# Game Log 4

Date: 17/07/29

Game Type: 特南喰赤

Link: http://tenhou.net/0/?log=2017073008gm-0029-0000-bebe9d92&tw=0

1位 A:Dasuke(+45.0) B:Danna(-20.0) C:t-shinjo(-31.0) D:ⓝ爆打(+6.0)

# E2-1 10th Turn:

Riichi?

In this, I don't think you should... Manzu being a a super dangerous suit aside, lets look at the board. After toimen declared riichi, Dealer seems to be pushing with a suji 5s drop After which came a South wind (shouldn't those be flipped around...?). If it was Very clear that dealer was folding in this case, fighing the riichi isn't that bad of an option. With a 7 tile wait and 2.3k out on the field, the criteria for fighting non dealer riichi is easily met. The problem here occurs when we through dealer with double ton into the mix. Throw in a number of unseen dora tile and this makes for a RUN AWAY fold.

# E3-0 7th Turn:

WWYD?

Block theory question. This one can seem tricky at first with the various pinzu tiles, and 4p8p2s all have the same ukeire(available tiles to advance to the next state). But looking at the various blocks in the hand: 1[78m], 2[344688p], 2[122345s] we can break these blocks down a bit. The souzu block is pretty tight since the tiles it can take in, 236s, are pretty stuck in place. But for pinzu block if we break it down: 344688p-> 344p+688p, we can drop the 4p and lock in the ryanmen! But how is this different than dropping the 2s and locking in the 12345 ryanmen? The big answer is more potential points, and helping out a weaker block. 344 shape has 10 tiles it can use, 34 has 8, 122345 has 9, while 12345 has 7. Rather than locking in the 12345 which lowers a chance for tanyao, we're left with a slightly weaker block than if we had the 34 left over. Under similar ukeire choices, maximize your yaku potential and widening choke points.

# E4-1 1st Turn:

A question of Intent, Full out for Honiitsu/Chiniitsu, or allow for other progressions as well?

with the 115566779m shape, pretty good chance to go for honiitsu or even chiniitsu. Since you have a lot of pairs which are also runs, a mentsu hand or even chitoitsu are both options here. Though in the case that you draw 3s, or even 40p, with a locked in iipeikou a riichi pinfu iipeikou dora 1 doesn't seem that bad. Though the allures of honiitsu chiitoitsu, or chiniitsu are nothing to scoff at, and with this point gap confirming them is probably the best idea. Not to mention while 3p is kind of nice since it could potentially take in the red 0p, the 12s doesn't have any added benefit. You're a LOT more happy with an honor tile pairing up draw than you are a 3s draw that penchan. So stick to the Honor tiles like glue here (for now at least).

# S4-1 10th Turn:

Do or Die, which path do you choose?

... well first off the choices aren't that great. Being 7.9k being 3rd, in order to escape last place, practically a 7.7k or mangan hand is needed. Luckily there's a 300 honba out so even a 7.7k ron suffices. Now lets look at the choices.

In the Blue corner weighing in at 4 ukeire we have the 8p6s shabo. While quite good in waits compared to the other contender, it lacks a punch so ura dora is required to escape, but for a comeback it could only ron 3rd place. Though this wait also has the benefit of being able to ron 1st place as well, since it would put them under 30k points.

In the red corner weighing at a mere 2 ukeire, on one tile that is the dora indicator, we have the 7s kanchan. Though it has less than half the tiles of the shabo option, a tsumo is 100% comeback, while a ron off 3rd or ura + ron on 1st/2nd also works.

Even though the shabo is wider I chose the kanchan. The reason being that even though the shabo is better it requires ura dora, and I rather take a kanchan with half the available tiles than a shabo that only has about a 33% (on avg) for ura. Throw in the ability to ron as well with the 7s and it seems quite nice in comparision.

# W2-2 7th Turn:

Another Orasu Do (and) Die situation. WWYD?

To get a good understanding of this problem lets look at the Rates for this game:

- 1st Place: +75
- 2nd Place: +30
- 3rd Place: 0
- 4th Place: -120

Last place hurts a good amount, so if possible I want to avoid that. But at hte same time completely folding here doesn't guarentee my survival. With 1st place in riichi and the game ending if they get over 30k points, we can almost guarentee they'll reach that threshold if they win their hand (1400 points). If I deal in I'm 100% guarenteed 4th, though if I win my had I'm 100% guarenteed to get 1st as well. Lets look at both cases and what other players should be trying to do.

First off regardless of who you are the rates in Tenhou say "DO NOT GET LAST", though its a lot worse for some than others. At its peak, a 10th Dan player would lose the equivalent of two 1st places with a single 4th.

Now on our table, 2nd place dealer has it pretty nice. Regardless of what they do as long as they don't deal in they're in pretty good shape. So unless they have something they can easily push safely with they'll probably fold if needed.

Last place has it bad, if 1st place wins this hand and doesn't ron another player, then they'll lose. Given that they're a single tsumo away from eternal 4th place they'll do everything in their power to Stay Alive. In other words they're not folding any time soon.

Finally there's me. As long as I don't deal in or 4th place wins, then I'll not get last. Even if 4th place wins, unless they have a close to mangan hand the game will continue. that being said, winning this hand does net me a nice +75 and its not like I'm guarenteed to lose if I push (or guarenteed to win). So lets look at some numbers. In a single hand of mahjong there are 16 common outcomes (we'll ignore ryuukuoku for now). Those are for each of the 4 people they can win in 4 different ways: Winning via self tile, winning form ron off each of the 3 people. Now in this case if 2nd place completely fold, and lets say they play perfect defense, then they remove 7 of those possiblities, so 9 remain. Assuming those 9 possiblities are of all equal chance, lets see how they play out.

Occurance: Points Gained

- 1st Wins Tsumo: +-0
- 1st Wins off Me: -120
- 1st Wins off 3rd: +-0
- I Win Tsumo: +75
- I Win off 1st: +75
- I Win off 4th: +75
- 4th Wins Off Tsumo: Into another orasu as 4th.
- 4th Wins Off 1st: Into another orasu as 4th.
- 4th Wins Off Me: Into another orasu as 4th.

For the points of "I go into another orasu as 4th", lets use the same estimation but with all 16 choices, and lets also assume anyone's win at that point would end the game. Though with everyone a good portion above the last place me, even if 1st or 2nd get hit they'll probably only drop 3rd. Under these assumptions: (4/16)*75+(10/16)*-120+(2/16)*0 = -56.25

So for the original estimate. In the case I push under these assumption, the estimated point gain is: -7.08

Now in the case that I play perfect defense and remove my winning ability as well, that removes 5 more options. So we're left with 4:

- 1st Wins Tsumo: +-0
- 1st Wins Off 3rd: +-0
- 4th Wins Off 1st: -56.25
- 4th Wins off Tsumo: -56.25

Which avgs to: -28.13

So if we were just considering the assumed averages it would be better to push here. Of course in the actual occurance of the game 4th place doesn't seem to be in tenpai quite yet so they're probably not as likely to win as 1st place or this hand. Another intesting tidbit is that if 4th place folded completely after seeing me push (unlikely but reasonable in Some cases), then under these assumptions my avg gain would go to: +7.5

# Some additional comments / analysis from totoro

In the above analysis, we did some pretty simple analysis to try and make the optimal decision - I thought we could definitely try and improve some of our assumptions and see what effect that has on the results.

**EV if we are 4th after this hand**

In the analysis above we estimated that if we were 4th then our ranking point EV would be:

(4/16)75+(10/16)-120+(2/16)0 = -56.25

While last either we are going to win the last hand or someone has to deal in for us to avoid last.

In the original equation we are suggesting that you’re going to win a hand ~25% of the time to claim 1st (and it has to be big enough for you to claim 1st – you’re on 22100 possibly less so you’re going to need mangan+) so that 25% is definitely not fair, i would say 15% is generous so let’s change the probability distribution and only assume we win the hanchan 15% of the time)

15%*75 + 60%*-120 + 20%*0 = 11.25 – 72 = -60.75

**EV assuming we defend perfectly**

Now let us revisit our EV if we defend. Given 2nd place has no incentive to push in this scenario we're going to take him out of the picture and as such this is a straight showdown between 4th and the bot.

In the original analysis we assumed that the probability of 4th place winning is the same as the bot's - this is pretty unreasonable given we can't be sure the person is in 4th is in tenpai. Even if he is 1-shanten he could be pretty far behind (this is a function of how close to tenpai and also bot's wait)

I'm going to change this assumption and drop his winning percentage down to 25% (this is still a pretty crude assumption feel free to comment on this one)

If we do this then the EV for this scenario becomes:

75% * 0 + 25% * -60.75 ~= -15.2

**EV assuming we attack**

Let’s focus on the following scenarios: (except grouping the last ones where 4th wins)

a) 1st wins tsumo 0

b) 1st wins off me -120

c) 1st wins off 4th 0

d) I win tsumo +75

e) I win off 1st +75

f) 1 win off 4th +75

g) 4th wins (i’ve grouped them up here, we use the previously calculated EV for this group)

Now back to our earlier assumption with 4th winning 25% of hands if we defend: if both myself and the bot are pushing then his win percentage will be lower in this scenario, let’s give him 20% (which i feel is a little generous but most importantly the percentage here should be lower than earlier)

For the other scenarios let’s stick with the equal probability assumption for now, but i’d argue this is the best case for you (given you are on a tanki wait while the bot could have a better wait + he goes first AND you still need to push a tile, although the wait has a bigger influence on this)

In this case scenarios a) to f) have probability (1 - 20%)/6 = 13.3% each and the EV we want is:

13.3%*-120 + 3*13.3%*75 + 20%*-60.75 ~= 1.8

So changing some of the assumptions doesn't change our original conclusion that pushing is +Ranking point EV here (and by a decent margin). Can we find a reasonable scenario where that might not be the case?

**Revisting the probability of the bot winning vs us winning if we push**

If you look at our EV calculations this parameter probably has the biggest effect on our EVs (and thus our final decision) which is why i've focused on this.

In our analysis we assumed that if we pushed, the probability of us winning the hand is the same as the bot's. As mentioned above our original assumption of equal probability is probably the best case scenario for us so we should test this a little. Let's look at a very likely scenario where the bot has a ryanmen wait with full 8 outs vs our 3.

In this case lets assign the bot 8/11 = 72.8% probability to win.

In this case a) to c) scenarios have probability (80% * 8/11 / 3) ~= 19.4% and d) to f) are 7.27% so our EV becomes

19.4%*-120 + 3*7.27%*75 + 20%*-60.75 ~= -19.07

If you use excel then we find that the EV of the 2 scenarios will match if the bot wins about 68.5% of the time. Can this occur? Definitely I do feel like this is the main point of discussion. It is pretty safe to assume that the dealer on average will have less than 8 outs (would love to know some stats on this for a random tenpai) but then on the flipside we might have less outs than we think (especially if we wait on the 4s in the hand above). Despite this I still think by default pushing is higher EV in the above scenario given discards but the margin might not be as big as we think.