Wow, that's very suprising that you guys have the same hand requirments with an M of 5 as you do with an M of 3.

When M goes from 3 to 5, it is true that we have more time and can therefore wait for a better hand. This implies that we should tighten up. However, there is an opposing force that dictates that we should play looser, especially in late position and unopened pot. That is stealing the blinds from late position is a profitable play and necessary for survival. We don't get enough premium hands to sustain our short stack without stealing.

The effects of stealing can be viewed in this thread:

https://www.cardschat.com/forum/tournament-hand-analysis-51/stealing-button-high-blinds-98634/
Even though that thread deals with one specific hand and position, the trends are the same for other hands and positions.

The bottom line is that even though we are dog when called, we pick up the blinds far more often than we are called, assuming our stack is not tiny. The cEV for one caller is:

cEV = (% they fold)*1.5BB + (% one call)*((% we win)*(1.5BB + Stack) - (% we lose)*Stack)

When we are called, the 2nd term is negative since we are usually dog. However, we win far more often the blinds to make this profitable. The tighter the players left to act, the better it is since the first term is where we make our money.

Because of these two opposing forces (wait more with a bigger stack, but steal more as well), the playing range for M=3 and M=5 can be very similar.

Let me now comment why we can play loosely with M<3. If we look at the equation for cEV, the first term is almost zero since it is not likely people will fold to our tiny stack push. The second term is negative. The looser we are(and we have to be since we are desperate), the more negative our cEV is. How can then be proftibale to play like that with a tiny stack?

The answer lies in the fact that $EV is what dominates desperation play. As some players know, marginal chip values are not constant. For example, if we had a stack of 1,000 when blinds are 5/10, losing 500 is much worse than winning 500. More extreme, losing 1,000 is much worse than doubling up. That means that our first 1,000 chips are more valuable than our next 1,000 chips.

An easy way to see this is to consider $EV which is the driving force in tournaments. If we lose our stack of 1,000, our $EV goes from whatever it was to zero. On the other hand, doubling up

**doesn't** double up our $EV. So a coin flip all-in early in a tourney has -$EV. Even if we are slightly favorite, it is still -$EV.

In most cases, additional chips have less value than what we already have. However, this is not always true. One situation when this is reversed is when our stack is way too small. When our stack is that small, we have lost all FE so we cannot steal. If we wait, we will be blinded out so waiting has zero $EV. That means that the chips we have are

**less** valuable than the chips we can get if we double up. So even though our super-short stack play has -cEV, we are still playing +$EV since waiting will surely mean we will not make the money.

There is an obvious exception to this if we are close to a bubble and can make it by folding.