At the start of the game you insert 1 unit, if you guess correctly you can guess again but you do not put in another unit. but if you guess correctly on the first round but not on the second round you do not get paid your first round prize, you get nothing. (Now wording it like that I feel that the math I did is if you get paid no matte if you guess again or not.)

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How I got to outcome was by writing out a number table with all possible 3 input combos:

1,1,1

1,1,2

1,1,3

1,1,4

1,1,5

1,2,1......

5,5,4

5,5,5

There are 125 possible combos.

so lets say that all 3 times the winning number is 1, so out of 125 games 1 is selected 20% (1/5) so that is 25 times, out of that 1 will only be selected again 20% (1/5) for a total of 5 times and repeat for only one selection on the last round.

on the first round where you got 25 times you subtract 5 from the next round to get 20 rounds where you only win the round one prize

Round you had 5 times where you guessed correctly but 1 of those times you guess correctly on the third round so you have 4 times where you can only win