What would you choose: $1 for sure or one chance in 100 to win $100? Most people would probably go with the bet in this case. After all, one dollar doesn't make much of a difference to most of us.
Facing a harder money decision
However, if you repeat the same choice with other numbers, you may feel different about the choice. Say that you either get $10,000 for sure or one chance in 100 of winning one million dollars. The two alternatives represent the same expected value if you consider the money pure.
Nevertheless, in this case you'd probably have a much tougher choice?
Would you be willing to give up $10,000 for a chance to maybe, maybe, maybe win a fortune - but very likely be left with nothing?
Some people would, some wouldn't. It probably depends on factors like the state of your finances and your economical needs, but also your feelings about risk taking.
Utility of money
Your preferences for each such choice define the utility of money - for you personally. A person who is prepared to part from $10,000 on a zero sum wager has a different utility for that particular amount than a person who isn't.
If you feel that one safe dollar is worth more than a remote chance of winning $100, you have another utility in that interval than someone who prefers to take the bet.
If you'll take the small bet, $100 is worth more than 100 times one dollar to you. If you won't take the big bet, $1M isn't worth 100 times $10,000 to you. This shows how your utility of money shifts depending on the amount.
Utility and poker
Let's move the utility concept into poker. If you enter a $5 multi-table online poker tournament with the prospect of winning a $500 first prize, elimination probably would be pretty inconsequential to you. A victory, on the other hand, could mean something. (Again those values vary from person to person.)
On the contrary, in a $10,000 tournament with a first prize of $1,000,000, like the WSOP Main Event, elimination could be very painful. A victory in this case represents a value that is hard to grasp for most of us. What would you do with a million bucks, anyway?!
Easy call becomes easy fold
A situation on the bubble that's an easy call in the $5 tournament could be an equally easy fold in the $10,000 tournament - because your utility of money differs between the two money intervals.
In the big tournament, the improved chance of winning really big probably wouldn't match the risk of losing the ten thou that are already halfway down your pocket.
If you consider only the money involved, the call is correct, but if you calculate with the utility of money, the call becomes theoretically incorrect.
Don't play above your comfort level
Of course, for a player with huge financial resources, the situation in the big tournament might resemble your situation in the small tournament. He wouldn't mind taking a marginal shot in that situation for an improved chance of going really deep.
Especially if he knows that players like you will lay down almost any hand to prevent elimination on the bubble.
This is a reason not to be playing above your comfort level. Beside risk-of-ruin calculations and the corresponding bankroll requirements, it's also a fact that you'll be playing suboptimal poker if the fear of losing overtrumps the value of winning.
Note: In any small interval of money, the utility is probably linearly proportional to the amounts of money. This means that ordinary pot odds calculations are not defaulted by the utility concept. It's more of a meta consideration, taking effect for instance when you choose between games, as we saw above.
/Charlie River
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