The idea of "betting for information" is generally flawed. Betting does help to narrow down the opponents range, since it gives them the option to fold, call or raise, whereas a check behind closes the action and leave their entire range intact. But narrowing the opponents range AKA "information" is an additional benefit and never the main reason to bet.
On the river the only reason to bet is to make better
hands fold (
bluff) or worse hands call (value). On the earlier streets an additional reason can be
equity denial AKA protection, which mean to make a worse hand fold, that still have significant equity against your hand. Like maybe we have AQ on a board of 822 rainbow and bet to make hands like JT or K9 fold. Those hands have 6 outs to spike a pair and maybe some backdoor equity as well, so making them fold is good.
The final reason is to keep the initiative against a passive opponent, who will hardly ever raise as a bluff. Continuing with the AQ on 822 rainbow example, if the opponent call, they will usually check to us on the turn, in which case we can check back and see all 5 cards for the price of just one small bet. This idea only work, when we are in position though.
