Math In Shuffle

If you know where they started at each pointas you go from left to right, you know there’s only oneof two cards that could be appearing.And actually there’s a number of magic tricksthat rely on this fact.So if you get a deck of cards and move one and then riffleshuffle, you can spot with–the moved card– because it won’t fit into oneof these rising sequences.As mathematicians have shown that for this kind of shuffle,you need to shuffle the deck at least half a dozen or so timesto get something that’s as good as random.And in casinos in that period, people were actuallyonly shuffling them once.So really if you can track what’s happened,you’ve got a huge amount of informationabout what’s going on.And in many cases, they would actually sneak in pieces.And again, another opportunity at confusing casinos–to track the cards that have come previously. Read more about shuffle and how to use math in there at CasinoSlots.

And whereas before card counters would measure what’s comeand then get a custom approximation of what’sleft, now they’d actually at each point in timeknow that there’s only one of two cards that could appear.So this is a terrific advantage that they had.But this poses a challenge, because how do you capitaliseon that?At each point in time, let’s say,there’s a card that’s advantageousand less beneficial.How do you make that decision about how muchto risk in that situation?And what I want to do is just start with a simple example.Let’s suppose we have a coin toss.And I’m going to offer you a biassed bet here.So I’m going to offer you two to one odds on tails.So in other words, you name an amount of money.If it comes up heads, you pay me that amount of money.If it comes up tails, then I will pay youdouble the amount you named.So clearly that’s a pretty stupid bet on my part.I’m giving you an advantage.But how much would you be willing to risk?After all, it is a coin toss, and you would stillhave a chance of losing money.Could I just get a quick show of hands?Who here would be willing to risk one pound on that bet?Show of hands–OK, so I think most of you.

Keep your hand out if you be willing to risk 10 pounds.OK, how about 100 pounds?OK, and 500?How many times do you get to play?Once.OK, so there’s a few people left.I’m not sure if they’re playing with monopoly money.But OK, so if you put your hands down.That wasn’t legally binding, anyway.But I waned to give you a chance to kind of geta feeling of measuring risk.How much are you willing to risk in that situation?And I don’t know if you can see, but actually the handskind of went down a lot between 10 and a hundred pounds.But this is quite an important question for gamblers.And actually in the ’50s, a physicistcalled John Kelly started thinkingabout this idea of biassed bets.Suppose you have inside information.And you have some edge over a book maker or casino.How do you exploit that?In this situation for you, although I gave all of youthe exact same bets– mathematically it’s the sameoffer–your perception of the value of that was very different.Some of you valued it at a pound, some at 10, some at 500.What’s the optimal thing to do there?