# Thread: difficulty with calculation of probability of retrigger in slot game

1. ## difficulty with calculation of probability of retrigger in slot game

I would like help figuring out how to calculate the probabilities for the free spins on this slot game.

Basically the question is “how do I calculate how often a free spin takes place given that they can ‘retrigger’ during the free spins?”

75% pay per spin during regular spin
200% pay per spin during free spins

It costs one point per each spin except for the free spins which are naturally free (the one point to play is given free).

Probability of a win during regular spins is 0.25 and pays 3 therefore the payout per regular spin is 75%.
Probability of a win during free spins is 0.25 and pays 8 therefore the payout per free spin is 200%.

0.005 Probability of winning 10 free spins (So every 200 spins or so you get 10 free games).
0.001 Probability of winning 15 free spins.
0.0004 Probability of winning 20 free spins.

Free spins can be retriggered during free spins.

If I do not figure for the retriggers I get .073 free spins per regular spin for a payout total payout of 89.6%.

My sloppy calculation of the retriggers yields .078749 free spins per regular spin for a payout of 90.7497%. I don't think that is correct.

Thanks for any solutions on how to calculate this.

2. Originally Posted by danno
I would like help figuring out how to calculate the probabilities for the free spins on this slot game.

Basically the question is “how do I calculate how often a free spin takes place given that they can ‘retrigger’ during the free spins?”

75% pay per spin during regular spin
200% pay per spin during free spins

It costs one point per each spin except for the free spins which are naturally free (the one point to play is given free).

Probability of a win during regular spins is 0.25 and pays 3 therefore the payout per regular spin is 75%.
Probability of a win during free spins is 0.25 and pays 8 therefore the payout per free spin is 200%.

0.005 Probability of winning 10 free spins (So every 200 spins or so you get 10 free games).
0.001 Probability of winning 15 free spins.
0.0004 Probability of winning 20 free spins.

Free spins can be retriggered during free spins.

If I do not figure for the retriggers I get .073 free spins per regular spin for a payout total payout of 89.6%.

My sloppy calculation of the retriggers yields .078749 free spins per regular spin for a payout of 90.7497%. I don't think that is correct.

Thanks for any solutions on how to calculate this.
Consider a single regular spin.

With probability $\displaystyle 0.25$ it pays $\displaystyle 3$, and with probability $\displaystyle 0.005$ it pays out the pay from $\displaystyle 10$ free spins, with probability $\displaystyle 0.001$ it pays out the pay from $\displaystyle 15$ free spins and with probability $\displaystyle 0.0004$ it pays out the pay from $\displaystyle 20$ free spins.

So the expected pay is:

$\displaystyle p=0.25 \times 3 + 0.005 \times 10 \times x + 0.001 \times 15 \times x + 0.0004 \times 20 \times x$

where $\displaystyle x$ is the expected pay as a result of single free spin (including all the extra free spins that may be won).

Now $\displaystyle x=0.25 \times 8 + 0.005 \times 10 \times x + 0.001 \times 15 \times x + 0.0004 \times 20 \times x$, or:

$\displaystyle x=025 \times 8 + 0.073x$, so $\displaystyle x=2.1575$

CB

3. ## sweet!

That is exactly what I needed, it did end up matching to my calculations but yours is precise rather than an approximation.

Thanks Again!