[baltostar]

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It doesn't matter if it is worth less than double your original stack. Just as in a rebuy, spending extra for double the stack can lower your roi and still be +$EV.

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The rebuy analogy doesn't work out. Here's why:

I can see a rational player choosing to rebuy/add-on to increase his $EV even if it reduces his expected ROI. He might do this because ROI is a very long-term concept but he needs a payoff soon (for whatever personal reason).

For rebuys to be $EV+ the player must be better than the avg player so that his $/utility/chip cost is less than that of the avg player.

But risking your stack is not the same as rebuying.

When you rebuy, your expected gain in stack utility per rebuy $ spent is very large. Not as large as your gain in stack utility per buyin $ spent, but still quite large (and if still in 1st level, the two are very close).

But when you risk your stack for a cEV of 0.1%, your expected gain in stack utility per effective $ spent is tiny.

Let's say you do this on the first hand: so effectively the $ risk of this play is your buyin. So, you are risking your buyin for an expected gain in stack utility of less than 0.1%.

(Less than 0.1% because for positive expectations, cuEV < cEV always, where cuEV = expected value of chip utility.)

Conclusion: The $/unit cost of expected gain in stack utility is far far higher for a marginal cEV+ allin than it is for a rebuy.


Interesting aside: for any allin play, your effective $/unit cost for expected gain in stack utility is astronomical compared to the real $/unit cost of the stack utility gained in your initial buyin. And this is why if tournaments allowed cashouts at any time at a $/chip rate equivalent to the initial buyin, no rational player would ever play a single hand.