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#11
10-04-2006, 11:27 PM
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Re: ??
[ QUOTE ]
[ QUOTE ] what do you mean by the value of a stack of chips in a tournament? Surely it is the expected amount the player behind the chips will win. [/ QUOTE ] On average, yes. [/ QUOTE ] "average" and "expected" should mean the same here. Then it, the value, depends on the player who owns the chips (and on other factors, like the other players at the table and their positions relative to him). It doesn't just depend on the number of chips in the stack. 
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#12
10-05-2006, 06:51 AM
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Re: ??
[ QUOTE ]
For the purposes of the discussion you can assume all players have equal talent. [/ QUOTE ] If all players have equal skill than the expectation of 100 chips stack is, well, $100 and not $150 nor $50. Trust me - I just played in a World Series of Flipaments (refer to some recent threads in MTT Community for more on that...). HOWEVER article speaks of a GOOD player's stack being worth MORE than face value at the outset and it STRESSES as the MAIN POINT that doubling the stack CANNOT effectively double the EV of the said stack FOR GIVEN PLAYER. I daresay that the fact that the increased initial value of the stack is DUE to the SKILL of the player... Do you now see why your statement is in contradiction to the main argument of David's article?
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#13
10-05-2006, 07:23 PM
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Re: ??
[ QUOTE ]
[ QUOTE ] For the purposes of the discussion you can assume all players have equal talent. [/ QUOTE ] If all players have equal skill than the expectation of 100 chips stack is, well, $100 and not $150 nor $50. Trust me - I just played in a World Series of Flipaments (refer to some recent threads in MTT Community for more on that...). HOWEVER article speaks of a GOOD player's stack being worth MORE than face value at the outset and it STRESSES as the MAIN POINT that doubling the stack CANNOT effectively double the EV of the said stack FOR GIVEN PLAYER. I daresay that the fact that the increased initial value of the stack is DUE to the SKILL of the player... Do you now see why your statement is in contradiction to the main argument of David's article? [/ QUOTE ] No. David is proving what he said and you quoted. No one, certainly not I, am claiming that a players skill doesn't change the value of his STACK. In fact the first two sentences of the paragragh you quoted say just that: [ QUOTE ] Bullying is a tatic. Correctly using it, and other tatics, will increase a players chances of winning, and hence the value of his stack. [/ QUOTE ] Again. The issue is the value of the individual chips in the stack, not the value of the stack. And to simplify that discussion I assert you can assume all players have equal talent. Especially since Snyder has asserted the opposite of conventional wisdom. David's article went beyond that but the underlying issue which is causing the discussion is whether chips won are worth more than chips already held. David not only proved that but that they aren't worth more in a skilled players stack either.
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#14
10-05-2006, 07:33 PM
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Re: ??
[ QUOTE ]
Then it, the value, depends on the player who owns the chips (and on other factors, like the other players at the table and their positions relative to him). It doesn't just depend on the number of chips in the stack. [/ QUOTE ] Okay. But that's not the issue. Snyder claimed that the individual chips gain value in a larger stack, while almost everyone else thinks they lose value. The fact that the exact value of each chip, or the entire stack, will be higher for a skilled player than for an unskilled player is irrelevant to that issue.
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#15
10-06-2006, 07:32 AM
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Re: ??
The CASH value of each individual chip in a tourney is $0. The UTILITY value of each individual chip is a different matter. I'll bet that the UTILITY VALUE distribution is anything but linear, and the graph would look different for plyers of different skills. There will be certain points in the graph where doubling the stack will more than double player's expectation. There will also be plenty of points where it won't.
So to David's argument - Let's say Average (or median? not really sure) stack is $50. Doubling up player's $10 chips may well result in $20.1 $EV. Doubling it up again may result in $40.4. $81. $170. $330. $600. You see where I'm going with this? The further away we are from the Average stack - the less we are able to utilize the EXTRA chips we get, and hence the value of the chips we pick up is LESS that the ones we risk.
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#16
10-06-2006, 03:34 PM
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Re: ??
[ QUOTE ]
The CASH value of each individual chip in a tourney is $0. The UTILITY value of each individual chip is a different matter. [/ QUOTE ] You're playing games with terms trying to define the issue the way that suits your argument. I don't agree that the cash value of an individual chip is zero. If the tournament were stopped prematurely for some reason and payouts were made on remaining chips, they would have value. Any additional value based on skill would be subjective and would have to be ignored. So the chips have value independent of skill. And I agree that the "utility" value as you use the term is not linear based on stack size. And trying to plot a curve based on stack sizes, and skills of the remaining players would be hard, and such a curve would be complex. And no two curves would ever look the same. But if you claim that chips added to a stack are worth more than chips already in that stack at any place on such a curve then the burden is on you to prove it. No one has done this. Some have demonstrated that they don't, at least on average. One place where a chip might be more than a previous chip is when such a chip gives you an additional hand, blind or round of hands. Example: You are last to act in a heads-up hand on the river. The game is a no-limit holdem tournament and the blinds are 50/100. The next hand the blinds go to 100/200. There is 400 in the pot and you have 650 left. If you check and take the pot you'll have 1050, enough for three rounds plus part of the big blind. If you bet 100 you have 1150 if you are called and win. You'll have enough for three rounds plus the big blind and part of the small blind. But if you bet 200 and are called and win you'll have 1250, enough for four rounds plus. The second 100 you win by betting 200 is probably worth more than the 100 you'd win by betting 100. But while the second 100 chip that you win may be worth more than the first 100 chip that you win, the second 100 chip you lose if you bet 200 and lose the hand is worth more than the second 100 chip should you win.
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#17
10-06-2006, 04:39 PM
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Re: ??
[ QUOTE ]
You're playing games with terms trying to define the issue the way that suits your argument. I don't agree that the cash value of an individual chip is zero. If the tournament were stopped prematurely for some reason and payouts were made on remaining chips, they would have value. Any additional value based on skill would be subjective and would have to be ignored. So the chips have value independent of skill. [/ QUOTE ] 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? [ QUOTE ] And I agree that the "utility" value as you use the term is not linear based on stack size. And trying to plot a curve based on stack sizes, and skills of the remaining players would be hard, and such a curve would be complex. And no two curves would ever look the same. [/ QUOTE ] Absolutely agree, obv. [ QUOTE ] But if you claim that chips added to a stack are worth more than chips already in that stack at any place on such a curve then the burden is on you to prove it. No one has done this. Some have demonstrated that they don't, at least on average. [/ QUOTE ] 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. At some point the line will level out to the point where doubling your stack will have ALMOST NONE additional utility value. At the early-middle of the curve (where it's steepest) is the place where typically chips added to your stack will increase it's utility value MORE than just the straight chip-count. 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. Ok, another old beat-up and much discussed (and not mine) example. Everyone at your table has 100 chips, you have 150, one guy has 50. If you can get your hands on those 50 chips - you'll have 2x chips of anyone else at the table, and that extra 100 chips has significant utility value that is (for some players anyway) is more than double of utility value of the 50 extra chips we currently have. Gigabet states in his theory of stack sizes (if you haven't read it - you should, it's an interesting read) that he will KNOWINGLY take a -EV gamble for those 50 chips for a chance to get to 200, since if he loses the "race" he's down to 100 and no worse off, really, but if he wins he is getting advantage that is sufficient to overcome the long-term -EV gamble he had to take to get those chips. The same, essentially, applies to taking a coinflip early in a tournamet - AS LONG AS YOU CAN EXTRACT MORE VALUE FROM LARGER STACK. Which, once again, brings us back to skill... By gambling to double-up you're giving up a certain edge (ability to outplay your opponents) in order to try and get a big stack because you feel that you have MORE of an edge over your opponents when you have a BIG stack. [ QUOTE ] One place where a chip might be more than a previous chip is when such a chip gives you an additional hand, blind or round of hands. Example: You are last to act in a heads-up hand on the river. The game is a no-limit holdem tournament and the blinds are 50/100. The next hand the blinds go to 100/200. There is 400 in the pot and you have 650 left. If you check and take the pot you'll have 1050, enough for three rounds plus part of the big blind. If you bet 100 you have 1150 if you are called and win. You'll have enough for three rounds plus the big blind and part of the small blind. But if you bet 200 and are called and win you'll have 1250, enough for four rounds plus. The second 100 you win by betting 200 is probably worth more than the 100 you'd win by betting 100. But while the second 100 chip that you win may be worth more than the first 100 chip that you win, the second 100 chip you lose if you bet 200 and lose the hand is worth more than the second 100 chip should you win. [/ QUOTE ] I see your point (even though it's a bit contrived - I'm not entering the pot with 8 BB's if I do not intend to get ALL of my chips on the table, EVER - even if it's a limit game). However, once again - being able to survive through blinds has little enough value - you need a stack to work with, you need FE, and in CLOSE situations like these you are looking to double-up or go busto...
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#18
10-06-2006, 07:24 PM
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Re: ??
[ QUOTE ]
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? [/ QUOTE ] 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. [ QUOTE ] 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. [/ QUOTE ] If so, as their "utility" value increases, their cash value decreases. Which magnitude is higher? Prove it. [ QUOTE ] 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. [/ QUOTE ] 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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#19
10-10-2006, 04:16 PM
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Re: ??
[ QUOTE ]
You're playing games with terms trying to define the issue the way that suits your argument. I don't agree that the cash value of an individual chip is zero. If the tournament were stopped prematurely for some reason and payouts were made on remaining chips, they would have value. [/ QUOTE ] And the value of each chip would be equal. Are you doing the same thing (defining the issue the way that fits your argument) or agreeing that an additional chip is worth the same as all the other chips?
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#20
10-11-2006, 02:23 AM
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Re: ??
[ QUOTE ]
[ QUOTE ] You're playing games with terms trying to define the issue the way that suits your argument. I don't agree that the cash value of an individual chip is zero. If the tournament were stopped prematurely for some reason and payouts were made on remaining chips, they would have value. [/ QUOTE ] And the value of each chip would be equal. Are you doing the same thing (defining the issue the way that fits your argument) or agreeing that an additional chip is worth the same as all the other chips? [/ QUOTE ] What? In that paragraph?
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Linear Mode
