Word/phrase for when someone places a bet which is similar to your own

If you are making a bet or wager with someone, and you are both trying to guess as close to a particular value as you can (for example, date, weight or similar) then one particular strategy is to wait until the other person has guessed, and make your guess as close as possible to theirs, but, say, slightly above. This essentially guarantees that you will beat them if they have underguessed, and guarantees you will lose if they overguessed.

For example: My mother and I are trying to guess the date and time of when my sister will give birth, and whoever gets closest wins. I have guessed 8pm on a particular date, and my mother guessed 8.01pm on the same date.

I consider this frightfully unsportsmanlike, and I was wondering if there was a word/phrase to describe this sort of behaviour?

I'd say that mom is trying to outwit you:

• to get the better of by superior ingenuity or cleverness; outsmart:

As for bidding, probably the strategy is:

Bid nibbling:

• Bid nibbling is arguably the most ideal strategy. Bid nibbling, as it suggests, involves occasionally or gradually placing bids on a single item, attempting to be the winning bidder the majority of the time. You do not have to bid your highest price upfront, rather just enough to outbid the current winning bidder. When buyers collectively "nibble" on an item by bidding in small increments, the resulting effect tends to ward off other prospective buyers, by driving the price up earlier in the auction closing timeframe to a more reasonable, yet under market value level.

The sort of behaviour exhibited by your mother (with all due respect) can be termed as one-upmanship

One-upmanship is a spirit of competition in which one tries to stay a point ahead—one up—of the competition, usually figuratively. The word connotes an unwillingness to back off and allow one’s competition to keep the upper hand.

[Grammrist.com]

Often, those who practice one-upmanship use silly, cunning or unfair means to stay ahead in the competition. Regarding the proper betting term, Josh61's "bid nibbling" is the most appropriate.

In the world of finance and trading, analogous behavior whereby an agent exploits information about a trading decision made by another agent by carrying out a nearly identical decision after applying a minuscule change is known as front-running, or, in a more limited context, penny jumping.

As an example from the Wikipedia article on the subject, traders who observe a large order of shares being entered into the system at a price of $1.00 may proceed to buy the same shares for $1.01, using the knowledge of the large buyer's order to limit their downside exposure while attempting to make a profit in the event that a random fluctuation in demand causes the share price to go up.

Unsurprisingly, this behavior is also considered unsportsmanlike and parasitic in the trading context, and in some cases is even illegal.