What about the size of the bet?

[PantsOnFire]

Let's take a coin flip (fair coin, no tricks). A dumb person says that his experience indicates that in general, heads comes up more often than tails. He is so sure of this, he is willing to put up $1.00 to your $0.90 on a flip of the coin. He will get heads and you get tails. So again, assuming a fair coin (regardless of what dumb person thinks), this bet is clearly +EV for you.

As a matter of fact, your bankroll is $1,000 so you ask dumb person if we can play this game for 1,000 flips (within your bankroll and will even out variance quite a bit). You tell him that you don't want him to get unlucky and wish to give him many chances to prove his point. OK, it is obvious that smart people will take this bet and more often than not, win several dollars from dumb person.

Now, let's get to the subject. We will keep the same proportion of each bet but increase the size of the bet. Let's say dumb person will lay out $1000 to your $900. However, this is now 90% of your bankroll. Do you still take this bet?

Would you take the bet if your bet size was your entire personal net worth and you had a chance to increase it by 111% in one shot? Of course, if a down and out gambler had $100 to his name, he might take the shot. But what about the guy with a house, family car, savings and it totalled $500K. Would this guy take a 50/50 shot at ending up with $0 or $1,111K?

Some corollary questions:

1. At what odds would you stake your entire life possessions to say double up? (Try to give a monetary figure of what you are willing to risk and life position like single college student or retired millionaire.)

2. At what odds would you stake your entire poker bankroll to double up?

[InstaCall]

too much math in there..

[soon2bepro]

http://en.wikipedia.org/wiki/Kelly_criterion

Do the math for your example, and you find out that the best bet is 5% of your bankroll (of course this assumes you can adjust the bet to fit the value of 5% of your bankroll after every bet)

I know this isn't quite what you asked, but it should help.

[plexiq]

Interesting OP, just a few random thoughts on this,...:

We all know that, as long as we are betting within our bankroll, maximising EV is a valid approach. But as soon as you "step outside" this comfort zone, things are quite different.

What we all really seek to optimize is our "personal comfort". And, comparable to our equity in a tournament when winning/losing chips - our living comfort decreases faster when losing money, than it increases when winning the same amount.

eg:
The difference between possessing 1mio$ <->0.0$ has a much stronger impact on our life, than the difference between 2mio$<->1mio$.

As long as the stakes are small in comparison to our total possessions, the difference between maximising EV and maximising "personal comfort" is vanishing. In this case maximising EV (which is a lot easier to do) will be a sufficient approximation to maximising "personal comfort". But this no longer holds once we bet for such high stakes in comparison to our total possessions.

Lets try to formalize this a bit. Take some function mapping our possession in $ to a score describing our "living comfort".

living_comfort($possession)->living_score

Of course, this function will look different for every person. But generally, we can safely assume it is monotonic increasing. And, using the logic described above, the first derivative should be monotonic decreasing. I would even assume that its converging for possession->infinity. (Imagine Bill Gates to "double up". How much impact will that have on his life? Next to zero, i would think.)

So, lets say that living comfort converges towards max_score with possession->infinity:
max_score = lim living_comfort(x)|x->infinity

(If you have troubles to imagine such a function, f(x)=x/(1+x) should do for now.)

So, about the questions:
1. At what odds would i stake my entire life possessions?

Hum, i guess most of us here are well above the max_score/2 level. (If you picture some scale with someone w/o any possessions at the lower end, and then some multi-billionaire on the upper end of the scale, would you be in the upper 50% of this? As everyone here can take time off to play games on the internet, i think we are in the upper 50%.)

If we are, the answer is obviously: We never stake our entire life possessions. No matter the odds, we will not be able to double our comfort level, so this will be a losing play - regardless of the odds.

2. Depends a lot on the ratio of our poker bankroll to life possession.

In my case, losing my poker bankroll will hardly have any impact on my living standard, so i would probably just look to maximise EV here.

[PantsOnFire]

[ QUOTE ]
http://en.wikipedia.org/wiki/Kelly_criterion

Do the math for your example, and you find out that the best bet is 5% of your bankroll (of course this assumes you can adjust the bet to fit the value of 5% of your bankroll after every bet)

I know this isn't quite what you asked, but it should help.

[/ QUOTE ]
That's an interesting and mathematical way to look at this. Thanks for that.

I guess that once you exit the comfort zone for your bankroll, you are in essence really gambling and this becomes a personal comfort decision.

Here is a final corollary question which is somewhat related.

Three players left in a major tournament. First place is $1M, second is $600K and third is $200K. You have 500,000 chips, Player 2 has 500,000 chips and player 3 has 1,000 chips. The blinds are 500/1000 and player 3 folds on the button. Player 2 moves all-in and you have AA.

You obviously have at least second place locked up. If call and win this hand, you obviously have 1st place locked up. With AA you are at least an %80 favourite in the hand (barring another AA). So you are risking $400K to win $400 and this call is clearly +EV.

However, this relates to my OP. If $400K is many times your bankroll or even your life possessions, do you risk it to double it? I know most poker pros would insta-call but what about average Joe who got into this major tourney on a $100 satellite and is facing life-changing prize money?

Personally, I wait for Player 3 to bust out and then take a 50/50 shot at first place.