Question on math of taking –EV in tournaments
Join Date: Dec 2004
Posts: 1,560
In a really extreme example:
You’re in a 1k total buy in tournament with a 150k first place prize.
You knowingly take a 70/30 chance as the underdog also knowing:
Every time you lose, you are out.
Every time you win the showdown, you go on to win the tournament.
If winning equals 150 k, then this is how it breaks down:
7 times out of 10 you lose = -7k
3 times out of 10 you go on for the win = +450k.
I think the point is that even though we don’t know if we’re going to win every time we win a specific pot, we can at least give ourselves some type of idea. Here’s the above example, but with far less of a chance of winning:
7 times out of 10 you lose = -7k
Of the 3 times that you win, you go on to win the tournament 2% of the time = +9000
How I got the 9000 is winning 100% of the time = 450k. 2% of that is 9000.
Is this in any way applicable? In addition, to me, this becomes less plausible as a concept, the earlier in the tournament you go. In the first two blind levels of a 1000 person tournament, I would think this would be meaningless. But, as early as that same tournament getting down to 200 people (not even in the money) I think you can have some type of expectation? Maybe combined with your skill level? I don’t know.
Join Date: Feb 2012
Posts: 14,122
You're discovering something quite true, that chip EV in an MTT doesn't always equate to $EV. It's a very important idea.
Join Date: Dec 2004
Posts: 1,560
A rebuttal might be that even without the huge gain in chips, you 'could' still win. I realize that.
However, let's take the above example that started with 1000 people, and is down to 200. You've just taken a 70/30 as the dog against the second biggest stack in the tournament, and you have 300k chips. The next closest to you is 180k, and average is approx 20k.
In this scenario, with 200 left, all skill being equal, I don't look at myself as having a 1 in 200 chance (.5%). I'm not a good player, but the better players in this situation likely have as high as a 10 in 200 chance (5%) which, again going by the above example, would equate to +22500. So, say I'm significantly not as good as one of those players, and I'm at a 4 in 200 chance, it would still be profitable.
I don't think 20% of the field left is the magic number, and I'm not advocating taking 70/30s as the dog, I guess I'm just saying that with a big stack, even as early as 20% of the field left, it could be profitable to take a lot more chances than some of us really are.
Join Date: May 2012
Posts: 1,060
Like TheDefiniteArticle says it does look like you are discovering the changeable value of chips within tournaments. The most common way at the moment is to use ICM to effectively convert the value of a chip stack to cash value.
It is easy to see that chips may not always be worth the same amount in tournaments. Imagine a game were 3 players are left and 2 get a $1000 ticket the third nothing. The third player has been sitting out for the last 20 hands and after the ante has only 1 chip left. You have almost the same chips of the leader and from the SB you see you have AA. If you pushed it is a great +ChipEV decision but a terrible +$EV one, you should obviously fold and just wait for the low stack to bust. Gaining chips at this point is basically totally worthless.
It is unusual to want to fold a +$EV point and sometimes it may be wise to take a -$EV spot. These points rely on the 'common' use of $EV though.
The term $EV meaning that somehow taking this action will result in a higher return in the long run rather than not taking it. The term +ChipEV, or +CEV, referring to the same except it indicates chip value counts exactly the same way as cash, always of equal value.
It will occasionally make sense to fold so called +$EV points if you have a big skill edge and refusing this action is likely to be followed by an easily more profitable one a bit later. Although this wouldn't make sense if the algorithm used to decide $EV and assess your profit actually took into account your skill level. Usually this isn't done, the algorithms used assume equal ability and it's up to you to adjust for your edge hence sometimes it may make sense to fold a +$EV spot.
Trying to find out what is +$EV is pretty hard and the most common algorithm used is ICM.
Sometimes it might make sense to call a -$EV spot if by folding the utility of your stack is too greatly reduced, again this is due to the algorithm to calculate $EV not taking all factors into account, a failing of the algorithm but in common usage we may use phrase "...it's best to call this -$EV spot due to ..."
In most situations pre-final table, the value of chips is still pretty close to the the same as treating them as cash, ie. 2k chips is worth exactly twice the value of 1k chips.
When it comes to taking calls early on I am quite happy to go with the the odds of the call. If I have 30% hand equity and I have to put in 30% of the final pot to realize this equity I would see this a break even spot and be unconcerned whether I folded or called. If I believed I had an edge over the opposition and by folding the stack left was still workable for this edge to exist I would fold.