Okay here an attempt, bit trickier with the place pools, so feel free to correct me if I am wrong.

Lets say the original pool is $10000. This is split 3 ways for a 3 dividend race.
So $3333 paid out on each placing horse. Lets say the divi shows a nice $1.50 in the original size pool which mean there was $2222 bet on that horse.

Now lets add your 100 to the pool. So the pool increases in size to $10100 and the pools payout $3366 for each placed horse. So the amount on that horse in the pool is 2222 +100 so 2322 in total. This means that your extra $100 has reduced the dividend to $1.44.

Does this sound right to anyone else?