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Following on from the form factor special with Willoughby & Taylor as mentioned in an earlier thread, one of the examples given was how much would you bet on the first spin of a coin if given 10 spins and received odds of 2/1 on each spin?
How much would you bet on the first spin?
Is it a fair coin? Who owns it? Who tosses it? (Tossing a fair coin accurately to land the way you want it to is a skill reasonably easily acquired.) Has it been previously used in such events by these people?
Having carefully studied all previous form of events where an easily calculated even money chance is being offered at 2/1, I have come to the conclusion that it is a bent game. Answer – no bet at all. Easy and obvious choice, really?
I hope this isn’t spoiling the game. Should I think outside the box, or crawl back into the box and hide for a while?
1/4 of your bank roll if using Kelly.
Most likely longest losing sequence of a coin toss is 7 though having sadly flipped a coin a few hundred times I recorded 2 sequences of 8, 1 for heads 1 for tails and 2 sequences of 7, again 1 for heads and 1 for tails. There was also 2 sequences of 8 flips where it was head, tail, head, tail etc, the chance of losing stays the same whether you stick with head or tail or alternate so these sequences were expected.
If staked levels on a coin flip and after 300 flips of calling nothing but heads you had a 50% strike rate taking 2/1 you would be 150 points up providing you did not run out of capital.
By the balance of probability it is unlikely you will flip 10 loses in a row, Kelly protects against if by chance you did, still preserving you some capital.
If you took 10 flips staking by kelly with a £1000 bank and hit the 7 loss marker by bet 7 you would have £133.35 left, by level stakes at £100 a bet obviously £300 left, the difference being if you go to 10 with no wins you would be out of the game at levels but still have £56.25 left using Kelly.
The difference is you would have been able to bet more aggressively with Kelly early while you had the capital, your starting bet would be £250 and it would take four losses consecutively till you went below £100.
A theoretical sequence of win, loss, win, loss etc would yield more profit over 10 flips using kelly than levels and a theoretical sequence of 5 loss 5 wins would again yield greater profit using kelly than at levels and another theoretical sequence of 5 wins 5 loss would yield a greater profit by kelly.
So, I would certainly take the option of betting to kelly if presented with the opportunity.
I would say most punters would go for the level stakes as it puts them in some control of the situation when really you have none as it all based on the coin landing one way up or another and accepting that fact you should just try to maximise your gain in the best possible way.
1/4 of your bank roll if using Kelly.
Most likely longest losing sequence of a coin toss is 7 though having sadly flipped a coin a few hundred times I recorded 2 sequences of 8, 1 for heads 1 for tails and 2 sequences of 7, again 1 for heads and 1 for tails. There was also 2 sequences of 8 flips where it was head, tail, head, tail etc, the chance of losing stays the same whether you stick with head or tail or alternate so these sequences were expected.
If staked levels on a coin flip and after 300 flips of calling nothing but heads you had a 50% strike rate taking 2/1 you would be 150 points up providing you did not run out of capital.
By the balance of probability it is unlikely you will flip 10 loses in a row, Kelly protects against if by chance you did, still preserving you some capital.
If you took 10 flips staking by kelly with a £1000 bank and hit the 7 loss marker by bet 7 you would have £133.35 left, by level stakes at £100 a bet obviously £300 left, the difference being if you go to 10 with no wins you would be out of the game at levels but still have £56.25 left using Kelly.
The difference is you would have been able to bet more aggressively with Kelly early while you had the capital, your starting bet would be £250 and it would take four losses consecutively till you went below £100.
A theoretical sequence of win, loss, win, loss etc would yield more profit over 10 flips using kelly than levels and a theoretical sequence of 5 loss 5 wins would again yield greater profit using kelly than at levels and another theoretical sequence of 5 wins 5 loss would yield a greater profit by kelly.
So, I would certainly take the option of betting to kelly if presented with the opportunity.
I would say most punters would go for the level stakes as it puts them in some control of the situation when really you have none as it all based on the coin landing one way up or another and accepting that fact you should just try to maximise your gain in the best possible way.
Great reply!
I’ve had a similar scenario in casinos with coupons to "double your odds". For example, 2/1 on evens bets in roulette. Not exactly the same because of 0/00 but close.By the way an interesting website if you are into this sort of thing is http://wizardofodds.com/ . Ignore the bodog adverts the guy is just making a bit of money to run the site, his articles are sound.
I’d suggest bankroll is 50% mathematical and 50% psychological in terms of how you decide how much you want to set aside to bet with.
In the ATR piece I watched the concept of tilt and how to effectively conteract tilt didn’t seem to be touched upon or dealt with in any real way which was a bit ridiculous.
This type of feature offers so much more to the viewer than the abc race reading previews you generally get on these channels (which RUK seem to specialise in) if its developed further with hugh taylor + willoughby allowed to make it a regular feature and maybe develop a community through the website it could be a real usp for the channel
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