Playing "half a scalp"

**Ganchrow** · 04-14-08, 12:27 PM

See my http://forum.sbrforum.com/handicappe...tml#post230201 for a precise solution to this problem and problems like it given any Kelly multiple.

Just set the original position "actual stake to 0", and then fill after line move probabilities and lines.

**HedgeHog** · 04-14-08, 12:29 PM

Originally posted by Justin7

You bet Pk +115 at a book where you know the line will be honored. Most of the world has both sides at Pk -110.

Do you scalp at -110, or keep your position? Assume your bankroll is large enough that the limits on the +115 is less than 2% of your bankroll.

Let the bet ride on its own--no hedge. Full Kelly on a +115 bet that has a 50% win probability is roughly 6.5%. And you're well below that bet size.

**Ganchrow** · 04-14-08, 12:33 PM

More to the point would be my Kelly Hedge spreadsheet, the usage of which is discussed in this thread.

**20Four7** · 04-14-08, 12:37 PM

If I bet it at say Pinny so the line will be honoured I'll just leave it. If I have no opinion and see the scalp opportunity I'll usually scalp. If further info comes to me during the day causing me to rethink my position I may hedge part or all of it depending. I have in college hoops rethought my position due to further info and "bought" out of my earlier bet.

**Justin7** · 04-14-08, 12:39 PM

Originally posted by HedgeHog

Let the bet ride on its own--no hedge. Full Kelly on a +115 bet that has a 50% win probability is roughly 6.5%. And you're well below that bet size.

Hedgehog went straight to the issue I wanted to focus on: estimating your win rate based on market prices.

Here's a bit tougher one:

The market price is Lakers +6.5. You find Lakers at +8. For this drill, assume the 7 and 8 hit 5%.

Would you take the other team at -6.5? Or if limits were high relative to your bankroll, would you max out the +8, and sell off some of the 6.5?

**Ganchrow** · 04-14-08, 12:46 PM

Originally posted by HedgeHog

Let the bet ride on its own--no hedge. Full Kelly on a +115 bet that has a 50% win probability is roughly 6.5%. And you're well below that bet size.

That line of thought is not correct in general. (Although it is in this case).

For example what if the max bet of the +115 were raised to 6% of bankroll? What you'd find is that even though 6% is less than the single bet Kelly stake of 6.522%, optimal strategy would nevertheless include a hedge (1.750% of bankroll at -110).

**Ganchrow** · 04-14-08, 12:48 PM

Originally posted by Justin7

Hedgehog went straight to the issue I wanted to focus on: estimating your win rate based on market prices.

Here's a bit tougher one:

The market price is Lakers +6.5. You find Lakers at +8. For this drill, assume the 7 and 8 hit 5%.

Would you take the other team at -6.5? Or if limits were high relative to your bankroll, would you max out the +8, and sell off some of the 6.5?

I believe this topic was discussed in detail in this thread.

The full-Kelly solution, btw, (obtained from the Kelly Hedge spreadsheet linked above and assuming no betting size contraints) would be 47.322% of bankroll for the +8 and 38.020% of bankroll for the hedge.

**HedgeHog** · 04-14-08, 01:34 PM

Originally posted by Ganchrow

That line of thought is not correct in general. (Although it is in this case).

For example what if the max bet of the +115 were raised to 6% of bankroll? What you'd find is that even though 6% is less than the single bet Kelly stake of 6.522%, optimal strategy would nevertheless include a hedge (1.750% of bankroll at -110).

Don't see the need to make a -EV bet with 1.75% of my bankroll. If I'm not comfortable with a bet near Full Kelly, I could bet something less and pass on the hedge.

**donjuan** · 04-14-08, 01:43 PM

HedgeHog,

The point of betting Kelly is to maximize expected growth, right? Ganchrow's solution does just that. Although counterintuitive, -EV hedges are often +EG.

**Ganchrow** · 04-14-08, 02:11 PM

Originally posted by HedgeHog

Don't see the need to make a -EV bet with 1.75% of my bankroll

What DJ said.

Originally posted by HedgeHog

If I'm not comfortable with a bet near Full Kelly, I could bet something less and pass on the hedge.

Just realize that at the less aggressive quarter-Kelly (with the same 6% of bankroll max bet), your optimal hedge would jump to about 5.507% of bankroll).

Remember that without wagering limits, optimal full-Kelly sizing given a pure arbitrage is determined without any regard to specific payout odds.

**HedgeHog** · 04-14-08, 03:05 PM

You're right about the arb situation and you need to take advantage of it-- up to 100% of bankroll if allowed.

However in your situation with the 6% limit, which is below full Kelly, wouldn't the guy who lets the entire 6% bet ride do better in the long run than the guy who sells off part at 1.75%? What would be the expected profit of each after say 100 trials?

**HedgeHog** · 04-14-08, 03:39 PM

Originally posted by Justin7

Hedgehog went straight to the issue I wanted to focus on: estimating your win rate based on market prices.

Here's a bit tougher one:

The market price is Lakers +6.5. You find Lakers at +8. For this drill, assume the 7 and 8 hit 5%.

Would you take the other team at -6.5? Or if limits were high relative to your bankroll, would you max out the +8, and sell off some of the 6.5?

Need a little more explanation. Was the Laker bet (+8) at -110? The current 6.5 market line on the fav-- is that at -110 or can you get say -105 (or less) elsewhere? Also, the 7 and 8 have a 5% shot each of hitting or is that a combined percentage? No betting restrictions, other than 100% of your bankroll?

**Ganchrow** · 04-14-08, 05:06 PM

Originally posted by HedgeHog

However in your situation with the 6% limit, which is below full Kelly, wouldn't the guy who lets the entire 6% bet ride do better in the long run than the guy who sells off part at 1.75%? What would be the expected profit of each after say 100 trials?

The EV after 100 bets of not taking the hedge would be 56.67%, while the EV after 100 bets of taking the hedge would be 44.74%.

But, unless you're risk neutral, the EV by itself of course rather irrelevant. The expected bankroll growth after 100 bets of not taking the hedge would be 27.43% (average growth of 0.2427% per bet), the expected bankroll growth after 100 bets of taking the hedge would be 29.21% (average growth of 0.2566% per bet).

Key to managing one's money as an advantage player is shifting from an EV-centric view of staking to a more growth-oriented outlook.

**Ganchrow** · 04-14-08, 05:11 PM

Here's how I took at:

Originally posted by HedgeHog

Need a little more explanation. Was the Laker bet (+8) at -110? The current 6.5 market line on the fav-- is that at -110

Yes and yes.

Originally posted by HedgeHog

or can you get say -105 (or less) elsewhere?

No.

Originally posted by HedgeHog

Also, the 7 and 8 have a 5% shot each of hitting or is that a combined percentage?

No. They each hit at 5%.

Originally posted by HedgeHog

No betting restrictions, other than 100% of your bankroll?

Correct.

If you clear you cache my Kelly Hedge spreadsheet is set up with all the values needed to solve this particular problem as phrased.

**HedgeHog** · 04-14-08, 06:26 PM

Ganch:

Someone else apparently did the work: I went to the spreadsheet and found this:

Bankroll $100,000.00
Kelly Multiplier 1

Position Decimal Odds 1.9091
Position Risk $47,321.91
Position Win $43,019.92
Win Prob 55.00%
Push Prob 5.00%
Loss Prob 40.00%
Edge 10.00%
Max Bet $100,000.00

Cur Opp Decimal Odds 1.9091
Rec. Hedge $38,019.92
Hedge Win $34,563.56
Win Prob 50.00%
Push Pron 0.00%
Loss Prob 50.00%
Edge -4.55%
Max Bet $100,000.00

Outcome Probabilities $ Result
Pos Win/Hedge Lose 50.00% $5,000.00
Pos Lose/Hedge Win 40.00% -$12,758.35
Pos Push/Hedge Push 0.00% $0.00

Pos Win/Hedge Push 0.00% $0.00
Pos Push/Hedge Win 5.00% $34,563.56

Pos Lose/Hedge Push 0.00% $0.00
Pos Push/Hedge Lose 0.00% $0.00

Pos Win/Hedge Win 5.00% $77,583.48
Pos Lose/Hedge Lose 0.00% $0.00

PS If I understand this correctly, then 47.3% of your bankroll should be on LA +8 while 38.0 % would be on the Fav -6.5???

**Ganchrow** · 04-14-08, 06:54 PM

Originally posted by HedgeHog

Ganch:

Someone else apparently did the work:

Yes, I entered the relevant values into the spreadsheet in order to demonstrate the solution.

Originally posted by HedgeHog

I went to the spreadsheet and found this:

Originally posted by HedgeHog

PS If I understand this correctly, then 47.3% of your bankroll should be on LA +8 while 38.0 % would be on the Fav -6.5???

Yes, as noted in this post, that is indeed the full-Kelly solution assuming wagering limits do not bind.

**Arilou** · 04-16-08, 12:50 PM

One note I'd make is that all this math assumes that the line we found has no bearing on what's going to happen in the game - the standard line is presumed correct. Even though this is a reasonably safe thing to assume in many situations, it isn't always the case.