[2Tone]

After your cohort hits, 410 cards remain. If he or she gets a two or three, one less is left for you; your chance of pulling either of these is then 63/410 or 15.36 percent. Conversely, if he or she draws a different rank, your prospect of receiving a two or three is 64/410 or 15.61 percent. Overall, the chance you'll get a two or three is (0.1557 x 0.1536) + (0.8443 x 0.1561). This equals 15.57 percent, as it was when the other player stood.

This example shows that your companion's decision changes the structure but not the value of the expectation for your hand. Similar analyses yield identical conclusions for any conditions. So, unless you think occult forces order the cards in a shuffled shoe, previous players' actions don't affect your chances.