This is what I am getting at: precisely calculating your (estimated) risk of ruin.
Why?
This is a hugely important calculation, because you must accept the risk to accept responsibility for your results.
I believe we may all reasonably agree that to be able to accept the risk, you must first know the risk. Specifically, you MUST know your risk of ruin. If accurately estimating your RoR is impossible in poker, then accepting responsibility for all your results in poker is also impossible. This risk-acceptance issue is actually a Psych Forum issue, and to address it, RoR must first be determined.
I'm calling on all probability experts on this Forum to help me solve this problem of defining a specific problem: tournament poker RoR. It’s a function of estimating the following player info:
per-session probability of winning,
the average win per session,
the average loss per session, and
the bankroll size.
Let’s say the game is a weekly rebuy tournament where it costs $40 to play and $20 to rebuy. You can rebuy during hour #1 if your chips fall below 50% of the starting chip count.
Let’s say you have a stop-loss rule of $80 per session: if you rebuy twice on top of the $40 ($40+$20+20) and you lose all your chips, you exit the event, EVEN IF it is during the 1st hour when you could rebuy again. Downside risk is thus precisely defined at a max of $80 per session.
Let’s say you have $2000 of bankroll to start with.
Further let’s say you have 30 observations of playing sessions, with wins and losses, as follows:
1 -$40.00
2 -$40.00
3 -$60.00
4 $60.00
5 -$60.00
6 -$80.00
7 -$100.00
8 $960.00
9 -$60.00
10 -$60.00
11 $300.00
12 -$40.00
13 -$60.00
14 -$80.00
15 $150.00
16 -$40.00
17 -$60.00
18 -$40.00
19 $200.00
20 -$40.00
21 $500.00
22 -$40.00
23 -$40.00
24 -$80.00
25 -$60.00
26 -$40.00
27 -$40.00
28 -$40.00
29 -$40.00
30 -$40.00
$890.00 (+)
What’s your estimated RoR? HOw does it change if you make the stop loss $60 or $100 instead of $80?
With these observations you can calculate risk of ruin for various bankroll sizes. And by sizing the bankroll, you can adjust RoR to a RoR-probability acceptable to you, if that probability is not currently acceptable.
Correct? Is 30 enough observations to construct a valid RoR estimate? Is using the last 30 ("rolling") observations the right approach, to incorporate subtle changes in the game and your play in it, over time?
Those interested in solving this problem may be interested in this paper, which discusses achieving these goals in another game of probabilities-- trading.
Position Sizing
http://www.traderscalm.com/psizinginterview.html
Thanks in advance for those who find this an interesting probability problem, and post some answers to this tournament RoR question.
If I have not provided enough info please post that. I believe 30 observations is enough to get it right in terms of a valid estimate of RoR.