Last Updated: May 15, 2015

# Deal or No Deal

## Introduction

Deal or No Deal is a casino game closely based on the popular television show. The Internet casino version was developed by Dragonfish, a company that provides software to Internet casinos. Based on YouTube videos, there appears to be a similar slot game in the UK. This page shall deal with the Internet version only.

## Rules

1. The game will consist of 26 prizes randomly places in 26 boxes. The amounts are the product of the player's wager and these amounts: \$0.02, \$0.04, \$0.06, \$0.08, \$0.10, \$0.12, \$0.14, \$0.16, \$0.18, \$0.20, \$0.22, \$0.24, \$0.26, \$0.50, \$0.60, \$0.70, \$0.80, \$0.90, \$1.00, \$1.10, \$1.20, \$1.30, \$1.40, \$1.50, \$2.00, and \$10.00.
2. The player makes a wager.
3. The player will pick one of 26 numbered boxes to be set aside as his box.
4. The player will open six other boxes, leaving 20.
5. The "banker" will offer the player a surrender value. The player may take the deal and quit or choose "no deal" and keep playing.
6. Assuming the player declined the banker offer he will open five more boxes, leaving 15.
7. The banker will offer the player another surrender value. The player may accept it and quit or play on.
8. Assuming the player declined the banker offer he will open five more boxes, leaving 10.
9. The banker will offer the player another surrender value. The player may accept it and quit or play on.
10. Assuming the player declined the banker offer he will open four more boxes, leaving 6.
11. The banker will offer the player another surrender value. The player may accept it and quit or play on.
12. Assuming the player declined the banker offer he will open four more boxes, leaving 2.
13. The banker will offer the player another surrender value. The player may accept it and quit or open his box and win what is inside.

Note that unlike the television show, the player may not switch his box/case when it is down to two.

## Example

First I select a bet amount. The possible wins are shown on the side, which are proportional to my wager.

I'm asked to choose a case. I select number 23, which is set aside.

I'm then asked to open six of the other boxes. After choosing six the amounts 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.

The phone rings and it is the Banker offering me \$1.03 to quit. This is also the average of the remaining cases. I choose "no deal."

I'm then asked to open five of the other boxes. After choosing five the amounts left 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.

The phone rings and it is the Banker offering me \$1.13 to quit. This is also the average of the remaining cases. I choose "no deal."

I'm then asked to open five of the other boxes. After choosing five the amounts left are: \$0.02, \$0.08, \$0.26, \$0.60, \$0.70, \$0.80, \$0.90, \$1.00, \$1.50, and \$10.00.

The phone rings and it is the Banker offering me \$1.58 to quit. This is also the average of the remaining cases if I round down to the penny. I choose "no deal."

I'm then asked to open four of the other boxes. After choosing four the amounts left are: \$0.02, \$0.08, \$0.60, \$0.70, \$0.80, and \$10.00.

The phone rings and it is the Banker offering me \$2.03 to quit. This is also the average of the remaining cases if I round down to the penny. I choose "no deal."

I'm then asked to open four of the other boxes. After choosing four the amounts left are: 2¢ and 80¢.

The phone rings and it is the Banker offering me 41¢ to quit. This is also the average of the remaining cases. I choose "no deal."

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

## Analysis

The average of the 26 cases is 95.46% of the bet amount.

The banker is kind enough to always offer fair value in his offers. Thus, you may do whatever you wish. Not considering the issue of the banker offers being rounded down to the penny, there is never a right or wrong decision.

The expected return is simply the average of the cases divided by the bet amount, which is 95.46%. In other words, a house edge of 4.54%. Contrary to what some may believe, as long as the banker makes fair offers, which he does here, there is no gaining any advantage on the banker.

## Video

I posted a video of my play on .