100xOdds
• Posts: 4394
Joined: Feb 5, 2012
September 19th, 2023 at 9:51:28 AM permalink
From this post in the "Am i good at picking winners or just lucky" thread:
https://wizardofvegas.com/forum/gambling/other-games/38566-how-do-i-know-if-i-am-good-or-lucky/#post900955

Is there an easy way of calculating variance of slots?
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Mental
• Posts: 1458
Joined: Dec 10, 2018
September 19th, 2023 at 10:14:11 AM permalink
Quote: 100xOdds

From this post in the "Am i good at picking winners or just lucky" thread:
https://wizardofvegas.com/forum/gambling/other-games/38566-how-do-i-know-if-i-am-good-or-lucky/#post900955

Is there an easy way of calculating variance of slots?

If you have a par sheet, you can calculate the variance from the probabilities and payoffs. Calculating it for must-hits is harder because you have to calculate the distribution of jackpot hits.

Do you have data for your slot machine payoffs? If you have the RTP of the slot, then you just calculate the expectation value of square of the difference between the (1-RTP) and the win/loss for each game (in bet units). If you don't have the theoretical RTP, then you can use the observed RTP.

I have my complete play record downloaded for three of my favorite online casinos. It is about 10 megabytes of data per casino per year. I have a program that culls out the tax reportable wins from the text data. I was planning on writing extra code to pull out the observed RTPs and variance for every game in the database. I will be travelling for most of the next five weeks, so don't hold your breath. I will post something if this project ever gets done.
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Mental
• Posts: 1458
Joined: Dec 10, 2018
September 19th, 2023 at 1:43:05 PM permalink
Here is another idea. If you are just looking for a rough estimate of the variance for your favorite game, you can use the additive property of variance to make data collection simpler.

If a slot has a variance of V (in units of bets^2), then the win/loss for N games will have a variance of NV bets^2. If you are using online auto-play, it is easy to count 100 spins. In a B&M casino, you can use points or meter movement. Let us say you want to get the variance of River Dragons. Just stop every \$5 of meter movement or whatever and record the current bankroll. Now, you can estimate the variance of the bankroll swings in terms of bet units. Just divide this by N and you have an estimate of the variance of a single spin.

For progressives, this will give you the variance for the base game spins only.
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Mental
• Posts: 1458
Joined: Dec 10, 2018
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September 19th, 2023 at 7:20:43 PM permalink
I went through all the slot games that I played at one site and picked out the 13 games I played the most. This table shows the number of times I played each game, the observed RTP, and the calculated variance. I am deliberately not naming most of the games.
`Number   RTP      Variance  1276  94.61%     30.1  1555  67.61%     25.0  1696  93.26%     11.2  2386  97.42%     43.7  5429  95.21%     49.5  5954  99.83%     22.4  6416  92.78%     52.3  6804  99.89%     14.8  7297  90.15%     27.8  9619  99.49%     43.3 19584  89.30%     28.1 30076 102.84%     68.7 40596  94.59%     17.2`

For the most part, these variances are similar to the range of video poker variances for single-line VP games without multipliers.

Two lowest variances are carnival games. They play very fast and have no reels at all. One involves simply popping a balloon and getting a prize, but it does sometimes give a short bonus round. Since they can be played at two games per second outside of bonus rounds, they can give big bankroll swings in a short period of time despite the low variance. The other low variance game is Blood Suckers, which is a game where the bonus round is just picking coffins for prizes. It is very difficult to hit a big payoff in that game.

The game with the variance of 68.7 has a user selectable variance. I always play this game in max variance mode, and it is my go-to game for loss rebate promotions.

Most of these games have a nominal RTP around 96-98%. You can see that I have not played any of these games enough times to expect to have the RTP measured to within one percent.
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