A S&G Parlay Strategy

[Daxonovitch]

Hi - Many of you have already talked about this at length with me on IRC, but I was interested to see if there are other thoughts involved with some other people.

I know this is going to be somewhat dry and complex, but I think that the resulting discussion (and computer analysis) should be insightful for those trying to make quick money: ie, increasing variance while lowering EV. Only the intelligent need continue. [img]/images/graemlins/smile.gif[/img]

Recently, I was given the opportunity to go to Foxwoods for the WPF (for the $200 multi-play event). I estimated that I would need $1500 for expenses and buy-ins, none of which I *expect* to get back as this is an "experience" trip.

I am rebuilding a bankroll, typically having played $50 and $100 S&Gs. It is (was) currently $800. I had *two* days to decide on whether or not I'd be able to go on the trip, so.. I started thinking of a strategy to make this feasable.

VOCABULARY:

A "typical" game is the game that I can afford 30 times the buyin for. For example, if I have $990 or more, I play $33 S&Gs. If I have $660 or more, I play $20s. The lowest level I will play is $10.

The "watermark" is the level that I start the day with (in this case, $800).

The "parlay" is the single table tournament whose buyin is greater than a "typical" game.

RULES:

I can play 50 S&Gs in one day.

I would like to end the day with $2300 or $800 (or less, provided losses are from "typical" games). That is to say, the only definition of "success" lies in making $1500 in the day. I am willing to make $0 if I have any probability of making $1500, however I am *NOT* willing to lose all of the $800. I am also extremely hesitant of losing any of the $800 (again, aside from losses to "typical" games).

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Now, the question is this: *what* is the optimal strategy for accomplishing this within the above guidelines? I would like to hear some ideas on the topic, but I will share my strategy first:

Play a typical game. Let's say it was a $33. If you are above the watermark before the game started, and you win 1st place (+$117), play the largest level you can with those winnings without a negative sum for the two events - in this case, a $109 would be acceptable. This is termed the "parlay" game. In any parlay game, should I win *1st* place, I continue the parlay to the next highest level that I could afford. If I win 2nd or 3rd, the parlay is over and I continue with SNGs at the "typical" level.

Example:

$800: play a $22, BR $778 "typical"
: lose -> $778

$778: play a $22, BR $756
: win 1st -> $856 *PARLAY*

$856: play a $55, BR $801
: win 1st -> $1051 *PARLAY*

$1051: play a $215, BR $846
: lose -> $846 (parlay ends here)

$846: play a $22 "typical"

And so on and so forth. Basically, you are sacrificing your ROI/EV in these events by cutting your first place wins to almost nothing. Let's say you're a 23% ROI player, with these stats for 1st, 2nd, 3rd:

1st: 0.1631
2nd: 0.1245
3rd: 0.0858

(incidentally, these are my stats for $30 S&Gs). I can see that my EV is:

($150 * .1631) + ($90 * .1245) + ($60 * .0858) =
24.465 + 11.205 + 5.148 =
$40.818

$40.818 divided by $33 gives 23.6%, which is the definition of ROI. However, let's say that my first place win in a $30 goes to a $109 event, making the actual first place win $150-109 = $41. My new ROI/EV is:

($41 * .1631) + ($90 * .1245) + ($60 * .0858) =
6.6871 + 11.205 + 5.148 =
$23.0401

Now, my ROI is actually NEGATIVE, since for every $33 I plunk down, I'm expecting about $23 back, for a loss of ten bucks. However, it's fairly obvious to see that should I win the $109, I'm up quite a bit. Hence, I've succeeded in lowering my ROI while increasing my variance at (hopefully!) little risk.

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I know that was a little bit Sklansky-esque to get through (sorry, DS!), but if you've made it this far, here is where we get to the fun stuff. What is the optimal strategy for a parlay to make quick money with the above guidelines? There are a few assumptions to think about here, too. Namely, I'm a winning player at all limit S&Gs. Since the math will change the constants to some minor degree in a given strategy, let's assume that I'm about 12% for 1st, 2nd, 3rd at *all* levels of S&Gs. This should simply things greatly (while probably somewhat untrue as the higher level buyins are lower ROI). If you really want to be nitpicky, we can use 10% for a -9% ROI (minus rake).

I'm currently writing a computer program to test various strategies (starting with my own) and am willing to implement anyone's strategy who responds to this post in an intelligent manner and post their results (including the: % success - making $2300, % failure - making less than $2300, and % loss - losing money under the water mark).

As a theoretical bonus question, assume that you have no data on the $200 S&G level. Personally, I do not have enough data to be considered relavent (although I do have a [censored]-eating-grin ROI of nearly 50%) but you feel that you should at least be breakeven. Does the strategy change?

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As a postscript, I succeeded in my quest, and will be going to Foxwoods to play in the $200 multi-play event. [img]/images/graemlins/cool.gif[/img]