As of 11/19/2007 the formula on this page no longer matches the game on the NBC website. The television version never did match this formula, to the best of my knowledge. This formula worked, at a minimum, from April 2007 - Nov. 2007. As of March 2008 - see update below.
“Big” $ values are $100,000+
All others are “small” $ values.
In the formulas below "big" represents the sum of the remaining "big" dollar amounts.
"Small" represents the sum of the remaining "small" dollar amounts.
EV is the "expected value" of the remaining dollar amounts.
(Sum of all the dollar values divided by the number of remaining values)
When there are 20 cases left the offer is .0077*big + .07*small.
(.154 * EV of big + 1.4 * EV of small)
When there are 15 cases left the offer is .0144*big + .09*small
(.216 * EV of big + 1.35 * EV of small)
When there are 11 cases left the offer is .0273*big + .13*small
(.3003 * EV of big + 1.43 * EV of small)
When there are 8 cases left the offer is .0442*big + .17*small
(.3536 * EV of big + 1.36 * EV of small)
When there are 6 cases left the offer is .062*big + .2*small
(.372 * EV of big + 1.2 * EV of small)
When there are 5 cases left the offer is .1025*big + .25*small
(.5125 * EV of big + 1.25 * EV of small)
When there are 4 cases left the offer is .1683*big + .33*small
(.6732 * EV of big + 1.32 * EV of small)
When there are 3 cases left the offer is .305*big + .5*small
(.915 * EV of big + 1.5 * EV of small)
When there are 2 cases left the offer is .355*big + .5*small
(.71 * EV of big + EV of small)
Update
A visitor to my page, Kevin Huculak, decompiled the code on the website. Together we determined the new formula. The new formula is a random number based on a percentage of the expected value.
Round 1: 20%-35%
Round 2: 20%-35%
Round 3: 20%-35%
Round 4: 20%-35%
Round 5: 20%-35%
Round 6: 30%-45%
Round 7: 40%-55%
Round 8: 50%-65%
Round 9: 60%-75%
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