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).

---

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.

--

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?

--

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]

[Daxonovitch]

Program is almost complete. Here's an example of "one run" for review. This was a failure in that I "played" 50 sngs, and didn't manage to make the $1500:

Playing a $22 game, bankroll is $800: 4 place, prize: +$0.
Playing a $22 game, bankroll is $778: 3 place, prize: +$40.
Playing a $22 game, bankroll is $796: 4 place, prize: +$0.
Playing a $22 game, bankroll is $774: 4 place, prize: +$0.
Playing a $22 game, bankroll is $752: 3 place, prize: +$40.
Playing a $22 game, bankroll is $770: 4 place, prize: +$0.
Playing a $22 game, bankroll is $748: 4 place, prize: +$0.
Playing a $22 game, bankroll is $726: 1 place, prize: +$100.
Playing a $22 game, bankroll is $804: 4 place, prize: +$0.
Playing a $22 game, bankroll is $782: 3 place, prize: +$40.
Playing a $22 game, bankroll is $800: 1 place, prize: +$100.
Playing a $22 game, bankroll is $878: 3 place, prize: +$40.
Playing a $22 game, bankroll is $896: 4 place, prize: +$0.
Playing a $22 game, bankroll is $874: 4 place, prize: +$0.
Playing a $22 game, bankroll is $852: 1 place, prize: +$100. Parlay!
Playing a PARLAY $55 game, bankroll is $930: 3 place, prize: +$100.
Playing a $22 game, bankroll is $975: 4 place, prize: +$0.
Playing a $22 game, bankroll is $953: 3 place, prize: +$40.
Playing a $22 game, bankroll is $971: 4 place, prize: +$0.
Playing a $22 game, bankroll is $949: 4 place, prize: +$0.
Playing a $22 game, bankroll is $927: 4 place, prize: +$0.
Playing a $22 game, bankroll is $905: 4 place, prize: +$0.
Playing a $22 game, bankroll is $883: 4 place, prize: +$0.
Playing a $22 game, bankroll is $861: 3 place, prize: +$40.
Playing a $22 game, bankroll is $879: 4 place, prize: +$0.
Playing a $22 game, bankroll is $857: 4 place, prize: +$0.
Playing a $22 game, bankroll is $835: 3 place, prize: +$40.
Playing a $22 game, bankroll is $853: 4 place, prize: +$0.
Playing a $22 game, bankroll is $831: 2 place, prize: +$60.
Playing a $22 game, bankroll is $869: 4 place, prize: +$0.
Playing a $22 game, bankroll is $847: 2 place, prize: +$60.
Playing a $22 game, bankroll is $885: 3 place, prize: +$40.
Playing a $22 game, bankroll is $903: 4 place, prize: +$0.
Playing a $22 game, bankroll is $881: 4 place, prize: +$0.
Playing a $22 game, bankroll is $859: 4 place, prize: +$0.
Playing a $22 game, bankroll is $837: 4 place, prize: +$0.
Playing a $22 game, bankroll is $815: 1 place, prize: +$100. Parlay!
Playing a PARLAY $55 game, bankroll is $893: 4 place, prize: +$0.
Playing a $22 game, bankroll is $838: 4 place, prize: +$0.
Playing a $22 game, bankroll is $816: 1 place, prize: +$100. Parlay!
Playing a PARLAY $55 game, bankroll is $894: 3 place, prize: +$100.
Playing a $22 game, bankroll is $939: 1 place, prize: +$100. Parlay!
Playing a PARLAY $55 game, bankroll is $1017: 4 place, prize: +$0.
Playing a $22 game, bankroll is $962: 4 place, prize: +$0.
Playing a $22 game, bankroll is $940: 4 place, prize: +$0.
Playing a $22 game, bankroll is $918: 4 place, prize: +$0.
Playing a $22 game, bankroll is $896: 4 place, prize: +$0.
Playing a $22 game, bankroll is $874: 4 place, prize: +$0.
Playing a $22 game, bankroll is $852: 4 place, prize: +$0.
Playing a $22 game, bankroll is $830: 4 place, prize: +$0.

You failed. You played 50 and ended up with $808


Here's a success:

Playing a $22 game, bankroll is $800: 4 place, prize: +$0.
Playing a $22 game, bankroll is $778: 4 place, prize: +$0.
Playing a $22 game, bankroll is $756: 4 place, prize: +$0.
Playing a $22 game, bankroll is $734: 4 place, prize: +$0.
Playing a $22 game, bankroll is $712: 1 place, prize: +$100.
Playing a $22 game, bankroll is $790: 3 place, prize: +$40.
Playing a $22 game, bankroll is $808: 4 place, prize: +$0.
Playing a $22 game, bankroll is $786: 4 place, prize: +$0.
Playing a $22 game, bankroll is $764: 4 place, prize: +$0.
Playing a $22 game, bankroll is $742: 4 place, prize: +$0.
Playing a $22 game, bankroll is $720: 4 place, prize: +$0.
Playing a $22 game, bankroll is $698: 3 place, prize: +$40.
Playing a $22 game, bankroll is $716: 4 place, prize: +$0.
Playing a $22 game, bankroll is $694: 4 place, prize: +$0.
Playing a $22 game, bankroll is $672: 4 place, prize: +$0.
Playing a $11 game, bankroll is $650: 4 place, prize: +$0.
Playing a $11 game, bankroll is $639: 1 place, prize: +$50.
Playing a $22 game, bankroll is $678: 4 place, prize: +$0.
Playing a $11 game, bankroll is $656: 4 place, prize: +$0.
Playing a $11 game, bankroll is $645: 3 place, prize: +$20.
Playing a $11 game, bankroll is $654: 2 place, prize: +$30.
Playing a $22 game, bankroll is $673: 2 place, prize: +$60.
Playing a $22 game, bankroll is $711: 4 place, prize: +$0.
Playing a $22 game, bankroll is $689: 1 place, prize: +$100.
Playing a $22 game, bankroll is $767: 2 place, prize: +$60.
Playing a $22 game, bankroll is $805: 1 place, prize: +$100. Parlay!
Playing a PARLAY $55 game, bankroll is $883: 1 place, prize: +$1000. Parlay!
Playing a PARLAY $215 game, bankroll is $1828: 2 place, prize: +$600.
Playing a $55 game, bankroll is $2213: 2 place, prize: +$150.

You did it! Your final bankroll is $2308. It took you 29 S&Gs to do it.


And finally, here's a LOSS:

Playing a $22 game, bankroll is $800: 4 place, prize: +$0.
Playing a $22 game, bankroll is $778: 4 place, prize: +$0.
Playing a $22 game, bankroll is $756: 4 place, prize: +$0.
Playing a $22 game, bankroll is $734: 4 place, prize: +$0.
Playing a $22 game, bankroll is $712: 4 place, prize: +$0.
Playing a $22 game, bankroll is $690: 4 place, prize: +$0.
Playing a $22 game, bankroll is $668: 2 place, prize: +$60.
Playing a $22 game, bankroll is $706: 2 place, prize: +$60.
Playing a $22 game, bankroll is $744: 4 place, prize: +$0.
Playing a $22 game, bankroll is $722: 4 place, prize: +$0.
Playing a $22 game, bankroll is $700: 3 place, prize: +$40.
Playing a $22 game, bankroll is $718: 4 place, prize: +$0.
Playing a $22 game, bankroll is $696: 4 place, prize: +$0.
Playing a $22 game, bankroll is $674: 1 place, prize: +$100.
Playing a $22 game, bankroll is $752: 1 place, prize: +$100.
Playing a $22 game, bankroll is $830: 4 place, prize: +$0.
Playing a $22 game, bankroll is $808: 3 place, prize: +$40.
Playing a $22 game, bankroll is $826: 2 place, prize: +$60.
Playing a $22 game, bankroll is $864: 1 place, prize: +$100. Parlay!
Playing a PARLAY $55 game, bankroll is $942: 4 place, prize: +$0.
Playing a $22 game, bankroll is $887: 4 place, prize: +$0.
Playing a $22 game, bankroll is $865: 2 place, prize: +$60.
Playing a $22 game, bankroll is $903: 4 place, prize: +$0.
Playing a $22 game, bankroll is $881: 4 place, prize: +$0.
Playing a $22 game, bankroll is $859: 4 place, prize: +$0.
Playing a $22 game, bankroll is $837: 3 place, prize: +$40.
Playing a $22 game, bankroll is $855: 4 place, prize: +$0.
Playing a $22 game, bankroll is $833: 4 place, prize: +$0.
Playing a $22 game, bankroll is $811: 4 place, prize: +$0.
Playing a $22 game, bankroll is $789: 4 place, prize: +$0.
Playing a $22 game, bankroll is $767: 4 place, prize: +$0.
Playing a $22 game, bankroll is $745: 4 place, prize: +$0.
Playing a $22 game, bankroll is $723: 4 place, prize: +$0.
Playing a $22 game, bankroll is $701: 1 place, prize: +$100.
Playing a $22 game, bankroll is $779: 4 place, prize: +$0.
Playing a $22 game, bankroll is $757: 4 place, prize: +$0.
Playing a $22 game, bankroll is $735: 4 place, prize: +$0.
Playing a $22 game, bankroll is $713: 4 place, prize: +$0.
Playing a $22 game, bankroll is $691: 4 place, prize: +$0.
Playing a $22 game, bankroll is $669: 4 place, prize: +$0.
Playing a $11 game, bankroll is $647: 4 place, prize: +$0.
Playing a $11 game, bankroll is $636: 4 place, prize: +$0.
Playing a $11 game, bankroll is $625: 4 place, prize: +$0.
Playing a $11 game, bankroll is $614: 1 place, prize: +$50.
Playing a $11 game, bankroll is $653: 1 place, prize: +$50.
Playing a $22 game, bankroll is $692: 3 place, prize: +$40.
Playing a $22 game, bankroll is $710: 4 place, prize: +$0.
Playing a $22 game, bankroll is $688: 4 place, prize: +$0.
Playing a $22 game, bankroll is $666: 3 place, prize: +$40.
Playing a $22 game, bankroll is $684: 2 place, prize: +$60.

You really failed. In 50S&Gs, you ended up with $722, less than you started with!

[Daxonovitch]

C:\java>java ParlayTest
Strategy submitted by ChrisD

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.

Running ten million iterations of parlay.............Iterations complete!
Successes: 2121686 (21.216862%), average BR: $2539
Failures: 4981715 (49.81715%), average BR: $1245
Losses: 2896599 (28.96599%), average BR: $679
Furthermore, you ROR'd your bankroll 0 times, around 0.0% of the time.

--

Apologies for using RoR as a verb. [img]/images/graemlins/smile.gif[/img]

It looks like on average, my strategy succeeds around 21% of the time, "fails" with an ending bankroll of average $1245 (+445) around half the time, and loses around $120 another third of the time.

Overall, not bad.. Basically, we can extrapolate the EV as follows:

.2121 * 2539 + .4981 * 1245 + .2896 * 679 = <font color="red">$1355.29</font>

However, let's just say I played "$27.50" SNGs (halfway between 22 and 33), and since I'm too lazy to write a program to do the proper analysis, I assume $7.15 profit per SNG (26% ROI) - 50 S&amp;Gs yields +357.50, or an EV of <font color="red">$1157.50</font>.

Very interesting! It turns out that in a given run of 50 S&amp;Gs, my parlay strategy is actually *better* than grinding out the "typical" safe S&amp;Gs.. food for thought...

Anyone come up with any alternative parlay strategies yet or am I just a little too excited for responses yet? [img]/images/graemlins/smile.gif[/img]

[Daxonovitch]

As an addendum, I ran it again with "pure" numbers for a totally break even player. This player wins 1st place exactly 10% of the time, 2nd place exactly 10% of the time, and 3rd exactly 10% of the time. Obviously, as expected, the parlay is a generally unsuccessful venture:

Running ten million iterations of parlay.............Iterations complete!
Successes: 431441 (4.31441%), average BR: $2541
Failures: 2212970 (22.1297%), average BR: $1087
Losses: 7355589 (73.55589%), average BR: $609
Furthermore, you ROR'd your bankroll 0 times, around 0.0% of the time.

Obviously, however, since you are now a -ROI player (since the rake is 7.5-10%), it's not surprising that the gross majority of time you lose $200 bucks. Interestingly, however, 1 in 20 times you actually do make the goal of $2300.

[Daxonovitch]

I do apologize to those reading my nonstop posts, most of the discussion on this is going on in IRC. [img]/images/graemlins/smile.gif[/img]

Requested were my stats for SNGs as it does have a bearing on the outcome. The point is not so much WHAT the EV is (since that's going to depend on everyone's stats) but rather the comparison of the parlay strategy versus the grinder strategy.

Here are my stats:

// $10
c1[BUYIN_10] = .1961f; //chance of winning 1 in a $10
c2[BUYIN_10] = .0980f; //chance of winning 2 in a $10
c3[BUYIN_10] = .0980f; //chance of winning 3 in a $10

// $20
c1[BUYIN_20] = .1472f; //chance of winning 1 in a $20
c2[BUYIN_20] = .1015f; //chance of winning 2 in a $20
c3[BUYIN_20] = .1218f; //chance of winning 3 in a $20

// $30
c1[BUYIN_30] = .1631f; //chance of winning 1 in a $30
c2[BUYIN_30] = .1245f; //chance of winning 2 in a $30
c3[BUYIN_30] = .0858f; //chance of winning 3 in a $30

// $50
c1[BUYIN_50] = .1649f; //chance of winning 1 in a $50
c2[BUYIN_50] = .0825f; //chance of winning 2 in a $50
c3[BUYIN_50] = .1753f; //chance of winning 3 in a $50

// $100
c1[BUYIN_100] = .0943f; //chance of winning 1 in a $100
c2[BUYIN_100] = .1698f; //chance of winning 2 in a $100
c3[BUYIN_100] = .1509f; //chance of winning 3 in a $100

// $200
c1[BUYIN_200] = .1f; //chance of winning 1 in a $200
c2[BUYIN_200] = .1f; //chance of winning 2 in a $200
c3[BUYIN_200] = .1f; //chance of winning 3 in a $200

Since I have only played a small number of $200s, I put my stats in as 10% 10% 10% - a breakeven (but losing to the rake) player. Obviously this is a fair leap of logic, but I submit (not so humbly, I suppose) that I am a winning player, even at the $200 level, and my results *should* be higher.

[fiyah]

Hello,

I wanted to tell you that I find your strategy quite interesting and I will be using it this week. Thanks for sharing it.

[RacersEdge]

Interesting - sort of like a reverse Martindale(?) from Blackjack....don't have time to study it, but your 846 should be 836 in your original write-up..good luck with your strategy.

[Daxonovitch]

Oops, you're right. $836. [img]/images/graemlins/smile.gif[/img]

Yes, it is essentially a revised Martingale, but the fundamental difference between this and Martingale is you (assume you) are playing a +EV game - with Martingale, you essentially could not win over time. With even a 1% ROI, you *could* win if you played an infinite number of games. The question is more about "what strategy is correct".

I may take my computer program further to attempt some more complex analyses to maximize the fastest growth possible - ie, there may be situations in which it is actually profitable *over time* instead of just over a short run of 50 S&amp;Gs.

Depends on how much motivation I can get, playing the S&amp;Gs takes enough effort. [img]/images/graemlins/wink.gif[/img]

[stupidsucker]

RoI is RoI.

As long as you are a winning player at each level you are playing at then it doesnt matter if you play 100 20s then 100 30s then 100 50s.

but

as long as you leave yourself enough bankroll to play the lowest level safely then it just depends on how things go.

Luck is the main factor in how much money you make, but your strat is designed to make money faster. This should work for that, but it wont always work.

For anyone interested in making a lot of money fast with a larger risk at stake then this seems to work just fine. If you want a safer route then just stay at the proper BR and move up to each level acordingly.

Interesting post. You put a lot of time into it.

[fiyah]

Daxonovitch

Would you mind emailing me at t_phu@hotmail.com, I have a few questions I'd like to ask you.

Thanks