Arnolds First Article

[George Rice]

In justifying his position that chips in a large stack are worth more than chips in a small stack, he wrote the following:

[ QUOTE ]
If a chip is a bullet, and I have 500 bullets, and you have 4500 bullets, you can utilize your ammo in many ways that I cannot. You can fire test shots to see if you can pick up a small pile of ammo that none of your enemies are all that interested in defending. You can engage in small speculative battles to try and pick up more ammo, and you can back out of these little skirmishes if necessary without much damage to your stockpile. Most importantly, because all of your enemies can see your huge stockpile, you can get them to surrender ammo to you without fighting, even in battles they would have won, were it not for their fear of losing everything.

[/ QUOTE ]

To that I ask the following:

If each chip in the large stack are worth more than each chip in the small stack, and since all players have to put equal chips, not equal value, in the pot of a given hand, then doesn't it follow that the larger stack is risking more value than the smaller stack every time it get's involved in a hand? And if that's the case, shouldn't it be the large stack who wants to avoid confrontations?

Not for nothing, if I had 500 bullets and Arnold had 4500 bullets I would make mine count where he could waste many and not change his chances much. To put it another way, I would use sharp-shooters where he could use machine guns.

[cold_cash]

I basically know nothing about this, and I don't know who Arnold is, but it seems like I read somewhere that in a tournament the chips lose relative value the more of them you have. (So the opposite of this guy's argument would be true, which makes more sense to me.)

[Cactus Jack]

Bullets are worth nothing if you're a lousy shot.

[BigAlK]

[ QUOTE ]
To that I ask the following:

If each chip in the large stack are worth more than each chip in the small stack, and since all players have to put equal chips, not equal value, in the pot of a given hand, then doesn't it follow that the larger stack is risking more value than the smaller stack every time it get's involved in a hand? And if that's the case, shouldn't it be the large stack who wants to avoid confrontations?

Not for nothing, if I had 500 bullets and Arnold had 4500 bullets I would make mine count where he could waste many and not change his chances much. To put it another way, I would use sharp-shooters where he could use machine guns.

[/ QUOTE ]

George,

I'm confused. The first paragraph seems to argue against the theory and the 2nd, unless i'm misunderstanding, for it.

Regarding the 1st - the theoritical monetary value of a chip at any point in time and whether each chip has a different value is an interesting discussion. Maybe the answer even matters. However Snyder's theory is that the extra value of chips in the larger stack comes from increased utility. Not due to a difference in the theoretical monetary value of each chip. I'd liken this to someone with a million dollars in savings. That's more than I have and, if both of us have the goal of increasing our savings, that person has more options to increase their savings without going broke. I couldn't risk my meager dollars in a high risk/high reward venture because that one investment could break me. The person with the greater savings could make several small investments in these type of ventures knowing that if one hits he'd make a tremendous amount. The greater utility of more viable investment options gives that person's money greater utility value than mine. This, despite each of our dollars (chips) having exactly the same monetary value. Your comment is akin to recommending he stuff his money in a mattress because "it's worth more."

I'm not sure I get your point in the 2nd paragraph. In this situation you've got little choice but to be selective, using a sharpshooter to take extremely selective shots (bringing it back to poker you're in push/fold mode, waiting for a big hand that you want to have called or pushing in those situations where you believe you can pick up the blinds without a fight).

Arnold has the same options that you do. He can push (or at least raise enough to force you to fold or risk all your chips). He also has the machine gun option as you suggest, sspraying the general area where he's spotted you. He could fire random shots (or bursts with the machine gun) toward the area where he knows you're hiding to make you adverse to raising your head to try and take a shot while, in the meantime you're running out of food and water (kind of like the blinds continuing to rise). If I had time there are probably lots more bad analogies that could be made explaining all of Arnolds potential options. All of these additional options are due to the added utility of the bigger stockpile of ammo.

Yes, I've done well in tournaments with a small stack. But this often requires specific table conditions and lucky cards. When I've built a big stack early my success rate has been higher. Obviously this is no great revelation and measuring the impact of acquiring the big stack is difficult to measure. However, just as in life, in tournament poker "the rich get richer and the poor get poorer." The reason for that is the utility value of the bigger bank account or bigger stack.

Al

[George Rice]

[ QUOTE ]
Your comment is akin to recommending he stuff his money in a mattress because "it's worth more."

[/ QUOTE ]

If the chips were worth more in the large stack this would make sense. And astute players with small stacks would take all kinds of chances to get a large stack, becasue dollar for dollar, it's worth more. Think about it. Wouldn't you? If your small stack was worth even less because the value of each chip is less, than what's the point of waiting? The goal would be to get chips NOW so you can gain all this advantage.

Any additional options a large stack has comes due to it being a large stack, not because each chip is worth more. And that probably because each chip is worth less, not more.

[ QUOTE ]
He also has the machine gun option as you suggest, sspraying the general area where he's spotted you. He could fire random shots (or bursts with the machine gun) toward the area where he knows you're hiding to make you adverse to raising your head to try and take a shot while, in the meantime you're running out of food and water (kind of like the blinds continuing to rise).

[/ QUOTE ]

He has this option because his bullets are worth less and he doesn't lose much value by wasting some. If larger stacks meant each chip was worth more then each chip lost means not only a loss of a chip, but also a lost of value of each chip remaining. You'd be taking two losses. Actually, four loses, as the chips are not lost, but go over to the other side (maybe rocks are a better analogy) and the small stack not only gains chips, but each of his original chips have gained value. So wasting these chips wouldn't make sense.

[George Rice]

Arnold is taking issue with accepted wisdom, hence his articles.

He hasn't fully explained this position, and in my view, his reasoning is flawed in the parts he has addressed.

[Grumbo]

I don't agree with the savings account analogy as poker is a zero sum game, what you win your opponents lose. Once you have the tall stack at your table, those extra chips are not as valuable since you already have your opponents covered and can take them out with your chips. The extra chips get value out of the small ball moves you can take to get their chips a little at a time.