Hello all,

I’m getting a hard time trying to calculate the Return to Player (RTP) for a 3 reel slot with the hold and nudge options available. I was wondering if anyone with good statistical knowledge could help me.

As I said the slot has 3 reels with 9 symbols per reel.

The odds for each symbol is the same for all 3 reels:

symbol 0 = 26.53%
symbol 1 = 19.73%
symbol 2 = 17.01%
symbol 3= 14.29%
symbol 4 = 9.52%
symbol 5 = 6.12%
symbol 6 = 4.08%

The payouts are:

Symbol 0 = x2 bet amount
Symbol 1 = x5 bet amount
Symbol 2 = x10 bet amount
Symbol 3 = x20 bet amount
Symbol 4 = x40 bet amount
Symbol 5 =x70 bet amount
Symbol 6 = x100 bet amount
Symbol 7 = x200 bet amount
Symbol 8= x500 bet amount

So for example if I wanted to calculate the probability of all 3 reels to have symbol 0, that would be : 0.2653*0.2653*0.2653 = 0.0187
And then if I wanted to calculate the payout per each spin for symbol 0, I would multiply the probability to the winning multiplier (lets say I bet 1 cent) = 0.0187 x (2 x 1cent)=  0.04 cents.

Now what I can’t do is calculate the total RTP when the player has the option to use Hold(hold reels) or Nudge(move reels one spot down).

The probability of having no option is 67.26%
The probability of having the hold option is 20.63%
The probability of having the nudge option is 12.11%

When Hold is activated, the player can either hold 1 2 or 3 reels but when he spins again, he bets another stake.
When Nudge is activated, the player has to move all 3 reels without betting again. The thing is, if he moves 1 reel and forms 3 symbols in one straight line, then he wins the respective amount and doesn’t have to move the rest of the reels. Same thing happens if he moves 2 reels and wins.

Now, I have to calculate the whole RTP. Could anyone help me with that?

Thanks in advance!