It’s the final furlong of a horse race, the betting market is chaotic, there are 7 seconds left and I find myself in the following position:
[ul]
[li]RunnerA has a 60% chance of winning, is currently priced at 2.0 and I currently stand to win $20 if it wins[/li][li]RunnerB has a 28% chance of winning, is currently priced at 3.2 and I currently stand to lose $100 if it wins[/li][/ul]
I have the options to back and to lay either runner.
Can anyone offer ideas for a formula that would equalize my positions?
If it helps any I’ve got a partial solution, or at least maybe something to work with. This formula equalizes liability as between the two runners - obviously I’m looking to equalize the relative liability (if that even makes sense!):
$20 + $100 = $120*
$120 / 2.0 = $60
$60 = the back stake on RunnerB
+/- are disregarded for this purpose
Fwiw, I did look at doing something with the back stake ($60 in this example), like using 60% of the $60, but I’m out of my depth to know if that’s logical.
I’d be surprised if a homework question featured horse racing and used so much of what I can only assume is betting jargon.
What does ‘priced at x’ mean in this situation? If you say that you ‘currently stand’ to those 2 outcomes, does that mean that you already have bets placed to that effect? Are A and B the only horses in the race, or is there a possibility that they both lose?
I assume that ‘backing’ the horse means betting that it wins - is ‘laying’ the horse ( ) betting that it will lose? In a two horse race, what’s the effective difference between betting on A to win or B to lose??
That’s correct. A parallel that sometimes works is the stock market. In my example one trade has gone against me (-$100) and the other has moved in my favour (+$20)
There are other runners, which is why the total risk associated with the two runners in question is only 88% - the other 12% refers to the chances of ‘the rest of the field’ winning.
Yes. Not always an easy concept to grasp.
Ximenean - Hi. I find it becomes interesting when you have the opportunity to back or lay, especially as whatever you do in relation to one runner impacts on the rest.
‘Lay x on A’ is exactly where I’ve go to (described in #2) - it seems to equalize the position as between the two at -$40
‘Bet x on B’ seems to go like this:
Position on RunnerA = 20 - 37.5 = -17.5
Position on RunnerB = -100 - (37.5 x 2.2) = -17.5
As you suggest, this is obviously the better outcome. If I can ask two questions:
Might there be a rule that determines when it is better to Lay than Back and vice versa?
‘Bet x on B’ is a good position but it does equalize the positions absolutely, that is it doesn’t take account the additional information (that RunnerA has a 60% chance of winning and RunnerB a 28% chance). Is it implausible to take things one step further and include in the formula the relative chances of winning?
I don’t have time to think about it much now, but I would observe that A is a good value bet, while B is a good lay (yes, it’s impossible to discuss these things without running into innuendos all the time ;)) – A’s odds of 2.0 imply a win probability of only 50%, compared to the actual probability of 60%. That’s a good bet, so a bad lay. Meanwhile, B’s odds of 3.2 imply a probability of 31.25%, but in reality it’s only 28%. A bad bet, so a good lay.
Since 28% is proportionally closer to 31.25% than 50% is to 60%, it seems to confirm that betting on B is less bad than laying A.
OK, if my algebra is correct, to calculate the expected return of a bet (what you get back for every dollar you bet), you take the real probability p (between 0 and 1, not percentage probability) and the decimal odds o. The expected return is p.o-1. The expected return of laying the same outcome, for every dollar that the bettor stakes, is the inverse of that, -(p.o-1). So to compare bet B to laying a different outcome L, they are equal in value when
If p[sub]B[/sub].o[sub]B[/sub] > 2 - p[sub]L[/sub].o[sub]L[/sub], the bet is better value. Otherwise , the lay is better value.
To equalise your position, you need bet(s) or lay(s) that counterbalance bets/lays you’ve already made. So just find the counterbet/lay with the best value, and calculate the amount to bet or lay with simultaneous equations as above.
I think it gets more complicated if your existing position consists of more than two bets or lays.
Incidentally, how much you already have staked on the outcome doesn’t change what your good choices are, with respect to expected value. It might, however, make a difference depending on how much risk you like.
You’ve already laid bets on the outcome, and there’s nothing you can do about that any more: Either those were good bets, or they were bad bets. But you might decide that you’re not comfortable with the amount you bet, and buy some “insurance”: This will mean that your losses (if you lose) will be less, but also that your winnings (if you win) will be less, too. Alternately (and perhaps more likely, since you’re at the track in the first place), you might enjoy the uncertainty and the big stakes, in which case you might want to chase more money where you’re already betting, to make your wins (or losses) bigger.
If I bet $10 to back A, and A wins, then how much do I get?
If I bet $10 to lay A, and A loses, then how much do I get?
Same questions for B.
(I’m assuming that I lose the ten dollars I bet if I don’t win the bet.)
Bet $10 on B at 3.2:
B wins – you get $10 x 3.2 = $32 back (including your stake).
B doesn’t win – you lose your $10 stake.
Lay $10 on B at 3.2:
i.e. you accept bets up to a liability of $10. At odds of 3.2, this means that the bettor(s) stake a total of 10/(3.2-1) = $4.55.
B wins – you pay out their $4.55 x 3.2 = $14.55 including their stake. So you’re down $10.
B doesn’t win – you get the bettor/bettors’ $4.55.
Chronos – At this point in this position I’m looking to mitigate as effectively as possible. I suppose the whole deal is damage limitation but with reference to market odds, back and lay options, a dynamic, chaotic market, and around 7-10 seconds to complete the play.
Crisk – It is tricky. To grasp the concept of ‘laying’ it can help to imagine yourself in the position of a bookie; it’s his job to lay. For example, if he’s offering 2/1 (3.0 decimal) about a runner, he will take your $10 and will keep it if the runner does not win. If the runner does win as I’m sure you know, you not only win $20 but you get your $10 back as well. I’m trying to understand whether to back or lay when I have one runner in profit and one losing money. It can hurt your head.
Thanks. May I say I’m impressed by your immediate grasp of the importance of value, as well as the principle of laying – I suspect you may not be a stranger to the general area!
My backward thinking brain sometimes needs to reconstruct in order to make sense of things, can I ask if you think this makes sense:
Backing B (or betting as you term it) is less bad than laying A because 60% is further from 50% (in a good way) than 28% is from 31.25% (in a bad way)?
I think it does though, using the principle you describe, I have modelled the first stage bet, used that to build a second and then simulated placing both together. It might even work . . .
I have now managed to build a table to model back and lay options in 2-runner scenarios so I’m very grateful for your help in something what would otherwise have been beyond my ken.
As a general point, a possible curve ball in this might be the ‘third way’, that is to back B (which we now understand is the preferred method) but only to the extent liability/exposure is covered i.e. to not equalize at all. That would leave more profit in A, which anyway has a 60% statistical chance of winning and currently a 50% implied chance.
This option would seem to make sense only when there is sufficient potential profit in A to cover the loss of B at the current market odds.
Perhaps this option might also consider the dynamism in the market to pre-empt the right conditions.
You are right, my grasp of the concepts is not all that immediate ;). When Betfair started up here I spent hours honing spreadsheets, looking for “arbs” (markets with guaranteed profit if you bet the appropriate amount on each outcome) and so forth. But for all that, I still used to lose money, so I haven’t played the betting exchanges for a long time.
I imagine there is better value to be found on the Lay side of betting exchanges, simply because it is a new concept to most people (it was to me). I bet a lot of users never play on the Lay side at all.
It would be stupid to lay A at all. It will win 60 out of 100 times returning 120 units for the backer.
It would be stupid to back B at all. It will win 28 out of 100 times returning 89.6 units for the backer.
So your only viable moves are back A and lay B.
To make any attempt to “balance” this book you would need to know your bets up to this point. For all we know you could have backed both A and B at $11 in which case your outlay is $20 to $2 A and $980 to $98 B. But you could have backed A at $1.50 and B at $3 so your outlay is $30 on A and $70 on B.
As a long time gambler, a former bookmakers clerk (the guy who writes up all the bets on course) and a current treasury data analyst I think I can point you in the right direction with some more believable data.
Yes, in the long run you could achieve a positive expected return by backing A and/or laying B, but I think the OP is seeking to minimise the downside rather than turn a losing position into a winner. He’s only got this one opportunity to bet/lay.
As it stands, the original position would exepct to earn (0.6 x 20 - 0.28 x 100 - 0.12 x <however much he’s already bet on A and B> ). That is probably worse than the riskless -17.5 he can guarantee by balancing the position.
) betting that it will lose? In a two horse race, what’s the effective difference between betting on A to win or B to lose??
though, using the principle you describe, I have modelled the first stage bet, used that to build a second and then simulated placing both together. It might even work . . .