This is an attempt at a different Eastern Front during WWI. It’s really only a rough idea so comments and criticism are not only welcome but expected.
When Hermann von François' first corps won the Battle of Stallupönen, he was able to convince General Maximilian von Prittwitz to launch an offensive at the Russians against the orders of Moltke. Unfortunately François attacked early because the Russians were out of ammunition, and while the attack started well, the artillery of the Russians led to its halt. The Russians had prior warning of the attacks by August von Mackensen's XVII Corps and Otto von Below's first reserve corps. They were forced to attack early and unprepared and the Russians had already moved their heavy artillery up, in other words a disaster. Prittwitz lost his nerve, ordered a retreat and Moltke fired him. Moltke hired Hindenburg and Ludendroff and sent troops from the Western Front to the Eastern Front. The rest as they say is history.
That was all OTL. In TTL, Prittwitz impresses on François the reasons for waiting and François doesn't ruin it. However, Colonel Max Hoffman, Prittwitz's deputy chief of operations who new of bad blood between the two Russian Gernerals (General Pavel von Rennenkampf and General Alexander Samsonov), came up with a rather brilliant plan which caught Prittwitz's eye. Using a faint retreat and a fully prepared German army, what basically amounts to a Tannenberg captures most of Samsonov's army. All a sudden the Russians look like a very easy target. In this Tannenberg, François, Prittwitz AND Hoffman take credit for the attack by the press, and the Western front isn't weakened. The Eighth German Army single-handedly destroyed the 2nd Russian Army and then ejected what was left of the first Army back across the border, where they went into defensive forts, waiting for the Russian tenth Army to form.
There were some who wanted to continue the fight into Russia but after the Western Front, Prittwitz thought better of it. Moltke agreed with Prittwitz stating that the Western Front needs to be allowed to continue and the Schieffen plan continue. When the Western Front turns into a bloody stalemate, the German position is stronger. Moltke decides that the Eastern Front looks more promising, a strong defence is called for, which is used to great effect by the Germans on the Entendre that throws away millions of lives on the same offences again and again. The more independent Germans soon learn important lessons in defence. Meanwhile new troops are sent east. The newly formed ninth army is erected just as the Russians pluck up the courage to launch a new offensive against the Germans. The Tzar is desperate for "just one victory". The 10th Army make very little progress and the numbers are not so heavily in Russia's favour. Now the superiority of the German Army comes into play. The Germans force the 10th back capturing more prisoners of war. Prittwitz and his staff then launch a counter attack on the weakened Russians to the North.
The reason for the move is simple but affective. Due to the early Tannenberg analogue, the Germans were in a very strong position at the very end of August/early September. The German High Command then realised Austria would be the weak link in the chain. Despite some useful victories, the Russians appeared to be about to overwhelm the Austrians. A diversion was needed, and the Eighth Army appeared to be in a position to deliver one. The Eighth Army became an irrational fear for the Russians and they began to overrate their power, this was not lost on the Germans. So the Eighth Army launched an offensive north which was hoped would spook the Russians into moving men away from Austria. What was happening in Austria that called for an offensive by the Eighth Army?
The Third and Eighth Russian Armies had routed the Austrians near Lemberg and the City was under threat. The first and fourth Austrian Armies had bee successful to the North, but those Russians were still a threat. Meanwhile the second and more urgently the third Austrian armies were facing dire problems from the aforementioned Russian armies. The solution was to move the forth Army to aid the third which created a gap which was utilised by the third Russian Army. The loss for the Austrians represented the first victory of the Russian campaign, but worse was to come. The Forth Army's movements south lead the fifth Russian army (stopped previously by the forth) to make use of the gap and the Russians drove the Austrians back. Disaster as the Russians took Lemberg and the Austrian Armies were about to collapse. [I hope that makes sense, basically it’s OTL]
If Austria lost Germany could have all the victories in the world and it wouldn't make a fat load of difference. The Eighth moved North as the Ninth stayed in defence. The progress was slow but the Russians were routed. The Germans got the panic they needed in the Russian High Command, as troops from the Austrian theatres moved North. The Offensive went better than planned and resulted in more troops been sent East. The decision to go North has surprised many Historians who believe an assault into Poland was more likely. However other historians like the American Robert Moore, have pointed out North led to St Petersburg, which Prittwitz confessed in his Published Dairies, was a key goal in his battle plan. Also moving Russian troops as far away from Austria as possible and the city of Riga were other factors that led to the decision. One drawback was the Russians could move troops other than the Austrian front troops, but that led to a greater weakening of the Russian position. Overall the offensive is viewed as a tactical victory for the Germans.
The Austrians meanwhile try to regroup and defend along the Carpathian Mountains with large areas of Austria under Russian control. Only Przemyśl remained in Austrian hands and it was under siege. Clearly the first goal of the Austrians was to lift the siege but that was easier said than done. The German offensive did move troops but not enough to give the Austrians an advantage. The arrival of the Second Army from Serbia was the only real bonus going into the Autumn period in 1914 along the Eastern front. A relief force was sent to relieve the siege during the German Eighth Armies' attack north under the command of General Svetozar Boroevic von Bojna. Conrad believed Boroevic's army and the Przemyśl garrison could give the Russians "A bloody Nose" and on the 10th of October, the offence went underway, what happened shocked everyone. The Austrians held their own and Conrad ordered more troops to take positions to support them. The Russians were suffering from supply problems and many troops had been sent north after the Tannenberg analogue. The Russians were numerically superior but the Austrians were technically superior. It was a small victory militarily speaking. But it is believed to be a very important part of the war. The Austro-Hungarians had some hope left, moral wasn't as low as it would have been. Przemyśl was safe and Lemberg was considered next.
But the Victory at Przemyśl left a large bulge in the front and the Russians began crushing attacks against the Austrian positions. At this point the first Germans sent by Molkte arrive in Austria and begin moving to the front. The Russians are perplexed that Germany had not launched an offensive on Poland. When a dead German man is found on the Baltic front carrying information about an assault on Walsaw mid October, the Russians are not surprised and covertly move troops to Poland. However this was a plant. The German's had the fake letter on many officers’ persons in oder to fool the enemy. It is Hoffman who is credited with this idea though we will never know for sure. While the Russians are defending Walsaw, the Germans launch an attack on Riga and the Austrians are back with Lemberg in their sights (this time with German troops to back them up). These two fights are drawn to a close due to bad winter weather while the Russians try a counter attack from Poland which is rebuffed. Neither city will be taken in 1914 but the Central Powers are in good positions for spring. One final point, winter clothes were provided to all troops, an initiative from someone... we don't know who, and many German soldiers would survive that awful winter.