Check with a toss-up hand if you are last to act.
One of the causative features to the definition of a toss-up hand would be that one or more of your poker
rivals either would have a made hand or would be drawing to beat you. In the case of their having a made hand, it would be likely that you would be beaten.
When you were to be in last position and the action would have been checked to you, it would be erroneous to bet if you were to feel your chance of holding the best poker hand was only fifty percent. The grounds for this would be that of the hands you could beat, a good number of them wouldn’t be able to call if you were to bet.
A busted straight or flush draw couldn’t call, so you couldn’t win any further bets from them. Still, the fifty percent of the time you would be beat, you could be quite certain that you would be called. So, there would be little or no value in betting.
For a bet to be correct, or at least a break-even proposition, the probability that hands you could beat would call you in relation to those that would be better than yours should be about equal. This would not be the case if you were holding a toss-up hand, since a high proportion of the time the reason you would win in those situations would be that your poker rivals would have missed whatever hands they were drawing at.
You shouldn’t bet the river for value in last position unless there would be at least a fifty percent you would win the pot if you were to be called. If this were not the case, then you should check and hope for the best.
Call with a toss-up hand if someone else bets.
You shouldn’t fold a toss-up hand on the river because, by definition, a toss-up hand would be one that 
you would feel would have about a fifty percent chance of being good. Even if the pot were to be very small, you would be getting the right price to call.
In fact, there would really be no situation in limit holdem poker in which you would have to fold a toss-up hand on the river, as you would have to be getting a price of at least three-to-one or four-to-one on an even-money proposition. (This is called an overlay.)
One of the worst mistakes you could make in holdem poker would be to fold the best hand on the river. If you were to play poker long enough, you would occasionally be culpable of this error. You shouldn’t let it happen with your toss-up hands, though.
With these hands, there would be realistic doubt, and whenever there would be realistic doubt, calling would be far better than folding. If you were to start folding toss-up hands on the river in an effort to protect your chips, you would have no chance of beating the game.
Playing a longshot hand on the river.
Longshot hands are those that you would feel are highly improbable to be the best on the river, based on 
both the value of your holding and the action in the hand. Classic longshot hands could comprise of a pair of nines when the poker board would be a king, a queen, a pair of sixes, and a five, or a queen and jack when the board would be an ace, a jack, a ten, a nine, and a ten.
When you were to be in last position and it would have been checked to you, you would have to check as well. Although you wouldn’t have a strong poker hand, you would have enough to show down.
Hence, betting as a bluff would not be a good choice. Poker opponents who would have your hand beat would call, and those who would not will fold. All that could happen would be for you to lose a bet here. Just as in Tip forty-three, you should check, and hope that nobody would have much.
If another poker player were to have bet, you would have a far tougher decision to make. You couldn’t routinely call as you would with a toss-up hand, as you would be beat here the vast majority of the time. Rather, you would have to ascertain whether the price you were receiving from the pot would substantiate your call. In a good number of cases, it would be a close decision.
If you would never fold a winning poker hand here (that is, if you would always call in these longshot situations), you would be calling too often. The times you would spend a bet ‘keeping them honest’ would tally up to more than what you would win when your hand would be good. Nevertheless, by following the action and focusing on your opponents’ playing styles, you would have to make the right decision most of the time.
Sometimes you will reach what would look like a break-even position; that is, the price the pot would offer would seems to match the amount you would have to invest to call. (For instance, the pot was to offer nine-to-one and you were to think you would win ten percent of the time.) In these cases, you should consider another factor.
When other poker players were to remain to act behind the bettor and you, you should lean towards folding your hand. The reason for this would be that someone might overcall, and if that were to happen, it would be almost certain that your longshot hand would be no good. If you were the last poker player to act, you could call more often with your longshot hand if you were to feel the pot odds were close.