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Now, both Greta and Opie know before each play which situation they will be confronting. Opie bets optimally, in proportion to her advantage, 2 units with a 2% advantage and 6 units with the 6% edge, while Greta bets grossly, 4 units whenever the game is favorable. Thereby they both achieve the same 3.6% of a unit expectation per play. Starting with various bank sizes, their goals are to double their stakes without being ruined. The results of 2000 simulated trials in each circumstance appear below.

Greta is obviously the more often ruined woman, but since they have the same expectation per play there must be a compensating factor. This is, of course, time-whether double or nothing, Greta usually gets her result more quickly. This illustrates the general truth (pointed out by Thorp in his Favorable Games paper) that optimal betting systems tend to be "timid", perhaps more so than a person who values her time would find acceptable.1c]

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I'm Better Than You Are!
Let's define the term narrowly and say that there are exactly 500 different skills available to master in poker.

Now, let's take two local club players, each of whom is pretty good-not duffers but no threat to win the World Series of Poker, either. Let's further say that these "advanced intermediate" players have attained that status because they have each mastered 300 of the 500 necessary skills.

This might make the two players equally talented and might mean that against equal opponents, they rate to achieve equivalent results over the long run, but it would take an astounding coincidence for each player to have mastered precisely the same 300 skills. They're probably good at different things. Let's say that Player X has mastered skills 51 through 350, while Player Y has mastered skills 176-475.
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