purpose of Dice game was 2.
1. Take away Pandavas Kingdom
2. Disqualify Yudhishtir as a King. So that under no circumstances Yudhishitir can justify his rights to be a king again.
Shakuni and Duryodhan were using the dicegame as a permanent solution to get rid of Pandavas.
Getting Yudhishtir to lose in the dice game was easy.
It was the second part that was tough for them.
A mere loss in a game of dice however stupid it seems would never sway public opinion or opinions of other king's on Yudhishtir's right to rule.
Kings routinely lost their kingdoms, Most in wars but also a few in gambling Mahabharat itself has story of Nala Of Nishada who lost everything in dicegame and won it back again after learning how to play the game from King of Ayodhya. EVM Harivansh has story of dicegame between Balram and Rukmi where Balram loses but angered by Rukmi's mocking of his loss kills him with the diceboard.
So Yudhishtir knew that dicegame itself wouldnt be a problem as he would either win the game or his brothers would win it back with their valor if he loses.
It was the second part of the strategy that stumped Yudhishtir. Shakuni's master plan was Yudhi's own brothers questioning his judgement. Castigating his actions. If Yudhi's brothers declared he was wrong or his actions wrong, then definetly the whole world will. Yudhi would then never be able to rise up again as a claimant.
When Shakuni asked him to stake Nakul. He didnt ask Bhima whom Dury would have prefered torturing as a slave as he was Yudhi's own sibling. Being step brother if Nakul was staked, DDSK hoped they would protest. But he didn't and as Yudhi kept losing and staking all his brothers didn't protest. Because they understood the game plan too. They knew sooner or later they would figure out a loophole to wage a battle and take back everything or Krishna/Panchal would attack and free them.
That is when Shakuni asks Yudhi to stake the 6th Pandava. Draupadi.
Her castigating Yudhi in public would be even better as she represented PAnchal and once she left Yudhi he will be again without any allies just like they were after Lakshagriha. Krishna under attack by Salwa would not be able to help either.
Though she has a outburst with the guard who comes to summon her about Yudhi being a drunk fool. She smartly understands the goings on. (There is also a messenger sent by Yudhi asking her to come to sabha in a shabby state and plead their case)
She refuses to castigate Yudhi and instead chooses technical point of her stake being invalid to upset the whole strategy.
That actually showed the tremendous intelligence and capability that Draupadi had, not as a woman but as ruler. Capability to not just know the law/Dharma like Yudhi the misproclaimed Dharmaraj. Rather use it as a weapon against evil.
The verbal assault on her and Dussasan's attempt at disrobing her was DDSK trying escalate and to somehow Make either Draupadi or BANS desperate enough to go against Yudhishtir for causing the humiliation.
Almost always evil men who go against a strong woman, use public molestation as a tool to push them to desperation.
Duryodhan says that infact if any of the brothers admit that or if Yudhi himself says he was wrong to stake her they will let Draupadi go. Draupadi again smartly spins it on Shakuni that he cheated being an expert playing against an untrained Yudhi
The whole point of the dicegame was to destroy Yudhi's credibity. To get Yudhi's brothers or his wife or both to say Yudhi was wrong. His gambling and staking them was wrong and once they said that it would be a permanent victory for Duryodhan