House Edge

As I have shared previously, I volunteer at local high school that has frequent "millionaire" event to raise money. These event are fully licensed by the state and, any game that is played at a casino can be played at our charitable games. With that said, we can set our own odds or payouts as we so determine. On some games, payouts are shaved by about 33%. For example, on roulette a single number pays 25:1 versus 36:1. On craps, a "12" pays 20:1 versus 30:1, and so on. Players don't mind as they know they money is going to a good cause. Plus, some actually win.

Having a discussion with a pal regarding our games at the school and the "house edge".

My pal contends that shaving payouts increases the house edge. I contend that the probability of a number and/or a combination of numbers appearing is constant that does not change irrespective of the payout. For example, if the true house edge is say 7.52% (to make up a number) that percentage is unaffected by how much we decide to shave or not shave. Who's right?

Thanks

The house edge is dependent on the payout. There are 38 numbers on a roulette wheel with a double zero. If the payout was 37:1, it would have a 0% House edge. Payouts are the only way to create house edge.

For example the house edge on a coin flip that paid $2 on a $1 bet would have a HE of 0 (.5 x 1 - .5). If you change the payoute to $1.50 it would have a HE of 25% (.5 x .5 - .5), and so on.

There cannot be a house edge without a payout being involved. If you spin a wheel and simply pay back the bet the HE is 0 and would be the same as not taking a bet at all.

Quote: Riva

My pal contends that shaving payouts increases the house edge. I contend that the probability of a number and/or a combination of numbers appearing is constant that does not change irrespective of the payout. For example, if the true house edge is say 7.52% (to make up a number) that percentage is unaffected by how much we decide to shave or not shave. Who's right?

You're both right (sort of), but you're talking past each other. The house edge is derived from two sets of numbers: the probability of each outcome, and the payout for each outcome. On something like a roulette wheel, the probabilities are fixed. Same for a deck of cards, a pair of dice, or a bucket of keno balls. In slot machines, the probabilities are variable because game designers can alter the frequency of symbols on the reels. In a game like roulette, where the probabilities are fixed, the only way to adjust the house edge is to adjust the payouts. For slots, you often see games with the same paytable but different house edges because the symbol weightings are different.

So in your examples above, your friend is right (1st sentence) and you're right (2nd sentence). The 3rd sentence is inaccurate because you used the phrase "house edge" when you should have used "probability."

Wizard's explanation of house edge:

https://wizardofodds.com/gambling/house-edge/

Half way down the page. I don't know if it explicitly answers what you're asking though.

I agree with you that it doesn't change the probability of any numbers appearing.

But when you short the payouts(shave), that increases the house's revenue(keep). And I think that is house edge.

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Quote: Riva

My pal contends that shaving payouts increases the house edge. I contend that the probability of a number and/or a combination of numbers appearing is constant that does not change irrespective of the payout.

Your pal is right, shaving the payouts increases the house edge. Never forget: an edge is not a guarantee. Given the limited time the event runs, they increase the house edge to decrease the chance of ruin, and an event that loses money instead of making it.

There was a church up the street that ran a spring festival. One year, they made a big mistake with their blackjack games. The game was double deck dealt to the last card, and whoever (including the dealer) had the option of accepting it or redrawing after the shuffle. Late surrender, double after splits, dealer stands all 17s, respilt aces and hit soft stiffs and double down on split aces were the rules. The only odd rules were no insurance, and a blackjack was an ace and a paint. An ace and a ten-spot was the same as a drawn 21.

The dealers were church volunteers, inexperienced with blackjack, so I was able to talk them into early surrender. Counting with the Uston +/- I hit that game so hard I probably put it into the red for the weekend. Next year, the rules became so hideous it was unplayable.

The rest of the games were your typical larcenous high-vig abominations. Not enough time to allow casino-level vig to do its job.

Quote: Impmon

Your pal is right, shaving the payouts increases the house edge. Never forget: an edge is not a guarantee. Given the limited time the event runs, they increase the house edge to decrease the chance of ruin, and an event that loses money instead of making it.

There was a church up the street that ran a spring festival. One year, they made a big mistake with their blackjack games. The game was double deck dealt to the last card, and whoever (including the dealer) had the option of accepting it or redrawing after the shuffle. Late surrender, double after splits, dealer stands all 17s, respilt aces and hit soft stiffs and double down on split aces were the rules. The only odd rules were no insurance, and a blackjack was an ace and a paint. An ace and a ten-spot was the same as a drawn 21.

The dealers were church volunteers, inexperienced with blackjack, so I was able to talk them into early surrender. Counting with the Uston +/- I hit that game so hard I probably put it into the red for the weekend. Next year, the rules became so hideous it was unplayable.

The rest of the games were your typical larcenous high-vig abominations. Not enough time to allow casino-level vig to do its job.

On that day, you were God.