Is there a theory of how a novice can be a favorite against a world class player with a stack advantage?

Question

The novice has a three to one stack advantage over the world class player. To make it simple, let's call it twelve chips to four. The novice knows enough to try to go "all in" if possible. So his advantage consists of the fact that if he goes all in with four chips versus four, he can break the world class player in one hand. And if he loses, he will go all in as soon as possible with eight chips against eight. That is, the world class player needs two "all ins" to win, the novice one. Assuming that the chances of winning are random, 50-50, this means that the novice's chances of winning could be as high as 75%.

Suppose the novice is the small blind for the first game, having put down one chip, the world class player two. The novice can then produce the above result by raising to four. Of course, it s/he loses, the world class player has the advantage for the second round. But if the novice is 50-50 for the first round, then any equity in the second round would make him or her an overall favorite.

Of course, a large part of the problem is the size of the blinds relative to the stacks. If the novice had 1200 chips versus 400 chips for the world class player, and the blinds were still one and two, the novice would not have so much of an advantage, and might be at a disadvantage.

Is there any theory regarding how large stack sizes need to be relative to the blinds before the value of differences in stack sizes is "small" relative to differences in skill?

Answer 1

If the blinds are 1 and 2 for a total of 3. Harrington green zone is 20 orbits. At 60 chips the pro is able to pick spots. Pro could play tight get it in 2:1 and still lose a couple early hands. Some where around 20 orbits the pro is probably even money.

Pro has to play at least 30% or get rapidly blinded off. At best he is going to be 3:2. He will lose two in a row like 15% of the time. If he sits 4 hands to get that top 30% he is out 6 so quickly into short stacked. Now he is in a position of needs to win two in a row.

Also how novice? They need to know pot odds. Need to not telegraph their hands. If the novice has a system (is not just stupid) then pro would likely need more like 40 orbits to be even money.

I am a novice and I would take 3:1 against a pro. Even deep stacked.

Answer 2

In cash game, this question would make no sense, as players are free to leave the table or add to their stack after any hand, and it would be a bad strategy for world class player to remain playing short stacked against a novice.

In tournament game, M-ratio theory addresses on how stack size should affect play style. With each round costing 3 chips in blinds, a 4 chip stack (M=1.3) is near dead (should push all in with almost any two cards) and 400 chip stack (M=133) is deeply in green zone (freedom to play as you choose).

Answer 3

I don't know if there's any theory out there that applies directly to this, but I'd say there's more of a consensus that the deeper the stack sizes get relative to blinds, the better the environment is for a world-class player versus a novice, and stack sizes relative to each other become less important.

In the example you give, you're right that the novice should want to increase volatility or variance in order to take down the pro. As stacks become deeper, the pro can exercise more selectivity in which hands they play; if the novice is still pushing with 20bb effective stacks, the pro can fold some and just call with the top tier hands. It may get to a point where the pro calls with such a range that they are 70% versus a random hand in which case they are about even to win it all (.70*.70 = .49). Now, the pro has probably folded some hands, losing chips, but winning two all ins still gives them a giant chip lead.

When things really start to turn in the pro's favor is when the two have deep enough stacks that the amateur realizes they can't just go all in every hand and must sometimes play more than just preflop situations. Total guess but somewhere in the 20-60 big blind range; Harrington zones go from yellow to green.

Beyond that, the more potential decisions to be made per hand is good for the pro and bad for the novice. Obviously the pro should be better at these decisions and the deeper the stacks are the more room there is for the pro to be selective and pick good spots rather than succumb to the volatility which the novice tries to inflict. Again, a gut feeling kind of guess, but I'd say if the stacks are 100+ bb's, the pro has enough advantage to overcome the stack differences and make it an even-money game. No doubt, someone can quibble with the inflection points I guessed at, but I don't know how you'd formulate an exact theory.