WWYD for 2011/08/31

[Shirluban]

I'll discard or .
At first I thought about and , but keeping enable to get iipeikou (while tanyao is not more likely for the same score) and gives more flexibility, in case won't show up.

Meanwhile, I don't see how can improve the hand at this point. Usualy it's a very good pattern to get a pair or a ryanmen... but we already have these here.

[Lespar]

Is there any real difference between the and ?

[xKime]

My choice:

Tonpatsu, hiraba.

If you discard it is true that the tenpai chance is 4 tiles bigger thanks to two and two remaining. However, even if you drew or the very next draw, what do you do? "Reach only"? In a flat East 1? The risk is far greater than the reward, and the EV is negative after the 6th draw, so those four tiles are actually useful only for three draws more. I won't say it's wrong to keep the tenpai chance for those tiles, but I just wouldn't recommend it here. If 8s or 9m, or any other tile in your hand was the dora, it would be perfectly fine to discard 4 or 7 of dots. However, the only tiles here that will actually make you happy are as they will grant pinfu (or in the case of , iipeikou as well).

However, here I believe in discarding as you still have a ryanmen-ryanmen one away from pinfu + ( + ) where whether you draw you will still be in tenpai for pinfu ( would give you a three sided wait, but I wouldn't count on it). The overlapping wait on there is bad, but now you have the chance for something to stick to those 4 and 7 of dots, as any will give you an even better one away from pinfu (of course, the best two would be and as they are three sided waits, making the one away even wider).

It's true that even if you keep , you can just get something to stick to for another ryanmen, but that's only and nothing more. Clearly the is actually helping in that case.

Let's get a tenpai with yaku first and watch the situation on the dora before we push ourselves in a situation where we have "only reach" on an East 1st with the whereabouts of the dora still unknown.

(Yeah, I tend to believe in Ukase-uchi in early stages)

[Shirluban]

However, even if you drew or the very next draw, what do you do?

I'll discard it.
As you said, the reach only hand would have a negative expected value, so there is no point in considering it.

By the way, pinfu+riichi would have a quite low expected value too.

any will give you an even better one away from pinfu

Or will it?
or will give a ryanmen on seven live tiles, at the cost of sacrificing the ryanmen on seven live tiles and the hope for a three sided wait in manzu. I won't say and will give a better wait.
Overall it's still a better wait since two tiles (3p, 8p) gives a three sided wait instead of one (5m), but it also kills the potential to make some value from this hand with iipeikou+pinfu.

I don't say you're wrong nor I'm right, I'm just not convinced the extra tenpai odds worth to lower the hand value.

[WaveMaster]

I keep the 9 character to hold on to the chance for iipeko.

If you discard it is true that the tenpai chance is 4 tiles bigger thanks to two and two remaining. However, even if you drew or the very next draw, what do you do? "Reach only"? In a flat East 1?

Yes.

I can't actually say that with absolute certainty, because an interesting discard in the next go around could potentially change my mind. But, depending on how the other players' ponds look, I might be willing to so up to somewhere around the sixth discard.

We can already see one copy of the dora, and it's a wind different from the round wind. Further, it's in our own pond, so I'm perfectly willing to bet you that after we reach with our fourth discard, the remaining copies of West will be discarded as safe tiles as they come up. Just because we know our hand isn't likely to be big, our opponents don't know that. I wouldn't pass up the chance to be aggressive so early in the first round.

[xKime]

However, even if you drew or the very next draw, what do you do?

I'll discard it.
As you said, the reach only hand would have a negative expected value, so there is no point in considering it.

By the way, pinfu+riichi would have a quite low expected value too.

My point is, if you're not taking tenpai on 8s or 9m, there is not much of a point in keeping the uke-ire for those tiles (and if you were taking tenpai in those 4 tiles, I won't judge you, but I won't like the play-style much). You're basically saying you're only satisfied with drawing 8m before any other tile.
Before the 6th go around, the EV for pinfu+riichi (especially in ura-dora+ippatsu ari rules) is actually quite high. NONETHELESS, I'm not saying to reach even if you get pinfu tenpai. Probably damaten would be a smarter move, as you have uke for all three red dora. I should research that. HAZ's sites has posted research from Houou tables at tenhou that it is better to riichi (higher EV), but Totsugeki's theory is highly against it. I think HAZ didn't consider a lot of other factors, so I'd have to look into that one.

Or will it?
or will give a ryanmen on seven live tiles, at the cost of sacrificing the ryanmen on seven live tiles and the hope for a three sided wait in manzu. I won't say and will give a better wait.
Overall it's still a better wait since two tiles (3p, 8p) gives a three sided wait instead of one (5m), but it also kills the potential to make some value from this hand with iipeikou+pinfu.

I don't say you're wrong nor I'm right, I'm just not convinced the extra tenpai odds worth to lower the hand value.

It will. Just the fact that you have one of those tiles in your hand already doesn't mean much, given that is a ni-do-uke for 5m. Instead of waiting for 16 (or 15) tiles for (yaku ari) tenpai, it's a mere 12 (or in our case, 11, as there is one 8m already in the hand). Long before there was an ever going argument about which was better, a pure ryanmen one away, or a one away with a double uke for a tile with a chance for 3-sided-wait if the middle tile fell in. It's a simple example, but research said:

From this shape (incidentally, the dora is West so you can't discard it)

What discard is more statistically profitable?

　Agari probability of the lone tiles by number
　　　2 wait＝０．９５％
　　 5 wait＝０．６０％
　　　8 wait＝０．９５％ (logically, same as 2 wait)

(Of course, the tsumo probabilities for all tiles is the same. 102 tiles non-visible)

（１）In the case of discarding 4m
　The useful tiles become 5-8m and 25p.
　　　（ａ）Probability to draw 5-8m　８÷１０２＝７．８４％
　　　　　　Ron probabilities for 5-8p wait　０．９５×４＋０．６０×４＝６．２０％
　　　（ｂ）Probability to draw 25p　　８÷１０２＝７．８４％
　　　　　　Ron probabilities for 58m ０．６０×４＋０．９５×４＝６．２０％
　（７．８４×６．２０）＋（７．８４×６．２０）＝０．９７％

（２）In the case of discarding 4p
　The useful tiles, 258m。
　　　（ａ）Probability to draw 2m　４÷１０２＝３．９２％
　　　　　　Probabilities of ron for 58m　０．６０×４＋０．９５×４＝６．２０％
　　　（ｂ）Probability to draw 5m　　４÷１０２＝３．９２％
　　　　　　Probabilities for 258m wait ron ０．９５×４＋０．６０×３＋０．９５×４＝９．４０％
　　　（ｃ）Probability to draw 8m　４÷１０２＝３．９２％
　　　　　　Probability for ron on 25m wait　０．９５×４＋０．６０×４＝６．２０％
　（３．９２×６．２０）＋（３．９２×９．４０）＋（３．９２×６．２０）＝０．８５％

　In the case of discarding 8m, ０．９７％ agari probability. Discarding 4p ０．８５％ agari probabilities. Therefore the former has better probabilities.
　The 4 useful type of tiles for tenpai discarding 4m and the only 3 useful types of tiles for tenpai discarding 4p, that's where the difference arised. If there was a fifth 5m, then the merits of the three sided wait would be superior.

But of course, our hand shape is different in that in case you don't draw the very far superior and instead you drew the little bit inferior , there is... one less tile? (our ideal 8m is also one less tile btw) Okay, let's redo the math taking that into account, with our actually to be non desired hand evolution's shape:



Ron agari % for lone tiles by number:

(others remain the same)
3: 0.69%
6: 0.60%

Non-visible tiles: 60 (remaining in wall) + 13 (dead wall; note the dora indicator is a visible tile) + 13x3 (the other players' hands) = 112

（１）In the case of discarding 6(7)m
　The useful tiles become 2-5m and 3-6p.

　　　（ａ）Probability to draw 25m　8/112＝ 7.14%
　　　　　　Ron probabilities for 36p wait　0.69×4＋0.60×3＝4.56%
　　　（ｂ）Probability to draw 36p　　7/112＝6．25%
　　　　　　Ron probabilities for 25m 0.95×４＋0.60×４＝6.20%

　（7.14×4.56）＋（6.25×6.20）＝0.71%

（２）In the case of discarding 4(5)p
　The useful tiles, 258m。
　　　（ａ）Probability to draw 2m　4/112＝3.57%
　　　　　　Probabilities of ron for 58m　０．６０×４＋０．９５×3＝ 5.25%
　　　（ｂ）Probability to draw 5m　　4/112＝3.57%
　　　　　　Probabilities for 258m wait ron ０．９５×４＋０．６０×３＋０．９５×3＝8.45% (note that 5m is only x3, as you'd have drawn one already!)
　　　（ｃ）Probability to draw 8m　3/112＝ 2.67%
　　　　　　Probability for ron on 25m wait　０．９５×４＋０．６０×４＝６．２０％
　（3.57×5.25）＋（3.57×8.45）＋（2.67×６．２０）＝ 0.65%

(God, I sure hope I'm not making any mistakes)

Therefore, even in that case, the 67m discard's 0.71% is still superior to the 45p discard's 0.65%.

And a superior yaku ari tenpai chance in early game has a huge effect on the EV of the hand. Do note that even with your 47p discard, once you draw 25m, you will still take on pinfu nomi.
You can still throw pinfu away and riichi with a kanchan for riichi+iipeikou, but that's for another research (in which the result has been that taking on riichi+pinfu is better than taking on riichi+iipeikou kanchan anyway).

It's the most valuable proof I can calculate. And I hope it fits in one post. Therefore, digitally, I'd say the answer is pretty much tilted towards

(PS: Also, this is a "worst case scenario" where 5p came in. If what came in was 3p or 8p, the agari% (and therefore, of course, the EV) skyrockets!)

I don't know about occult, though. Atmospheric pressure and "feel" or "read" are not my main field of expertise.

[mrrrx]

Well using my noobular senses, I would also discard because I feel that it will be easier to get tanyao than iipeikou since it's more likely to draw something that sticks to 4567p before the 8m comes. That wouldn't technically put you closer to tenpai, but you'd most likely be able to switch a closed wait for ryanmen or better, and that'd make pinfu guaranteed. If the 8m DOES come first, then you missed out on a han point, but at least you're still in tenpai with pinfu. I think that's less of a loss than discarding 4p and then drawing 3p.

The only danger is drawing 9p. I know you're there, 9p... plotting with 8p...

[Shirluban]

I feel that it will be easier to get tanyao than iipeikou since it's more likely to draw something that sticks to 4567p before the 8m comes.

With , only gives you tanyao so you have the same chance than for iipeikou.

But thanks to your comment, I realize we've missed an important point: if we get this 6m, we still can have iipeikou.

So the hand would worth pinfu+tanyao+iipeikou (+riichi), the best value so far.

@WaveMaster: Is there a reason you choose the and not the ?

[WaveMaster]

@WaveMaster: Is there a reason you choose the and not the ?

It's not hugely important, but if I do riichi within the next few discards, having the 7 in my pond reveals less information than the 4. If the 4 is out, anyone trying to play defense but short on completely safe tiles would guess that 1 and 7 are safe against me, and be correct. With the 7 out, I leave the possibility that I am waiting 1-4 in dots open.

[xKime]

I feel that it will be easier to get tanyao than iipeikou since it's more likely to draw something that sticks to 4567p before the 8m comes.

With , only gives you tanyao so you have the same chance than for iipeikou.

But thanks to your comment, I realize we've missed an important point: if we get this 6m, we still can have iipeikou.

So the hand would worth pinfu+tanyao+iipeikou (+riichi), the best value so far.

The that you can still use (and be happy to draw) for the very same purpose even after discarding though. Doesn't really help either case, as one thing isn't canceling the other.

In any case, I took my time writing a long reply to you, I expected some more insight.

[mrrrx]

I feel that it will be easier to get tanyao than iipeikou since it's more likely to draw something that sticks to 4567p before the 8m comes.

With , only gives you tanyao so you have the same chance than for iipeikou.

A ton of tiles put you on the path to tanyao after discarding :

The main difference to me seems that it would take 2 tiles to get to tenpai with tanyao (discarding 9m) as opposed to only 1 tile to get to tenpai with iipeikou (discarding 6m/4p/7p)

So, since in either case you'll have to draw 2m/5m to win, are you more likely to get
(iipeikou track)

OR

( + ) or ( + ) or ( + ) or ( + ) or ( + ) or ( + ) or ( + ) (tanyao track, 7 possibilities)
?
My gut tells me the latter is more likely, but I never studied probabilities. But instead of leaving it there, I'll try to figure out how to calculate this via google because why not...

So if you were to draw 2 tiles after discarding 7p, then your iipeikou chance of drawing 8m would be
(# of 8m left) * (# of non-8m tiles) / (# of ways of drawing 2 tiles over the 112 tiles left)
(3 * 109) / (112!/(110!*2!))
5.26% iipeikou chance over 2 draws

If you discarded 9m then the chance of getting tanyao in one of the above situations is roughly (for simplicity, assuming the average of 3 of one tile left and 4 of the other)
(# of first tile left) * (# of second tile left) / (# of ways of drawing 2 tiles)
(3 * 4 ) / (112!/(110!*2!))
0.19% - (or a 99.81% chance of this not occuring)
99.81% ^ 7 (for 7 different chances) = 98.67%
1 - 98.67% = 1.33% tanyao chance over 2 draws

So, damn, I thought, my gut was totally wrong! But instead I decided to calculate the chance over drawing 10 tiles...

for iipeikou the chance of drawing 8m over 10 tiles would be
(# of 8m left) * (# of ways to draw anything from the other 111 tiles over the next 9 draws) / (# of ways of drawing 10 tiles)
(3 * (111!/(102!*9!)))/(112!/(102!*10!))
26.8% iipeikou chance over 10 draws

for my tanyao chances over 10 tiles (again assuming 3 of one and 4 of the other on average)...
(# of first tile) * (# of second tile) * (# of ways to draw anything besides those 2 tiles (105 tiles) over the next 8 draws) / (# of ways of drawing 10 tiles)
(3 * 4 * (105!/(97!*8!)))/(112!/(102!*10!))
5.91% - (or 94.09% chance of not occuring)
94.09% ^ 7 chances = 65.28% chance of not occuring
1 - 65.28% = 34.7% tanyao chance over 10 draws

So, unless I totally messed up that logic (not unlikely), it seems that you have a better chance in the short-term (1-5? draws) going for iipeikou, but a better chance in the long-term (>6? draws) going for tanyao. So maybe if it were later in the round, I think discarding 4p/7p/6m would be the way to go, but this early I think it makes more sense to get rid of 9m.

I didn't realize it took so many draws for switching your waits around like that to pay off.

[Shirluban]

In any case, I took my time writing a long reply to you, I expected some more insight.

Sorry.
My point was that while improving the agari%, discarding lowers the maximum hand value.
It may or may not increase the expected value, anyway EV gives the best result on the long-term and since it's an East-only game (if I decipher correctly the blue pixel mixture on the top right) we don't have much time/hand, so I'd rather favor immediate score (as long the agari% is not too low and the danger is not too high, of course).

Here, thanks to the tanyao possibility my argument is invalid.
I should have said explicitly than if both options (discard 4/7p VS 9m) leads to the same score, the choice giving the better agari% is, obviously, the best.

(And I should avoid replying when I'm not fully awake too.)