Ask the Slot Expert: Choosing same item each time in a pick'em bonus

I saw the movie Inspector Sun and the Curse of the Black Widow today. Aboard a flying boat from Shaghai to San Francisco, Inspector Sun is called upon to investigate the death of Dr. Spindlethorp. While he's examining the body, another character pointed out that the Inspector and the doctor are both missing the same leg and asked what the odds of that are? One out of eight, replied the Inspector.

Did I mention that Dr. Spindlethorp was a funnel-web spider and Inspector Sun is a huntsman spider and this is an animated movie?

This scene reminded me of the situation I had planned to discuss today -- the odds for a pick'em bonus round.

I've been spending too much time the past few days playing Clue - Mansion:West Wing on the Quick Hit Slots play-for-fun casino site. In one frequently occurring bonus event, you get to add a certain number of wild symbols to the screen before a spin. The number of wilds you get is determined by a pick'em. You choose one of six icons at the bottom of the bonus screen. The icons reveal either two, three, or four wild cards or a clock symbol, which spins the clock at the top of the screen to award between five and fifteen wilds. There is only one clock symbol in the mix.

The question for this bonus and any other pick'em is whether it's better to pick the icon randomly each play and hope you and the RNG are in sync or to pick the icon in the same position each time and make the RNG hunt for you. It seems that by making the same pick each time, you're eliminating one of the random variables in the bonus event and it should be more likely to pick the best reward.

Does picking the same icon each time you play the Clue bonus round make you more likely to choose the clock symbol?

Let's see.

If we choose an icon at random, what are the chances that it has the clock symbol? The RNG has randomly placed the clock symbol under one of the icons. So each icon has a 1-in-6 chance of having the clock. We have a 1-in-6 chance of choosing the icon with the clock.

If we choose the same icon each time, what are the chances that the RNG has placed the clock under it? Again, the RNG chose one of the six icons at random, so the chances of any icon having the clock is 1-in-6, so the chances that our regularly chosen icon has the clock is 1-in-6.

It doesn't matter whether we go hunting for the clock or let the RNG hunt for our regular pick, the chances of getting the clock is always 1-in-6. It doesn't matter whether we ask What are the chances that I chose the same icon that the RNG chose? or ask What are the chances that the RNG chose the same icon that I chose?

The character in the movie implied that both spiders missing the same leg must be a rare event. After all, biting off this leg on a spider is the calling card of the movie's primary villain, the Red Locust, who would be the main suspect in the doctor's murder except for the fact that the Red Locust is in jail, having been arrested by the Inspector in the opening scene.

The chances for two spiders missing the same leg are similar to the chances for the RNG and the player picking the same icon in the Clue bonus. Given that the doctor is missing a particular leg, there is a 1-in-8 chance that the Inspector is missing the same leg. Turning it around, given that the Inspector is missing a particular leg, there is a 1-in-8 chance that the doctor is missing the same leg.

Reading between the lines of the dialog, the character thought that because both spiders have eight legs, there must have a 64 in there somewhere. We can get a 64 if we ask what are the chances that both spiders are missing their back left (or any specific) legs? That's 1-in-64. That's also a very different question from What are the chances that both spiders are missing the same leg?

I usually pick the same item -- the one farthest right -- when I play a pick'em bonus, but it doesn't matter whether I pick the same item each time, systematically walk through the different choices, or pick an item at random. My chances for picking the item with the best reward is the same no matter what method I use.

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