Re: ??
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I do not play my hands (nor does anyone else to my knowledge) with is consideration, so I do not see how it can ever apply to the strategy?
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The point is the chips have value. If you had one chip and were in the money, stategy has no value at that point, yet your chip is worth a lot.
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If you graph the utility value of a single chip based on the stack size in relation to eiter blinds or average stack - you will have a basic sideways hyperbole(SP?) pattern where the less chips you have - the less utility value they have (can't do MUCH with a single chip), as you get more chips their utility value will increase.
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If so, as their "utility" value increases, their cash value decreases. Which magnitude is higher? Prove it.
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Easy example - your M is 4, you are in push-fold mode, almost no FE. Once you double up - you are now in push/fold mode but with some FE - congrats, the UTILITY value of your stack has grown by MORE than just the straight chip count. If you double up again - you now have M=16 and now you can start re-stealing with FE and maybe even playing small pots in position and what-not.
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Even if your "utility" value has quadrupled, which I doubt, the cash value per chip has decreased. You've raised an interesting point which doesn't necessarily prove the individual chips gained value.
David's example of doubling chip stacks and comparing that to doubling ev's PROVES the chips are losing value, at least on average. PERIOD. END OF DISCUSSION.
Claiming that "utility" value is increasing on each successive gip gained at some range of values for stack sizes is an interesting thought which has not been proven. Until you PROVE it by some clear example it's just your opinion how much extra "utility" extra chips may have. Since you'te not recognizing any cash value they may have you're assuming any extra "utility" means the chips are worth more.
If indeed more chips mean more utility and this translates into greater ev, and assuming this utility factor includes all variables (your skill, skills of others, blinds structure, position of players, etc.) then I'll submit the following equation which I feel address the situation:
Total Value per chip = Cash Value +/- Utility Value
Although I think utility value should not be so broad a term, so perhaps:
TV = CV +/- UV +/- OF
Where OF are other factors such as seating, how close to blinds, blind structure, etc., which are obviously hard to quantify. Utility Factor would in itself be complex as it would vary depecding on the skills of the other players and other factors, and like OF, would be hard to quantify. The reason for the +/- is that it would be negative for opponents lacking comparative skill.
This is obviously a ridiculously simplified equation. But I hope it demonstrates my opinion on the cash value of the chips and how other factors would effect it. It's the base value, and in almost all cases, the most significant factor (imo).
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