Deal or No Deal

Introduction

The game Deal or No Deal is a casino adaptation inspired by the widely-loved television series. The online version was created by Dragonfish, a company specializing in casino software solutions. Based on videos found on YouTube, there appears to be a similar slot game available in the UK, but this discussion focuses solely on the Internet variant.

Rules

1. In this game, there are 26 boxes, each containing a prize, randomly assigned. The prizes are multiples of the player's initial wager, including amounts such as $0.02, $0.04, $0.06, and reaching as high as $10.00.
2. The player makes a wager.
3. Participants will select one of the 26 numbered boxes to designate as their own box.
4. The player then proceeds to open six additional boxes, leaving a remaining total of 20.
5. The 'banker' will present the player with a cash offer, providing an opportunity to either accept the deal and leave the game or refuse it and continue playing.
6. If the player chooses to turn down the banker's offer, they will open five more boxes, narrowing the total down to 15.
7. The banker will again extend an offer to the player, who must decide whether to accept it and walk away or keep playing.
8. If the player rejects the banker's proposal, they will open five more boxes, leaving only 10.
9. The banker will again extend an offer to the player, who must decide whether to accept it and walk away or keep playing.
10. Assuming the player still opts out of the banker’s offer, they will then open four additional boxes, which will leave them with just 6.
11. The banker will again extend an offer to the player, who must decide whether to accept it and walk away or keep playing.
12. Continuing in this manner, if the player declines the banker's latest offer, they will open four more boxes, bringing the total down to just 2.
13. At this stage, the banker will make another offer. The player has the option to accept and cash out or to reveal their chosen box and find out what prize awaits them inside.

It is important to point out that, unlike the televised version, players in this online setup cannot switch their box when only two remain.

Example

Initially, I choose an amount to wager. The potential payouts are displayed on the side, reflecting the scale in relation to my bet.

Next, I am prompted to select a box. I choose number 23 and set it aside for myself.

I then proceed to open six of the remaining boxes. After my selections, the amounts that are left are: $0.02, $0.06, $0.08, $0.12, $0.14, $0.16, $0.18, $0.20, $0.24, $0.26, $0.50, $0.60, $0.70, $0.80, $0.90, $1.00, $1.20, $1.50, $2.00, and $10.00.

Suddenly, the phone rings, and it's the banker proposing a cash offer of $1.03 for me to quit the game. This amount reflects the average value of what remains. I choose to decline the offer.

I am then instructed to open five of the other boxes. After making my selections, the amounts remaining now are: $0.02, $0.06, $0.08, $0.14, $0.18, $0.24, $0.26, $0.50, $0.60, $0.70, $0.80, $0.90, $1.00, $1.50, and $10.00.

Again, my phone rings; this time the banker offers $1.13 if I decide to quit. This also matches the average of the values still left. I once more say 'no deal.'

I am asked to open five more boxes. After this round, the amounts that remain are: $0.02, $0.08, $0.26, $0.60, $0.70, $0.80, $0.90, $1.00, $1.50, and $10.00.

The banker calls yet again, this time extending an offer of $1.58 to quit the game. This figure, rounded down, is also the average of what remains. I opt for 'no deal.'

Following that, I'm asked to open four more boxes. The amounts left now are: $0.02, $0.08, $0.60, $0.70, $0.80, and $10.00.

The banker rings again with a new offer of $2.03 for me to exit. This, too, is the average value of the remaining boxes when rounded down. I refuse the deal.

Once again, I'm prompted to open four more boxes, after which only 2¢ and 80¢ remain.

In the next call, the banker offers me 41¢ to quit. This figure represents the average of the remaining amounts. I choose 'no deal.'

My case is opened to reveal my prize — 2¢.

Analysis

Calculating the average prize across all 26 boxes amounts to 95.46% of the original bet.

The banker consistently provides fair offers, allowing you the freedom to make your own decisions. Despite potential rounding of offers to the nearest cent, there is no definitive right or wrong choice in this game.

The anticipated return here is simply calculated by dividing the average value of the cases by the wager, resulting in 95.46%. This indicates a house edge of 4.54%. Contrary to popular belief, provided that the banker gives equitable offers, there is no way to gain an advantage.

Video

I posted a video of my play on YouTube .

Written by: Michael Shackleford