# Hi-Lo Card Game Probability

I have looked online and found several similar questions and answers to those however I am not able to understand the formulas given in those answers. So I was hoping you guys might be able to help me.

With a deck of shuffled playing cards the player takes the top card and then guesses the next card is higher or lower than the current card. If correct the newest card becomes the new benchmark and continue through the deck guessing higher or lower. Once a card is revealed it is never returned to the deck. In the event of a tie the new card is set off to the said and the player gets to try again as though that draw had not happened.

I am trying to figure out the probability of guessing correctly on the 1st through 7th try.

An example I found that is very similar to mine would be:

higher-or-lower-an-easy-card-game-part-i

followed by

higher-or-lower-an-easy-card-game-part-ii

The part I get lost on because it has been years since I needed to do high level math is where they start using the sigma. Which if I remember right has something to do with limits and upper and lower bounds but I am not sure how to calculate those anymore. I addition while I think the second link gets really close to what I want we have a different approach to the tie and I have no clue where to begin trying to adjust for that.

• Maybe post links to the formulas that you found (or better, describe them here). Maybe also explain what part(s) you don't get.
– John
Commented Mar 14, 2018 at 22:28
• Added as requested. Hope that helps you better understand my problem if I can add more to make this easier let me know and I will do what I can. Commented Mar 14, 2018 at 22:44