| Re: Риск-аверсионные индексы vs обычные ID:5956 ответ на 5887 |
Ср, 8 ноября 2006 14:10 [#] |
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Да вот оно, а то Грамазека истомится в ожидании 
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IV.(3). Risk Averse (Kelly) Indices for Insurance
The Insurance side bet also carries a degree of risk, but trying to guess where that risk might be can be surprisingly difficult to do successfully! So if you wish, make your guess and then read on.
Probably every Blackjack expert worth his salt has, at one time or another, advised that Insurance is a side bet totally incapable of altering the outcome of the initial bet on your hand, and so the Insurance decision should be made with no regard for the strength of your cards. Well, this is true if your objective is to maximize expected value. But to play optimally, taking into account the risk, you really SHOULD take your hand into consideration, albeit for rather different reasons than you might imagine! Consider this situation:
Assume the system is Hi-Lo and the Count suggests the expected value for the Insurance side bet is around zero, and the dealer has an Ace. So, superficially, it looks as if the decision is about as marginal as possible, with the preference being to decline Insurance. But appearances can be deceiving, and it turns out that the Insurance decision here really can have a significant effect on performance! This effect once again stems from the element of risk in the equation. And here are a couple of examples to show you how it works:
Holding hard 20 vs. Ace
Make the Insurance side bet with hard 20, and the possible increase or decrease in bankroll, represented as a fraction of the initial bet is:
Win 1/2 a bet (dealer makes less than 20 or busts)
Win zero (dealer makes Blackjack)
Lose 1/2 a bet (dealer makes 20, rather unlikely)
Lose 11/2 bets (dealer makes 21, very unlikely)
Don’t make the Insurance side bet with hard 20, and the possible increase or decrease in bankroll, represented as a fraction of the initial bet is:
Win 1 bet (dealer makes less than 20 or busts)
Win zero (dealer makes 20)
Lose 1 bet (dealer makes Blackjack or 21)
Careful analysis of these alternatives reveals that the Insurance side bet reduces the risk (Variance) for the initial bet, and yet there is no reduction in expected value (given that the Insurance decision has zero expectation).
At this point it should be clear that the correct decision is to make the Insurance side bet because it reduces risk completely free of charge. And so the truth is revealed that there is hidden value in this seemingly inadvisable Insurance bet. And in fact it can be correct to make the Insurance bet even when it has a slight negative expected value -- the deciding factor being that the reduced risk should outweigh the reduced expected value.
Holding hard 16 vs. Ace
Using the same method of analysis for this hand reveals that making the Insurance bet has exactly the opposite effect — it increases risk! And so here it can be correct to decline the Insurance bet even when the Insurance bet itself offers a slight advantage!
If the size of the Insurance bet is flexible, then the situation is further complicated. Theoretically, it may be optimal to make a partial Insurance bet i.e. less than 1/2 the initial bet. For example, with hard 20 vs. Ace, it can be correct to take partial Insurance with disadvantage, and if you have hard 16 Vs. Ace, it can be correct to take only partial Insurance with advantage!
For practical purposes you need to draw the line somewhere on the depth of analysis. Suppose that you play a shoe game and use Hi-Lo. The insurance index is then +3. It would be reasonable to make the Insurance bet a little earlier (say at TC +2) with hard 20, and a little later (say at TC +4) with hard 16.
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