Is there a general rule of thumb I can use to determine the likelihood of being assigned depending on how far ITM I am when short an option? For example - at expiration - if you are 0.01 ITM then there's a 15% chance of actually being assigned, whereas if you are 0.15 ITM then there's a 95% chance of being assigned.
US Securities options the auto exercise is .01. Probability does change at .02 or deeper as it's done automatically. There can be some unusual circumstances, but they are so rare I wouldn't worry.
The general rule of thumb is that it is very rare for your ITM options to be assigned as long as the shares are cheaper than the cost of buying the option just so they can get the shares. In other words - check your extrinsic value and make sure your options are still more expensive than the equal cost of shares. One thing that is a definite risk however that you should always worry about is when your underlying has a dividend ex-date and the dividend is more than your extrinsic value. This happened to me just two weeks ago. I had covered calls in T and I was hoping for a nice gain when the dividend was taken out of the stock price, but instead the price of the stock fell to the point where my extrinsic was less then the dividend so my (written) calls were assigned (I lost the shares) and someone else not only got my shares but also my dividend. You have to think about how dividends work. If a stock has a $.50 dividend that money is deducted from the stock price the morning it goes ex-div. So, if your extrinsic is less than $.50 people takes your shares and get the dividend. They made a little money from it, (and I still made the extrinsic value profit but lost my shares and missed the dividend).
I've seen slightly OTM options get assigned before. It's rare, but it does happen. The tell is to watch the underlying after hours. For example, if someone was short a $100 call option on XYZ, XYZ closes at $99.96, but then in the after hours it drifts higher to $100.15, then what would a holder of a call option do? Instead of simply allowing their option to expire worthless, they would try to short the underlying and exercise the option to end up flat on Monday, but with a ~$0.15 profit per share. That doesn't always happen, but it can.