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I shall provide you with the information necessary to make that decision. There is a table for bettors who like to bet half the Kelly fraction, one for full-Kelly bettors and additional tables for bettors with persuasions to bet one and one-half, two, two and one-half, and three times the one-Kelly fraction.

I would not try to discourage proportional betting.

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Its replacement is a thing of personal decision. The results of this part of the simulation process are shown in the tables under the heading of "Composite Projections.

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Make the most of those good, positive expectation situations. But it is unlikely that they approach a full Kelly betting fraction.

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The composite projections give you a good approximation of what to expect of our "investment" budget in head-to-head play at single-deck. But if you wish to really understand proportional betting, and to find your comfort zone as a function of expectation, The Leib Criterion and the accompanying tables should give you what you need.

Leib may draw fire for some of his unorthodox conclusions, but I find his basic idea here appealing. Where does this leave us? The conversion factor in going from Kelly to Leib is simple and wasy to remember: It should also be noted that these SCOREs are all far higher than we would see without using optimal betting theory at all.

Such an FOM will include the positive value to you of average win in terms of your initial bankroll and the negative value to you of the probability that you will reach your "chickening out" level during the trip. So, if the "ruin" probability is too great for the desired absf black jack x40 win, blame it on the really good hands!

The "ruin" percentages, however, are likely to be quite accurate.

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The Leib Criterion vs. In other words, to bet according to The Leib Criterion you must bet twice what you would in following The Kelly Criterion. This is because the average tends to be dominated by particularly profitable, and quite unlikely, series. Now I am going to ask you to perform that ever-popular task: For purposes of the rest of us, I have assumed trips to Las Vegas or other gambling Meccas, be they occasional or frequent, are made with a total budget determined at the moment of leaving home.

ALL entries show positive average wins. John Leib proposed The Leib Criterion. Two possibilities not including "barring" exist that may cut short your gambling activity: It is this old "risk versus reward" concept revisited. Let's change this to a more reasonable set of bets: You will see a couple of jogs in the green line. The red area signifies the loss from switching to rational bets.

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These are a special class to which I am guessing you do not belong, and to which I shall not presume to give advice. The betting fraction is always some fixed multiplier times the instantaneous expectation for all wagers. You probably already have some idea of what kind of bettor you are, assuming you are more or less a proportional bettor. Normally, we consider our total bankroll when estimating our optimal Kelly bet.

A skeptical person might say this is why every book claims that the strategy in that book has a higher advantage than other strategies. The wisdom of table-hopping shoe games becomes very apparent with a divided bankroll, as your investment dollars increase as your expense dollars decrease.