Tuesday, May 30, 2006

Bubble insurance

Hmmm, a 3 post day. I'm really bored.... (I'm running some tests that are taking hours to complete...)


Apparently there is a new promotion running at Hollywood Poker that offers protection for players in the 2006 WSOP main event if they bust in the last 5 positions before the bubble bursts. It doesn't matter how you get your seat for the Main Event, the qualifier for the insurance is to earn 1500 Poker Points. Given the small/medium stakes LHE games I play, this probably works out to about 1000-1200 raked hands. Averaging 2 short handed tables, this is close to about 7 hours of effort.

How would you estimate the value of this insurance (to justify the time investment)? I assume the most beneficial situation the insurance would provide for is if you have a stack with an M around 3-6. Other stack sizes obviously benefit, but my feeling is that players with modestly low Ms get the most bang for the buck. With this insurance, you can open push almost 100% of the time during the bubble+5 -> ITM until you either get to a slightly healthier M (perhaps ~10) or bust.

All things being equal (in terms of the calling standards of your opponents), the number of times you will have the opportunity to steal the blinds is simply proportional to the number of hands that will be dealt in the bubble+5->ITM period.

Assuming a field of ~8000 entrants and top 10% paid, then the bubble would hit at the ~800 player mark. Thus hand-for-hand bubble play would involve 80+ tables.

I imagine that time-wise, the bubble period is pretty long. In terms of number of hands played, it may be pretty small, given 80 tables in play. What is a reasonable estimation on the number of hands this will be?

Naturally you need to avoid letting anyone at your table know you are carrying this insurance policy.... (Given that I have a big mouth, I would need to remind myself to zip it...)

I guess another situation this has significant value is if you are in the dead zone (M ~1) at the bubble + ~10 mark. If card dead, you might be able to play like Broomcorn's uncle to make it to your artificial bubble.

Again, how can you translate these potential situations into a present value?

Basically the value is composed of two parts: 1) value gained given the percentage of the time that you would have busted without the insurance. 2) net value gained by building a larger stack because you have a license-to-steal (NET value because the probability of busting is much higher).

These are my current assumptions:
- my probability to reach the bubble zone is 10%.
- bubble + 5 -> ITM lasts 2 orbits
- Stack size distribution:
--- 5% of the time I have an M < 1 at bubble + 10
--- 70% of the time I have an M of <6
--- 20% of the time I have an M of 6-20
--- 5% of the time I have a very healthy stack.
- For each of the 4 stack size distributions, there should be 4 numbers estimated: i) probability of busting OOTM given you have no insurance, ii) probability of busting OOTM given you have insurance, iii) increased tournament equity due to increased blind/ante stealing, iv) tournament equity lost by busting OOTM (due to larger risk taking from insurance)
- For each of the 4 stack size distributions these are my estimates for those 4 numbers:
--- M < 1 at bubble + 10: 95%, 95%, $0, $0
--- M of <6: 25%, 50%, $2000, $0
--- M of 6-20: 15%, 35%, $1000, $2000
--- very healthy stack: 5%, 10%, $500, $4000

Punching these numbers into excel yields a value for the insurance at $468. (Close to an hourly rate of $66/hr assuming 7 hours to earn enough points to qualify). The one assumption that has a dominating effect on the estimate is the probability of reaching the bubble zone. 10% is very very optimistic. Perhaps 5% is a better number. Even then $234 of value is worth the time investment given the stakes I play at.


One other thought on bubble play relates to my understanding that Harrah's (Binion's) traditionally gives the bubble boy a free roll into the following year's WSOP main event. Assuming this is the case and considering the point of view of satellite qualifiers to the main event who reside in the retarded-taxation-on-recreational-gambling-USofA, getting a freeroll into the 2007 WSOP is worth almost $3k more than a ~$12.5k bottom tier cash (when taxes are taken into consideration). Thus with any stack with an M less than 3, I think I would jam 100% of the time on every hand regardless of the action in front of me on the real bubble, insurance or not. (actually even more so with the insurance since finishing on the bubble is worth much more than finishing with a tier 1 payout; closer to the payout for top 5% of the field; better check the T&C at Hollywood, maybe they don't cover the true bubble boy because of that loophole)

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