That is a good question. But I am generalizing it to include stacks all the way down to 1BB so that we can see the trends more clearly.
In addition, I am generalizing 9Ts to SC and 88 to small and medium pairs.
Value here means "How much can we extract from our opponent as a percentage of our stack?" It is important to define it in this way because all we have at risk is our stack. So our reward is measured in terms of our stack. This is why when the stacks are small, we LOVE AA because we usually win a very large percentage with it.
When the stacks are very low, we like pairs and high cards.
When the stacks are above all-in range (>10BB), but not deep, we have a hard time drawing, so we like big cards and big pairs.
When the stacks approach 30-50BB, we have implied odds to draw, and we are not afraid of reverse implied odds because our stack is not that big. So we like everything.
When we get deeper, reverse implied odds diminish the value of big pairs, while implied odds make drawing hands our friends(especially small and medium pairs).
When we get really deep, everything levels off because we don't have enough betting rounds to get all the chips in the pot.
The attached graph shows the value trends for these 3 groups of hands. The absolute values are arbitrary and used solely to illustrate the trends.
When stack is up to 20-30 BB, it has the most value. We can usually get all our chips by the flop or turn and we win most of the time. I am of course assuming good play, not limping like an idiot pre-flop.
When stack goes to around 50-100, the value begins to decrease due to two factors:
- We can't always get all the chips when we are ahead
- When we do get all the chips, we often lose the pot
The reason is basically a "guaranteed" TPTK. It doesn't improve easily, and even when it does, it doesn't make money. It is very unlikely someone will make top pair with a good kicker when we are holding the two aces.
As the stacks get very deep, reverse implied odds dominate this hand. With deep stacks, there is no way to go all-in preflop. So we start with the best hand, and the further in the betting we go, the worse our hands gets.
Despite the shortcomings of AA with big stacks, we win OFTEN small and medium pots, whereas we DON'T win often with drawing hands.
Small and medium pairs)
When we are short stacked in the all-in range (<10BB), they have a lot of showdown value, so we like them.
As the stacks get bigger, say 10-20BB, their value drops significantly. It is foolish to go all-in preflop with such stacks, yet these hands are terrible post-flop unless we hit a set. However, in this stack range, we don't have the implied odds to draw. The odds of making a set are 8.2:1. When we include the cases when we lose with it, it is roughly 10:1. With a stack of 10, we have no odds to even limp in late position, let alone call a raise. So basically in this range, these hands are mostly trash.
As the stacks go beyond 20BB, we have odds to draw if we limp or call a small raise. So we make up with them and become friends again.
As the stacks continue to increase, our implied odds get better and better and they become our closest friends.
When the stacks are very deep(>>100BB), we can (and should) raise pre-flop because if we hit in an unraised pot, we will rarely be able to get our stack in the pot.
When stacks are short in the all-in range, they don't have much value because we are looking for pairs and high cards. There is no way to draw with such stacks. So compared to pairs, SCs score much worse in this category
When stacks are 10-20BB, we still don't like them, although some of the higher once can be played for high card value in position.
As the stacks grow beyond 20BB, they become mroe attractive assuming we limp with them or use them as high cards in position. The odds to make a str8 draw or a flush draw are about 4 to 1. But makeing the draw is far from making it. We are still 4 to 1 on the flop to make it by the turn and usually must put more money in the pot. So they are much worse than pairs.
As the stacks become deep beyond 50BB, they also become our friends, but never as good as pairs.
Finally, a remark on the original setting betting 5BB with a stack of 50BB with 88. This is NOT GOOD! This is shooting yourself in the foot because such bet completely kills our implied odds. If we limp, our implied odds are 1 to 50 with odds to make it 1 to 10. When we raise to 5BB, we make this about 0EV proposition. We might as well fold since folding has smaller variance.
Similar argument applies to raising that much with 9Ts.