Usogui - Vol. 31 Ch. 334 - "Certain Pass" Or "Duel"

Fed-Kun's army
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Jeez, I initially didn't understand why they had to stand on the steps depending on how much they bet. But since the banker's naturally going to single out the person with the highest bet, it makes sense that everyone else can't just follow accordingly. Lol
 
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Well indeed, Travolta was significant.

That being said, Baku will probably win more often than not, but I can't imagine winning this game in particular being too crucial (he just can't lose). I assume he's planning on what he's going to do with these guys now that he's "liberated" them from their "slavery".

Soon would be a really great time to show off what the other two have been doing in their kingdom's slave quarters. Hopefully it's not the same type of liberation.
 
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Pretty simple. Bk's strategy is simple. All he did was trick that other guy into getting the top stair by making him think that it's the most advantageous spot, thus making the dealer target him since he's the one with the highest bet. Then, "in exchange" to betting the 10 bios as promised, he made the top stairs guy point up in the first round. Now all Bk had to do was go with any other direction and not lose. Then, in the second round he'll go for the certain pass, and since he knows that the banker will target the player on the highest stair, the banker will choose the direction that the highest betting player chose on the first round, in this case the agreed upon "up" that Bk surely "exchanged" (tricked) for betting the 10 bios. Bk's second round pass is guaranteed due to the certain pass, and his third round pass is almost guaranteed by the Banker choosing the direction the highest betting player chose in the first round, in oder to have a 50% chance duel with the highest betting player. It's in the banker's best interest to do that, unless the player realizes this as well (which they did) and thus chooses the more risky option of going for one of the free directions, thus keeping the certain pass for the third round. But even if the banker foresees this and chooses a random direction instead of the direction the highest betting player chose in the first round, you can get by the second round with the certain pass, and then the banker would be at a disadvantage if the highest betting player didn't choose the certain pass, so it's unlikely that the banker would go for this. It's unlikely for you to be targeted if you're not the top stair player, so no matter what the Banker chooses you have the advantage as long as you know what the top stair player played in the first round, and you choose smth else in the first round. If the banker chooses the direction you chose in the first round, and then tries to duel the top stair player, it's highly unlikely that they'll choose the direction the top stair player chose in the first round for the duel in the last round, since the top stair player can't choose it anymore. Thus by choosing that direction in the last round, you increase your chances significantly no matter what. So by not choosing the same as the highest betting player and by figuring out what he'll choose in the first round, you almost guarantee your win as long as you bet less and manage to pass the first round.
 
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Batch will stop here for now, next one will begin in a few days.

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@299792458
That sounds right. It's funny how Bk tricked him into the top spot by saying it has a lot of advantages, but proceeds to say nothing substantial about those so called "advantages".

I guess if there was a weakness to the strategy, it would be if the other player bet the same amount and shared the top step instead. Then there would be a chance for Bk to become the target himself. But otherwise it seems pretty solid.

@Eiz
Yeah, I wonder about that too, they might not have enough to make Baku a citizen. If Baku really does make everyone broke here, and if he still doesn't make 10,000 bios, he'll remain a slave and have to deal with the anger of all the slaves after. And now that I think about it, his allies will be slaves as well, since Hal is probably a slave, so he'll need 30,000 more bios for them.

--

Strategically, the game seems pretty difficult for the banker, as you can't really focus on multiple people at once even though you want to. While each player just has to focus on the one banker.

Also, the rules from last chapter about exchanging bankers is quite weird. The banker can't quit even if they want to, another banker has to agree to take over, so if the banker's getting destroyed he'll likely have to keep going until he's broke, since no one will want to take over the position unless he's winning a lot.
 
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There's nothing better than seeing the phrase "There's a certain-win strategy" in a gambling manga.

Thanks for the batch as usual.

edit: this is probably all but certain, but I wonder if someone will try to game the system here. you are forbidden to look behind you or talk while the game is going on, but there doesn't seem to be a rule about someone behind the banker signaling to a player what the person on the top step picked, giving them information.
 
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isnt dueling and the certain pass identical? it just changes the order of when you win. You either win on the 2nd round or the 3rd, its still a 50/50 each time. the only difference is the higher you are there is some mindgames for whether you choose to win at the 2nd round or 3rd for the banker
 
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Thanks Team Duwang for these chapters! <3

The new game seems quite fun. As I understand it, one choice guarentees your win if you're the target, while the other guarentees your win if you're not. If i'm not mistaken, we should have something like this :

TARGET :
Certain pass -> 50% win (you'll survive this round, but your victory will be decided by luck on the third round)
Duel -> 100% win (you'll just have to use the certain pass next round)

NOT TARGET :
Certain pass -> 100% win (since you're not the target, the banker just gave you another certain pass to use for the third round)
Duel -> 50% win (you can lose right here out of luck, but if you don't, you'll have your certain pass for the third round)

So, basically, it's a game where the banker selects (or targets) a group of players that survived the first round with the same direction. and then, each player has to bet on whether they're in the selected group or not.

Now, let's consider a team with two players that will :
- always bet the same amount of bios
- always choose the same direction in the first turn
- always choose different options in the second turn : meaning one will use the certain pass and the other will duel

As long as they pass the first round (75% chance), no matter if they're both targetted or not, one of them will definitely win (100%), while the other is not even guarenteed to lose (50%). Thus, taking the first round into account, we can say one player has 75% chance to win, and the other 37,5% chance to win. Assuming they'll share their earnings afterwards, in the long term, the team will win 56,25% of the time, which seems like a good plan. And I wonder if the "certain win strategy" has something to do with this.

That being said, there'll also be a time where one of players becomes a banker. And in this situation, I can't really think of any useful team play.
In fact, I don't even know how the referee will react if one player wants to bet an amount of bios that equals the banker's purse. Will he prevent every other player from betting more? Will he force him to reduce the amount? Will a bios lending rule come up?

Too many mysteries, man... I love this manga.
 
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@Jonui Dueling only guarantees your victory as a target if the banker always chooses the direction the target chose in the first turn. Which won't happen if the banker realizes this strategy, meaning dueling as the target doesn't guarantee your victory, as you suggest. Unless you define the banker 'targeting' someone precisely as the banker choosing the target's chosen direction in the first round. In my view, you can choose to target a player as the banker and try to mind game him and see if he will duel or not, which wouldn't guarantee the target's victory if he chooses to duel.
 
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@299792458 Oh yeah, I was defining the targets as the ones who will be copied by the banker, regardless of the mind games and intentions behind it. Sorry if it wasn't clear.
 
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@the9813
Besides the mind game differences, there is also a difference in probability.

In the 2nd round, these are the main outcomes as the player vs the banker:

If you duel:
1) You win because the Banker thought you would certain pass, and picked your 1st round direction.
2) You win because the Banker picked the other dueling option you had.
3) You lose because the Banker picked the dueling option you picked.

If you certain pass:
1) You win because the Banker picked the first of your two dueling options, so you get another certain pass for round 3.
2) You win because the Banker picked the second of your two dueling options, so you get another certain pass for round 3.
3) You have to duel in a 50/50 scenario in the 3rd round because the Banker picked your 1st round direction.

Assuming the Banker picks options equally (ignoring mind games), this means:

Choosing to duel = you get a 66% chance to win, if you fail, you lose.
Choosing the certain pass = you get a 66% chance to win, if you fail, you get another 50% chance to win in the 3rd round.

So choosing the certain pass is better, which is probably why everyone was so surprised at BK not choosing it in the first round.

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@Jonui
Referee Ikon mentioned earlier that he would make sure that the bios bet won't go over the banker's wallet.

For banker strategies, I was actually thinking of a way to improve BK's strategy, which already has close to a 75% win rate, to get it to 100%, and I came up with this:

What if BK makes a deal with the banker and promises to leak the top player's direction, and in exchange, makes the Banker promise not to choose his directions? So he'll get a 100% win rate, and the 'price' would be, the difference in bios bet from the top player and BK. This would make it so BK would always win. Though the top player will get suspicious if he always loses in the 1st round, and also the top player would need to bet a bit more in order to make it worthwhile for the banker.

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@Bosscrab
That would be a pretty good strategy! It doesn't seem like it's against the rules, but even if it is, I don't think Ikon is even looking at the other slaves behind the banker, so he probably wouldn't be able to catch it.

--
PS: Batch should be starting by tomorrow latest!
 
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@catx3
Indeed, the referee said he'll make it so the bets won't exceed what the banker has. But my question is: how?
It's not like the banker has only one opponent who can be forbidden from betting too much. There are multiple players, here.

What would the referee do, for example, if the banker had 10 bios and the players bets were 3, 3, 2, 2, 1 (11 bios in total)?
Will one of the 3-bios players be forced to bet only 2 bios ? And if so, which one of them exactly?

We don't really know these things, for now.

EDIT : Also, just wanted to say you're right with your probabilities. Considering a Banker picking options equally, "duel" wins 66,7% of the time, and "certain pass" wins 83,3% of the time.
 
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author is so amazing making me this tense over children's games
 
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@Jonui
The banker has to verify the amt before each round, so they have a chance to check if they can pay if they lose completely. If the banker can't pay, then probably they'll revise the bets or change a banker; if the banker fakes out and loses without having enough to pay, then I suppose "extralegal measures" come in...

@catx3
This breakdown is great and fits what I've deduced so far about this game too.
I'm also wondering the pros/cons that being higher on the steps give; since the banker is incentivized to target high-rollers, having information on where the high-rollers faced in earlier rounds gives an advantage - only issue is how to acquire that information.

Then there's also the banker being able to read if the players will duel or pass in the 2nd round; in an ideal situation the banker will be able to force multiple duels with priority targets in both the 2nd or 3rd round by adjusting to their individual personalities or abilities accordingly.

Of course, who knows what kind of meta plays BK will pull this time to win a landslide victory...
 

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