you will find a TON of listings, many un-used. There is very little demand for used chains. People buy them, keep them in their trunk for the "just in case" times and never actually use them; selling them when they sell the vehicle. Very common to pick up a set of new diamond patterned chains for about $20 when they sell new for $80+.