My Math Forum Payout percentage of a slot with free spins and changing multiplier

September 29th, 2014, 04:27 AM   #1
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Payout percentage of a slot with free spins and changing multiplier

Hello community of mymathforum,
I have run into a problem that I can't solve, hopefully somebody here knows the answer or he/she can point me to the right direction.
I'm writing a tool to test a slot game. I don't know the reels (symbols composing the reels) of the game, but through my tool, I can collect all (hopefully (Tongueout)) of the information I need.
The thing that I'm missing is the formula to calculate the payout percentage.
The game has reelset for the "main" game and another one for the "free spins".
I calculate the PoP of the main game which is 60.746115 %.
Every time a free spin is triggered is gives the player 15 free spins.
The free spins have an initial multiplier by 2 (first time they get triggered in the main reelset). So every win combination in here gets multiplied by 2.
Every time a free spin is retriggered in the initial free spins round (free spins reelset) the multiplier gets up by one. So if the initial trigger of free spins is 2 if it retriggers it becomes 3, and if it retriggers again it becomes 4, and so on.
The probability of a free spin to be triggered from a normal reelset is 0.05859375
The probability of a free spin to be retriggered from a free spin reelset is 0.2447047766
The virtual PoP of free spins (virtual because you don't spend any actual credits in them) is 162.1783335454 if you don't count the 2 multiplier or 324.3566670908 with the multiplier (2).

Up to now I can get the PoP of a game where the multiplier is stable throughout the retriggers. But in this game thing are different.

By the way here is the output the tester gives me

Quote:
 +======================== SUMMARY ======================== +====================== NORMAL GAME ====================== +-NORMAL GAMES - CREDITS PLAYED: 318504960 +-NORMAL GAMES - CREDITS WON: 193479390 +-NORMAL GAMES - PAYOUT PERCENTAGE: 60.746115 +-NORMAL GAMES - COMBINATIONS PLAYED: 35389440 +-NORMAL GAMES - WINNER GAMES: 11836800 +-NORMAL GAMES - LOSER GAMES: 23552640 +======================= FREE GAME ======================= +-FREE GAMES - CREDITS PLAYED: 257662359 +-FREE GAMES - CREDITS WON (WITH MULTI): 835745040 +-FREE GAMES - CREDITS WON (NO MULTI): 417872520 +-FREE GAMES - PAYOUT PERCENTAGE NO MULTI (RAW): 1.62178333545413 +-FREE GAMES - PAYOUT PERCENTAGE NO MULTI: 162.1783335454 +-FREE GAMES - INITIAL MULTIPLIER: 2 +-FREE GAMES - PAYOUT PERCENTAGE WITH MULTI (RAW): 3.24356667090826 +-FREE GAMES - PAYOUT PERCENTAGE WITH MULTI: 324.3566670908 +-FREE GAMES - COMBINATIONS PLAYED: 28629151 +-FREE GAMES - COMBINATIONS WINNER: 20480832 +-FREE GAMES - COMBINATIONS LOSER: 8148319 +-FREE GAMES - FREE SPINS TRIGGERED COUNTER (FROM NORMAL GAMES): 2073600 +-FREE GAMES - FREE SPINS RETRIGGERED COUNTER (FROM FREE GAMES): 7005690 +-FREE GAMES - TOTAL FREE SPINS: 9079290 +-FREE GAMES - RETRIGGER PROB (RAW): 0.244704776610386 +-FREE GAMES - RETRIGGER PROB: 24.47047766104 +-FREE GAMES - FREE GAME PROB (RAW): 0.05859375 +-FREE GAMES - FREE GAME PROB : 5.859375 +-FREE GAMES - Prt (RETRIGGER PROB): 24.47047766104% (RAW: 0.244704776610386)
Any help will be greatly appreciated. Sorry for the long post.

Last edited by uruz7; September 29th, 2014 at 04:32 AM.

 September 29th, 2014, 08:25 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms I don't know enough about slots to help you.

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