updated feb. 9, 2008

take-the-deal  analyzer

go for the multi-millions or not?? see analysis of whether to take the deal or to try for the $1m. based on the trade-off of greed vs. need. go for the million.


based on the tv show, deal or no deal, how do you decide when player should take the deal?   that decision should be based on the belief that the odds of coming out ahead are in your favor.  just like in playing poker or video poker games.  that probability and gambling factor is called the expected payoff, or ep.


our spreadsheet software calculates that figure and individual next level payoffs based on the actual case value chosen.  this allows the player to see the probable new ep, and bank deal that is partially based on this figure. partially because the show must be entertaining and so the deal gets manipulated somewhat from the ep, and is generally a little lower.  it answers: what happens if i picked the $200,000 case?  or, the $10,000 case?


remember, it�s a game of chance where everything is possible, but not probable.   there are no guarantees, just lots of fun.


you need to download the software in order to follow the following explanation on how to use take-the-deal analyzer.  download the zip file.   requires ms excel.


this is a free 30-day trial version.  the standard version without any time constraint is available for just $10 us.  for any questions, ask george.



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note:  you can have family and party fun at home by playing deal or no deal online at nbc.  open take the deal analyzer as you play











when to take the deal














1.   when the spread between the ep and deal amounts are worthwhile and meaningful.


     this will also be indicated by the bk fair game being a decent plus amount.











2.  for example, loading the values from round 1 shown in the historical area,



     the deal is $310,000 with a 50% chance of selecting amounts lower than the deal.


     selecting a lower amount would bring the new deal somewhere in the $390,000 area, but usually

     lower than the eps shown.  is the gamble for a $80,000 increase worth a possible decrease in the

     new deal offer of about the same amount?  it could also be as low as $100,000 if the $1,000,000


     amount is picked.















3.   you must remember that the player is not choosing the amount in his case, but trying to eliminate

      those lesser amounts.  that is the objective of each choice whether to deal or to not deal.










4.   the two probablility, expectation to win how much, questions are: 



      a)   what's the chance of eventually eliminating all the cases less than the  highest


            amount shown, or $1,000,000 in this instance?  there are 6 choices yet to be made in order to get

            the $500,000.  that comes to an 83% chance, after 6 choices, that you lose.


            if you win the 1 out of 6 chance and pick the $1,000,000, you lose, not win!


            next round, there is a 1 of 5 chance to pick the $1,000,000 and lose, etc.



      b)    when should i accept the deal?  this is the important on-the-spot-decision discussed in (2) above.

            there is a 50 -50 chance to beat the bank, or to lower the next deal.  the player must look to the

            next round deal amount that will be offered.  the player is not playing the lottery, but a game

            of surviving each round until the very last, if there is a chance of winning much more than being

            offered, or will be offered, by the bank.





            for example, suppose the player's highest win is only $50,000 at a 50% chance of beating the bank

            deal of $35,000, with a new down-side deal of $20,000.  deal or no-deal?  that should be a deal! 

            take the money and run!






            in historical game 3, the bank deal is greater than the ep. deal or no deal?  deal!






































go for the $1,000,000

why hasn't anybody won the $1,000,000? based on the odds, a winner should occur about every 26 times, and in the 143 games aired, there were 14 occaisions where the jackpot was in the case. why didn't these 14 players go for it!!??

in my view, the answer lies in the concept of the "safety net", a term being used quite frequently on the show. a rational person will weigh the value to them of winning $1m, or taking the deal. and that will depend, obviously, on the size of the safety net. what would a rational person use to decide, deal or no deal? let's say that's $300,000 or more, based on the assumption that the banker's offer will be about half that amount, or about $150,000. this "foundation" could be more or less, but for our purpose here we will go with that bottom amount.

that's to say, the player will continue to go for the $1m case if there's a safety net amount equal to $300,000 or more -- that's 1 out of 4 cases (300k, 400k, 500k and 750k, since the 1m has already been choosen and is safely tucked away next to the player).

how does that affect the odds of winning? the probability of winning the jackpot is not an "equally probable" choice of 1 out of 26, but has been biased as a result of the players choice of his "fallback position", or what will i get if i choose the $1m? is it worth the risk, is what the player unconsciously decides. of course, some are more of a gambler than others, and that safety net amount will fluctuate person by person. but, as i said here, we need some basis for our analysis of the failure to win the jackpot, and $300,000 was set as the safety net.

the table shown below shows an analysis of the likelihood that these favorable events will occur, that is, after so many picks, there will be at least 1 case left with $300,000 or more, in addtition to the $1m case. the figure contains 2 table, the upper showing the probabilities of there being a case over 300k left, and the lower table showing the chances that both the $1m and safety net cases remain after the indicated picks.

for example, in the upper table under the "1 nbr" column for the "4 - 21 picked" row (read: 4 cases left, 21 were picked already, after choosing the player's case). the entry shows "0.16", or a 16% chance that 1 safety case remains. under the "2 nbr" column, there is a 2% chance that 2 of the 4 safety cases remain after 21 picks.

the lower table shows that, for this same condition as above, and now including the possibility that $1m was already chosen by the player, this highly desrieable game condition has only a .6% chance of happening. what these tables show is odds of ending up with 4 cases where 1 case is over $300,000 and the player's case is the $1,000,000 case. that .6% chance translates to 1 out of 153 games that this condition will occur. reading these tables at the "1 - 24" row, showing that there are now only 2 cases let -- one safety case and the $1m case -- we see that the chances of getting to this condition or game position is a measely .2% (actually .15%), an event that will occur in 1 out of some 650 games!

so hang in there folks, we have, as of this writing, some 507 games to go!! now that explains why the show has introduced the multi-million games with multiple $1m entries. you now ask, how has that increased the chances of a $1m winner??

when will a $1m winner happen with multiple $1m entries?

as expected, increasing the number of $1m entries has a significant impact on the chances of actually becoming the first jackpot winner. well, by how much you ask? the figure below shows major increases when there are 10 "repeats" of $1m. ("r" on the bottom row now shows "10").

you will note that the upper table has not changed. that's because it is still based on 4 safety amounts, but this time they happen to be all equal to $1m. it remains at 16% for just 1 jackpot entry left, not counting the player's case. however, the likelyhood to arrive at a winner position with both $!m as the player's case and $1m as the only case left has jumped from .2% to 1.5%. that's a 1 out of 67 games. since the show is only up to 11, we have several more games to go, 10 times less games to go.

one final word. it is interesting to note that as the number of repeats increases, so does the chances of becoming a winner, and we need not wait 67 more games, on the average. at 16 jackpot entries, that's 10 non-safety net entries, the chance of getting to a winner position is 1 out of 41.

of course, the "gambler" types may choose the "all or nothing" gambit and go for the jackpot, and may even win.

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