I made 4th dan and 1800R a couple days ago. So we're doing this again.
If you go back and look at Akagi or Saki (or really, any MJ story) you'll see a cliche that comes from a real game situation: the hand is progressing well...
"But this hand won't do... I need more points!!"
Then the protagonist swiftly changes the ordinary hand, usually by magic, into some incredibly high-scoring, unlikely hand as onlookers gape in disbelief. Comeback victory, confetti, etc.
I said earlier that I value taking the initiative and that I won't often wait around for a hand to improve. This isn't to say that every hand is a 1000-point open tanyao or yakuhai hand-- that won't get you anywhere either-- but I don't often go for the long shot. If I have a decent hand that can be won on one tile or improved by one tile... I'd rather just win it. I look for the yaku, but I don't chase them. Not unless the situation is desperate, anyway.
4th: 14,000 (me)
Here is one such situation. 10,000 points from third place in the final round. Desperately behind in all last is about the worst situation you can be in (aside from say being under 1500 points). I've got five of seven pairs here and one red dora in the hand.
The hand is developing towards seven pairs (chii toitsu) and I've been thinking about a half-flush (one suit and honors, hon itsu) in the sou suit since the hand began, but I was hesitant to throw out the pair of 9-man and set my seven pairs hand back a big step. As every tile that isn't an honor or sou has been discarded, I'm forced to finally make this decision.
The hand is nearly done, but what could it possibly get me? Putting aside completely lucky stuff like ippatsu tsumo or uradora, this hand is going to top out at mangan, 8,000 points. That barely puts me in third. At lowest it's just seven pairs with riichi, which is 3200 points. At any other time in the game, even in last, I'd be okay with those results because I go for the quick win. But this is the end, and in the final round you have a different gameplan.
On the other hand, a hon itsu chii toitsu is mangan by itself, guaranteed. With reach it's at least haneman, 12,000 points. One hand might keep me from losing, if I'm lucky. One hand is further away, but it will definitely keep me from losing. It's a long shot, but I have nothing to lose and I let go of the pair.
I get in tenpai for chiitoi hon itsu with a red dora, and even though it makes no point difference for me I reach. With ippatsu, tsumo, or uradora I could have a baiman (18,000), which would win the game. I'm going all or nothing. The dealer, unshaken by my reach, reaches after I do... and deals into me. Second place with 27,000.
A funny thing happens here. Because I have brought the leader below 30,000 points, nobody has over 30k at the end of the final round. In Tenhou's rules, when this happens play continues into a west round (after east and south) until someone gets over 30k and wins. I won the next hand by reaching early on a hand with no yaku and a crap edge wait... and I took first place. The next game I placed second and took fourth dan. So yes, the cliche "I need more points!!" actually happened to me and I was able to pull it off.
Now more often, a move like this just doesn't work out at all, but if all your possibilities lead to death except for one... well then you've got no choice but to run after that long shot, right?