Kelly betting for Wong teasers

[TomCowley]

I've searched, and I can't find anything on the web. If somebody has actually worked this out already, great, but here's my hack at it for low numbers of games. It has some VERY interesting results. I assume all teased games have a constant win percentage, are independent, and treat all outcomes as either win or loss (ties being pushes, reduced-team teasers, etc, are not accounted for at all- this means my numbers will be too low).

First, for 2 games, there's only one bet, and it breaks down as follows (% of teased games that win, odds on the teaser, % of bankroll to bet, and the expected bankroll growth for +100 and -110):

Win% +100 -110 Growth%
73% 6.58 1.90 .217/.0166
74% 9.52 4.99 .455/.113
75% 12.5 8.12 .786/.301

For 3 games, there are 4 bets- 3 2-team teasers and 1 3-team teaser. These break down as follows:

Win% +100/+180 -110/+180 Growth%
73% 3.64/0 0/4.96 .358/.218
74% 5.29/0 0/7.48 .773/.496
75% 6.98/0 0/10.1 1.31/.896

In this case, optimal strategy depends completely on the odds for the 2-teamer. For +100, the win% would have to rise to 85% (ridiculous) before betting the 3-teamer ever becomes correct. For -110, it's flat wrong to bet any 2-teamers, and this is true for all profitable win%.

For 4 games:

Win% +100/+180/+300 -110/+180/+300 Growth%
73% 2.51/0/0 0/1.91/0 .494/.334
74% 3.66/0/0 0/2.91/0 1.04/.760
75% 4.81/0/0 0/3.94/0 1.80/1.38

Again, at +100, it's completely wrong to bet the 3-4 teamers. The win % needs to be 83% (3) or 80% (4) to make these bets correct. And again, unsurprisingly, at -110 it's never correct to bet the 2-teamers. What's interesting is that it is correct to only bet the 3-teamers at this range of win%. At slightly lower (below 72.8%) and ridiculously high (above 87.8%), betting the 4-teamer as well is correct.

5 games:

Win% 100/180/300/465 -110/180/300/465 Growth%
73% 1.92/0/0/0 0/.598/.585/0 .628/.490
74% 2.78/0/0/0 0/1.56/0/0 1.32/1.02
75% 3.65/0/0/0 0/2.12/0/0 2.29/1.85

The behavior here is similar. With access to +100, the higher-level teasers don't come into play until 78% win percentage. With a small edge, the 4-team teaser makes an appearance, but isn't played for bigger estimated edges. The 5-team teaser isn't played until a ridiculously high win%.

Exact solutions to higher numbers of games are intractable with the (lame) mathematical tools I have available.

Edit: UBB formatting is [censored] ridiculously horrible, tab and multiple spaces are just eaten up.

[Thremp]

Tom,

I asked this a few days back.

http://forum.sbrforum.com/players-ta...ed-wagers.html

Seems the conclusion is the same. Seems my guesses for 2/3 teamers were actually correct. Only quibble is win %s. But that is up for debate as well since the sample size is rather small.