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I just watched an episode of "Deal or No Deal" the other night, and for those of you unfamiliar with that show, the object of that game is to select suit cases containing a hidden dollar amount ranging from $0.01 to $1M, each of which eliminates that possibility as being a final prize amount. As you select more suit cases and slowly eliminate them as potential prize amounts, there is a banker that periodically makes you offers to buy you out of the game for an assured amount of money.  The player is then asked, "Deal or No Deal?" and they proceed to make a decision between taking the guarantee money and gambling further in hopes of winning a larger prize amount.

During this show, I could not help but reflect on the many similar scenarios that I have encountered while playing tournament poker. This particular episode had a spunky Polish woman who did a great job selecting suit cases containing lower dollar amounts and increasing the dollar amount of the banker's offer, but her poker illiteracy in the end cost her a lost opportunity of about $250K.
 
The contestant had already been offered a settlement deal of $172K, which she turned down with dissatisfaction, and after a round of poor suit case selection, the offer got lowered further to $161K. Then, however, as she eliminated more lower dollar amounts, the offer got bumped to $222K. She continued to gamble with only five suit cases remaining, and after picking one more case, the offer increased to $247K.

At this point, it came down to only four suit cases containing: $200, $10K, $400K, and $1M. Basically, you can look at it as a one in four chance of becoming a millionaire, which are incredible odds! She could take the guaranteed $247K offer and walk away or gamble one more time for an even more lucrative offer. My fiance was screaming from my living room couch to take the offer and run, and I looked at her and explained that she would be crazy to NOT select one more suit case!

This could be a direct analogy to a high stakes tournament poker game where it came down to the final four players with payouts heavily weighted to the top three places. The banker's offer in the game show is essentially the other three players offering to chop the total prize pool among four players, in order to provide some guaranteed winnings regardless of where you finish out of the final four. Now this point is clear: the woman was unhappy with the offers of $172K and $222K. Somehow, though, she seemed unsure about whether she should accept $247K (which is only $25K more than the previous offer) or select one more suit case for a possibly greater offer from the banker.

Of the four remaining suitcases, the probability of NOT selecting the $1M prize amount was 75%, and as long as she avoided the $1M case, the banker's offer would surely increase to over $400K, reflecting the improved one in three chance of becoming a millionaire. Even if she got unlucky, the poker equivalent of getting a bad beat, and had the misfortune of selecting the $1M suit case, there would still be a one in three chance of winning $400K, and the banker's offer would probably decline from $247K to about $185K, which is the worst case scenario. (Editor's Note: If the $1M case was selected, the EV of the final case would actually be about $135k, and the likely next offer would be something ranging around $75k-$85k). So the correct decision was to select at least one more suit case for a worst case downside risk of about $70K relative to best case upside reward of an extra $200K or more. (Editor's Note: again, the downside risk is approximately $160k-$170k, not $70k). This is why you avoid agreeing to a chop at this stage of a tournament and continue on until only three players remain (or suit cases); it was a no brainer!
 
It is a shame she was poker illiterate, because then she would have understood concepts such as odds, probabilities, payouts, and risk/reward and avoided taking the safe money offered by the banker for $247K, which is what she ended up doing. This incorrect decision significantly lowered her potential prize winnings!
 
You can take this concept further and relate it to the final table of the WSOP 2006 main event when it came down to the final three players, where Jamie Gold had a dominating chip lead of $61M over both Michael Binger's $11M and Paul Wasicka's $18M stacks. One pivotal hand had all three players seeing a flop of 10c 6s 5s, after Binger raised to $1.5 million from the big blind. Wasicka checked, Binger bet $3.5M, and Gold moved all-in, having both players covered. Paul Wasicka held the glorious 7s 8s for an open ended straight flush draw, but he knew he was behind on the flop. Basically, it came down to whether he was looking for guaranteed safe money of a likely second place finish if he folded or going for the win and the $12M payout, as this would possibly be the best opportunity to bridge the huge gap between chip stacks of first and second position and give Paul a realistic chance of winning.

The worst case scenario was Paul calling all-in, Michael folding, and Paul losing the hand and ending up finishing in third place for a prize payout of $4M. The likely scenario however had Michael also calling all-in behind Paul, since he had invested about 45% of his stack into this hand already and was probably pot committed. If there was a double knock out, then Paul would still finish in second place, since he had more chips. The upside by calling all-in was the possibility of winning the hand and taking over the chip lead and maybe winning the tournament for increased winnings of an extra $6M over second place. The correct decision was to call all-in for worst case downside risk of $2M in lost profit relative to the expected event of a second place finish for $6M and possible best case upside reward of an extra $6M or more; it was a no brainer!
 
Regards, HonestAbeX1

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