I have been thinking about bankroll management a lot leading up to the WSOP this year. Most bankroll calculators use Kelly Criterion which assumes you can move up and down in stakes marginally with no change in ROI. Of course this is not even close to true. For the $1500 WSOP tourneys you can't move down to a similar tourney in terms of ROI and entrant size but lower buyin. Your only real option in moving down is to reduce your relative stakes by selling action or getting a backing deal. And there is nowhere to go to the upside, because ROIs go down as we go up in stakes from here except for a handful of the field.

I think in this case Risk of Ruin calculations are more applicable.

Anyway the guy in this thread made a simulation program
http://forumserver.twoplustwo.com/19...lator-1091724/

I input the payout structure of the opening weekend $1500 from last year and what I think to be a realistic distribution of finish positions, gradually going from 2.3 times more likely to win to 1.2 times to mincash than the normal distributed breakeven "average" player.

Sims 10000.000000
BuyIn 1500.000000
BR (in Buyins) 300.000000
ROI % 66.250760
SD 27019.189471
Trad. Ruin % 29.372132
Iter. Ruin % 5.101826
Sim. Ruin % 4.630000
Sim. Win % 95.370000


So that player would have a 14% ITM (10% payout structre) and 66% ROI but would have a 5% percent chance of running through a $450k bankroll (before they get to $1.5 million in profit) if that was all they played.


I will post a few more Simulations after I run them.


Finish Dist% in spoiler for those who might want to suggest better ones

Some fascinating #s imo:

Selling 50% at 1.2 with 45k bankroll = $642 avg profit/tourney and 26% chance of going broke

BuyIn 600.00000
BR (in Buyins) 75.00000
ROI % 107.81345
SD 13515.94292
Trad. Ruin % 72.70979
Iter. Ruin % 26.21671
Sim. Ruin % 26.83000



Selling 65% at 1.2 with 45k bankroll = $543 avg profit/tourney and 1.2% chance of going broke

Sims 10000.000000
BuyIn 330.000000
BR (in Buyins) 136.363636
ROI % 164.464739
SD 9465.861958
Trad. Ruin % 57.975998
Iter. Ruin % 1.228852
Sim. Ruin % 1.140000
Sim. Win % 98.860000

So the hypothetical player with 45k bankroll and 66% ROI has is 2600% more likely to go broke but only makes 14% more money selling 50% instead of 65%

And for the other side of the transaction to invest in this player (and many clones of them):

Sims 10000.000000
BuyIn 360.000000
BR (in Buyins) 555.555556
ROI % 38.542244
SD 5401.963298
Iter. Ruin % 4.130548
Sim. Ruin % 4.240000

With a 200k bankroll you would have a 4% of going broke before getting to 1.5 mill buying a bunch of 20% pieces ($360)

Thanks for doing all this work, really fascinating stuff.

Can you elaborate on the difference between these please?

Trad. Ruin % 72.70979
Iter. Ruin % 26.21671
Sim. Ruin % 26.83000

Are these supposed to be the same player with respect to ROI and SD? Looks like the numbers are different for those.

Trad Ruin % = Traditional risk of ruin
It seems to me that the script might be calculating this wrong but it doesn't matter because the whole point of the program is to not calculate it this way. This is because our finish distributions as winning players are not normally distributed, which the Traditional formula assumes. For example our 66% ROI player would have to finish in each position 1.84 times (not 1.66 due to rake) more likely than a breakeven-minus-rake "normal" player. While we can agree ROIs of 66% are possible in large field MTTs, nobody has ever cashed 1.84 times the payout ratio (would correspond to 26% ITM on Stars longterm). And since we have an edge for the entirety of thee tourney it stands we "should" finish it each spot a little more often than the previous spot. which takes us to

Iter. Ruin= Iterative Risk of Ruin %

I don't fully understand this one so I'll just quote
Sim Ruin%= Simulated Risk of Ruin%

This just takes the distribution of finishes % we put in and picks randomly a finish position according to those %s. It continues to do this until your bankroll hits 0 or hits your "winning" number. Which I just arbitrarily set to $1.5 million. Sim Ruin % equals the % times it hits 0 first.

Yes for both these players I used the same overall ROI and finish distributions from the underlying $1500 tournament. The numbers in the output are the ROIs on the money the player invests in himself. They are so different because the player selling 65% only has to put up $330 while the 50% seller has to invest $600 in himself. The standard deviation is affected by the same phenomenon.

I just adjusted each payout $ amount to account for what each player can win for himself. For example the 50% seller gets $390,699 for winning and the 65% seller gets $273,489.

Its easier to compare the sellers' 2 choices using avg profit/ tourney because the ROI # gets skewed as people sell a higher % of action. For example a player freerolling the WSOP for 20% of himself has an infinite ROI even if he is a losing player. But everyone will have a lower average profit the more action they sell.

i dont fully understand these calculations you are doing, yet i appreciate the work you are putting in. the numbers do seem fascinating, even with my limited grasp of them.

good luck in vegas

ok thanks

Interesting... Does the risk of ruin change proportionally with the size of the bankroll.

For example if the player has a 90k bankroll do they have half the chance of going broke or is it less because of the extra amount of buyins

While this is very interesting in theory, we can't enter $1.5k WSOPs year-round nor make them our sole form of income. So I'm all for taking shots and keeping a larger % of myself even if it gives me a high theoretical risk of ruin since there are only a finite number of $1.5k's each summer. Then I can just bust my ass a little harder at online stuff if I do poorly.

I guess things would be different if I weren't so overrolled for online play, or if mid-high stakes MTTs required a bigger roll. Like, I only need a $50k roll to play a $80-$100 ABI at small field online MTTs/low-midstakes cash games. But then I step into the live arena and I'm technically not rolled for even the lowest of WSOP tourneys.

My guess is that the relationship isn't linear and that the chance of the 90K guy being ruined is much less than half the chance of the original 45K guy. But that is a total guess on my part, based solely on hazy, long-ago-formed intuition.

gl with that 50k Roll, pretty sure your risk of Ruin is much much higher than you expect.

@op

Great work, did you do it with Excel or did you code something yourself? Would you make this public ? That would be awesome!

I have more than 50k, but I'm pretty confident that's an adequate roll for $90 ABI with an avg field size of 300 especially given my edge over the fields

That's what I thought as well

How did you decide on a SD of 27,019?

Probably from a combination of finish distribution, prize structure, and assumed ROI. You input your data into the function, run it through the program, and it calculates everything for you.

No I just used the program that is linked to in the OP. I didn't do any programming myself. I just used Excel to calculate my expected finish distribution %. Its 100% free, just go to my links in the first post.

The problem is if you take 100% of yourself at the WSOP on a $50k roll (even if that is just an effective roll that wouldn't be comfortable having a nonzero chance of going through) is that so much of your expected profit and expected peak downswing for the year will happen during this month. Your basically gambling that you won't have an online downswing soon after leaving Vegas.

If you sandwich a couple median WSOPs (i.e. iirc losing >15k is the median result playing all the low WSOP stuff) between a bad run online in the 10 months in between you could easily run thru 50k especially if expenses are coming out of that. I'm sure you know what is possible even in 300 person fields.

taking 100% of your action on a 90k roll and 65% ROI

Sims 1000.00000
BuyIn 1500.00000
BR (in Buyins) 60.00000
ROI % 66.25076
SD 27019.18947
Iter. Ruin % 55.14995
Sim. Ruin % 54.70000
Sim. Win % 45.30000

Same thing on a 45k roll

Sims 1000.00000
BuyIn 1500.00000
BR (in Buyins) 30.00000
ROI % 66.25076
SD 27019.18947
Iter. Ruin % 74.26301
Sim. Ruin % 73.90000
Sim. Win % 26.10000

Simulations using a similar simulation program (that calculates median profit and other stats related to MTTs) but with the same inputs. Using 20 as the number of WSOP events played. First number is $ if average buying is 1500, 2nd number is in # of buyins



Simulations 10000.00000 10000.000000
Tournies per Sim 20.00000 20.000000
BuyIn 1500.00000 1.000000
ITM % 13.82000 13.820000
ROI % 66.25076 66.250760
SD 27019.18947 18.000605
Worst Profit -30000.00000 -20.000000
CI Lowerbound -13556.00000 -9.037333
Avg. Profit 21159.92160 14.106614
Median Profit -12395.00000 -8.263333
CI Upperbound -11456.00000 -7.637333
Best Profit 1272806.00000 848.537333
Longest OOTM Streak 20.00000 20.000000
Longest ITM Streak 4.00000 4.000000
% Finishes with Loss 70.00000 70.000000

this is intriguing. thanks for posting.

For those asking he is saying the traditional risk of ruin finish distribution would look something like this:



Basically you have an equal chance of finishing in the top 25% and the lowest 25% which is a gross oversimplification of any poker player's finishing distribution (winner or loser) so you can ignore that number.

As the bankroll increases the risk of ruin will exponentially decrease. We are assuming said player has an edge.

Lets say there's a 40% chance you're stuck at the end of each week of grinding.

1 weeks in a row 40%
2 weeks in a row .4 x .4 = 16%
3 in row .4 x .4 x .4= 6.4%

Because you're always more likely to win than loose, it gets exponentially harder go broke the bigger your allowed sample size (bankroll).