Deal Or No Deal USA:

Playing the odds, how to play smart

Looking at the odds to deal at the right time and beat the banker!

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This website is the creation of Richard Steel, a Deal or no Deal fan analysing the popular USA TV gameshow Deal Or No Deal.

Deal Or No Deal in the USA, is hosted by Howie Mandel and aired on NBC. Many people ask when is it the right time to deal? Knowing the odds can help you deal smart. Let's look at some scenarios:

1c
$1 $1,000
$10 $5,000
$100 $500,000
$500 $750,000
$750 $1,000,000

The odds of not taking out any of these: $500,000, $750,000, and $1,000,000 in the next 3 suitcases = 33.9%
The odds of taking out all of these: $500,000, $750,000, and $1,000,000 in the next 3 suitcases = 0.6%
The odds of taking out both the $500,000, and the $1,000,000 in the next 3 suitcases are 5%
The odds of taking out either the $750,000, and/or the $1,000,000 in the next 3 suitcases are 50.9%
The odds of taking out the $1,000,000 in the next 3 suitcases are 27.3%
The odds of not taking out the $1,000,000 in the next 6 suitcases are 45%

In this initial scenario, the contestant has taken out 15 suitcases, including the $400,000, the $300,000, and the $200,000 but it is still an excellent board. The banker now makes his highest offer so far of a respectable $330,000. The contestant declines the deal, a sensible choice based upon the odds, and elects to play on taking out the $750,000, an obvious disappointment, and then the 1c goes to great cheers, and the final of these 3 suitcases selected is the $5,000, by no means a disaster in gameplay terms at this stage, and these are the 8 suitcases left:

$1 $750
$10 $1,000
$100 $500,000
$500 $1,000,000

The odds of taking out the $1,000,000 in the next 3 suitcases = 3/8 or 37.5%
The odds of taking out both the $1,000,000 and the $500,000 in the next 3 suitcases = 3/28 or 9.3%
The odds of not taking out the $1,000,000 and the $500,000 in the next 3 suitcases = 5/14 or 36%
The odds of taking out the $1,000,000, the $500,000 and the $1,000 in the next 3 suitcases are 1/56 or 1.8%

Let's assume that the banker now offers $355,000 for the contestant to deal. Is it worth not dealing, and consequently going on? In my view no, based upon the odds of 64% that one of the two big numbers will be selected in the next 3 suitcases. Should that happen, then the banker's offer is not likely to increase, and if anything it would be lower. For some the risk might be worth taking for the opportunity of going home with a life changing amount of money, but if you play the game sensibly with a combination of calculated risk and caution, you have a greater chance of beating the banker! Let's assume then, that the contestant plays on, no dealing amidst almost unbearable tension, and takes out the $100, no deals to receive a higher offer of $290,000, then the $750, no deals, and the offer increases to $390,000, and then they take out the $500,000 safety net, leaving the $1,000,000 very exposed but still in place. Here's what's left:

$1
$10 $1,000
$500 $1,000,000

The odds of taking out the $1,000,000 in the next 3 suitcases = 3/5 or 60%

The banker is not sure about the contestant who has given the impression of being a bit of a gambler! His offer is slighty low though, $190,000 to deal. On the face of it, with 5 suitcases left, you would think that a fairer offer to make might be at least $250,000 yet the banker has probably calculated that in the next 3 suitcases the contestant has an odds-on chance of taking out the $1,000,000, 60% to be precise, and there is no significant safety net. The smart move is to deal one more time, unless the loss of $190,000 would be too great to bear! The contestant chooses to play on in our hypothetical game with the lure of a possible million dollars. They have a 20% chance, 1 in 5 of hitting the million dollar suitcase. With great relief the first of 3 suitcases they pick off is the $10, so they now have a 50% chance of avoiding the $1,000,000 in the next 2 suitcases. The offer increases to $290,000. The odds are now 25%, 1 in 4 that they will pick the big one for their next suitcase. It may be prudent to deal now. The contestant no deals, and unfortunately they pick out the million dollars in the very next suitcase, and after receiving a new offer of $300 it is scant consolation that the next of their 3 suitcases selected is the $1. So here's what's left:

$500 $1,000
The contestant is offered $700 to deal, takes it, and their decision is vindicated when they discover that all along they had just $500 in their suitcase, but by dealing too late, they have lost a lot of money, thousands of dollars! While fortune favours the brave, sometimes discretion is the better part of valour!

Let's consider another scenario where there are 8 suitcases left:

$1 $750
$10 $200,000
$100 $500,000
$500 $1,000,000

The odds of taking out the $1,000,000 in the next 3 suitcases = 3/8 or 37.5%
The odds of taking out both the $1,000,000 and the $500,000 in the next 3 suitcases = 3/28 or 9.3%
The odds of not taking out the $1,000,000 and the $500,000 in the next 3 suitcases = 5/14 or 36%
The odds of taking out the $1,000,000, the $500,000 and the $200,000 in the next 3 suitcases are 1/56 or 1.8%

The banker offers $240,000 to deal. I think it is worth going on this time because there are three significant sums of money left, and only a 1.8% chance of taking them all out. Let's assume the player no deals, and takes out the $1, an excellent start. They then choose the suitcase with $500 to a crescendo of audience delight. The offer is now $400,000. The contestant no deals again, not the smartest move in my opinion, and their good run ends when the next suitcase taken out is the $500,000. Here's what's left:

$10
$100 $200,000
$750 $1,000,000

The odds of taking out the $1,000,000 in the next 3 suitcases = 3/5 or 60%
The odds of taking out the $1,000,000 and the $200,000 in the next 3 suitcases = 3/10 or 30%
The odds of taking out the $1,000,000, the $200,000 and the $750 in the next 3 suitcases = 1/10 or 10%
The odds of taking out the $10, the $100, and the $750 in the next 3 suitcases = 1/10 or 10%

The banker now offers $200,000 to deal. I think it's worth dealing now because there is a 1 in 5 chance of taking out the $1,000,000 and a 30% chance of walking away with a relatively very small sum of money should they go on to the 2 suitcase stage. The contestant deals, and then the post-deal openings vindicate their decision, because although they pick $10 and $100 first, the third suitcase opened is the $1,000,000. Here is what's left:

$750 $200,000

The banker calls to say he would have offered $70,000 to deal which the contestant says they would not have accepted but gone on, and are relieved to find that $750 was in their suitcase all along.

Let's look at another scenario where when there are 5 suitcases left, there are still two significant amounts of money:

$1
$10 $500,000
$500 $1,000,000

The odds of taking out the $1,000,000 in the next 3 suitcases = 3/5 or 60%
The odds of taking out the $1,000,000 and the $500,000 in the next 3 suitcases = 3/10 or 30%

The banker offers $380,000 for the contestant to leave at this point. There is a 30% chance that they will take out both the big numbers if they go on for three more suitcases. They choose to play on in the hope of keeping the $1,000,000 in play. The very next suitcase they pick to gasps from the audience is the $1,000,000. Now there is a 50% chance that the most they can walk away with at the very end is $500. The offer decreases to $135,000. No deal. It is all about the $500,000. The next suitcase opened is $10. The offer increases to $180,000. Deal is the smart option now surely? The audience can hardly bear to watch. The final of the 3 suitcases is revealed to contain just $1. So here is what's left:

$500 $500,000
The banker makes an offer of $220,000 which the contestant takes. Their suitcase is revealed to contain just $500 so they were wise to deal, but in dealing too late they have lost $160,000. However, as we saw in our earlier scenario, if a contestant had taken the deal at the 11 suitcase stage, then they would most likely have dealt too early.

Let's look at another scenario where when there are 5 suitcases left, there are still three significant amounts of money:

10c $200,000
$50 $500,000
$1,000,000

The odds of taking out the $1,000,000 in the next 3 suitcases = 3/5 or 60%
The odds of taking out the $1,000,000 and the $50,000 in the next 3 suitcases = 3/10 or 30%
The odds of taking out the $1,000,000, the $500,000 and the $200,000 in the next 3 suitcases = 1/10 or 10%
The odds of taking out the $200,000, the $50, and the 10c in the next 3 suitcases = 1/10 or 10%

The banker's offer at this stage is $250,000 to deal. Although there is an element of risk, the statistical odds are in favour of going on, so the contestant no deals. The $200,000 is taken out first which gets a mixed response from the audience. The offer does not change. No deal. The 10c is chosen. The banker has to increase his offer, and does so to $390,000. No deal is smart, because in the next suitcase there is only a 1 in 3 chance of taking out the million dollar suitcase, and there is the insurance of $500,000 still out there. No deal. Then amazingly the $50 is the last of the three to go. An almost dream scenario is left:

$500,000 $1,000,000

The banker now offers the contestant $700,000 to deal, and adds that he respects the contestant. The response is no deal. The contestant is prepared to gamble because they would be quite happy to walk away with $500,000. They have a 50% chance of losing $300,000, and a 50% chance of gaining $300,000 on the deal. It is because they will walk away with a life changing sum of money whatever happens that makes it easier to go on to the end. The contestant is offered the opportunity by the banker of swapping the suitcases but they decline, and open up their suitcase to find:

For me Deal Or No Deal is fascinating because it is all about nerve, the psychology between the contestant and the banker, and perfect timing!

Do you have a question? Please email me, Richard Steel:

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Richard Steel last modified March 2013

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