EOS token can be bought in two ways:

1. On the exchange.
2. On the daily ICO.
   

   Thesis

If EOS price in given day of ICO is lower than price on exchange, we can buy it at the end of daily ICO and immediately sell with profit on exchange.

EOS ICO terms

Everyday 2 000 000 tokens are distributed.
You gain tokens by sending Ether to the EOS ICO smart contract adress.
Amount of EOS tokens is at the end of day calculated with formula:

Your amount of EOS tokens=(Your amount of contributed ETH)/
(Total ETH contributed) * 2 000 000

Analysis

I've collected data from last week EOS ICOs and prepared charts.
Let's analyse, if there was possibility to profit on the price difference.

1. EOS ICO
12 October 2017, 02:00 - 13 October 2017, 01:00

13 October 01:00. Amount contributed: 3816.521 Eth.

EOS for 1 ETH on exchange (13 October 01:00):
(ETH price)/(EOS price)=303.04/0.573916=528,021
EOS for 1 ETH in ICO:
1/3816.521*2 000 000= 524,037

Profit: (528,021-524,037)/524,037 = 0,7%.

Buying for 1ETH, EOS tokens in ICO you could earn 0,7% contributed Ether.

Fig. 1: Correlation beetwen amount of Ether contributed and time. X axis- time, Y axis- Total ether contributed. Link to chart: https://plot.ly/~biustek/2/

2. EOS ICO
13 October 2017, 01:00 - 14 October 2017, 00:00

14 October 00:00. Amount Contributed: 3520.762 Eth.
EOS for 1 ETH on exchange (14 October 00:00):
(ETH price)/(EOS price)=338.59/0.58397=579,807
EOS for 1 ETH in ICO:
1/3520.762*2 000 000= 568,058

Profit: (579,807-568,058)/568,058 = 2,06%.

Buying for 1ETH, EOS tokens in ICO you could earn 2,06% contributed Ether.

Fig. 2: Correlation beetwen amount of Ether contributed and time. X axis- time, Y axis- Total ether contributed. (There is shift on chart, caused probably by node desynchronization with blockchain) Link to chart: https://plot.ly/~biustek/5/

3. EOS ICO
14 October 2017, 00:00 - 14 October 2017, 23:00

14 October 23:00. Amount Contributed: 3319.851 Eth.
EOS for 1 ETH on exchange (14 October 23:00):
(ETH price)/(EOS price)=335.41/0.589540=568,935
EOS for 1 ETH in ICO:
1/3319.851*2 000 000= 602,437

Profit: (602,437-568,935)/602,437 = 5,56%.

Buying for 1ETH, EOS tokens in ICO you could earn 5,56% contributed Ether.

Fig. 3: Correlation beetwen amount of Ether contributed and time. X axis- time, Y axis- Total ether contributed. Link to chart: https://plot.ly/~biustek/4/

4. EOS ICO
14 October 2017, 23:00 - 15 October 2017, 22:00

14 October 23:00. Amount contributed: 3358.633 Eth.
EOS for 1 ETH on exchange (15 October 22:00):
(ETH price)/(EOS price)=334.41/0.569934=586,752
EOS for 1 ETH in ICO:
1/(3358.633 )*2 000 000= 595,48

Profit: (595,48-586,752)/595,48 = 1,46%.

Buying for 1ETH, EOS tokens in ICO you could earn 1,46% contributed Ether.

Fig. 4: Correlation beetwen amount of Ether contributed and time. X axis- time, Y axis- Total ether contributed. (There is shift on chart, caused probably by node desynchronization with blockchain) Link to chart: https://plot.ly/~biustek/8/

5. EOS ICO
15 October 2017, 22:00 - 16 October 2017, 21:00

14 October 23:00. Amount contributed: 3355.084 Eth.

EOS for 1 ETH on exchange (16 October 21:00):
(ETH price)/(EOS price)=333.08/0.567834=586,579
EOS for 1 ETH in ICO:
1/(3355.084 )*2 000 000= 596,11

Profit: (596,11-586,579)/596,11 = 1,59%.

Buying for 1ETH, EOS tokens in ICO you could earn 1,59% contributed Ether.

Fig. 4: Correlation beetwen amount of Ether contributed and time. X axis- time, Y axis- Total ether contributed. Link to chart: https://plot.ly/~biustek/0/

Conclusions

If only exchange fees are lower than profit estimated, there was possibility to profit in all discussed periods.

12 October 2017, 02:00 - 13 October 2017, 01:00 -> 0,7%
13 October 2017, 01:00 - 14 October 2017, 00:00 -> 2,06%
14 October 2017, 00:00 - 14 October 2017, 23:00 -> 5,06%
14 October 2017, 23:00 - 15 October 2017, 22:00 -> 1,46%
15 October 2017, 22:00 - 16 October 2017, 21:00 -> 1,59%

Especially high was profit in third discussed period, when it reached 5,06%

Just by buying EOS for Ether in ICO and then selling EOS for Ether on exchange there is possibility to earn Ether.