hi, for those who red MOP u know what im talking about here on the chapter of optimal play vs the nemesis.


its bout the first matrix. odds and even game.

first off it says if u think u cant outguess your opponent (nemesis),the best way to play is than to use an optimal strategy, correct ?

in this game theirs only 2 variable (x,y for odds ansd even) and usually, when we say optimal strategy we means mixed strategy right?

since their 2 variable, mixed strategy to play optimally vs the nemesis is to play 50% of time x and 50% of the time y ,correct ?

it says has soon has u play more then 50% x , the nemesis then play 100% of the time y ( wich its called pure strategy) and show a profit and so ure play of playing more then 50% x is -EV, i hope till now i get this right...

but lets say we play heads or tail with a coin, the coin is a obviously a random varaint and i wager vs my friend wich side the coin flip, my friend might bet like 75% heads and 25% tail . me , knowing its a 50,50 bet i woulkd need to bet half tails and half heads and i wouldnt looose while him he should loose in the long run, correct?

but because we arent trying to outgues each others in the coin flip game, where his strategy (75%x and 25%y) could be apply correctly in the odd and even games if i dont use optimal play, since the coin flip is random, shouldnt pure strategy here(100% heads or 100% tail strategy) be working has well has an optimal strategy about using a 50% tail/heads start ?
since the coin is random wich means the result would be 50% heads/tails.
kind like the nemesis is actually the coin while my friends and i are trying to outguess each other on the wager ?
and so if i know the coin is the nemesis where he can be -EV because he use a strategy wich his random, i cant loose by using pure strategy ( 100% tail or heads)

im not sure if i make sense for u guys but if u follow me it would be great if u dp....cause it means im starting to comprehend a bit if im right ...

ty

ps: more question to follow ....if u have time ty

You are confusing two concepts here.

Concept 1: betting 75% of the time that the coin will come up heads next time, and the remaining 25% of the time betting that it will come up tails next time. Betting heads on the next flip is equivalent to betting tails on the next flip, for a fair coin, so this strategy does not lose compared to making the bet on heads 50% of the time, or 100% of the time, or 0% of the time, or any other ratio. Each bet is separate.

If the coin is weighted even a tiny bit towards heads, however, the optimum strategy, for each single flip, is to bet on heads.

Concept 2: betting that, in the next several (say 100) coin flips, heads will come up 75% of the time (so 75 times). This is much less likely than heads coming up 50% of the time. But the odds of exactly 50% are still quite small, and become smaller for increasing values of "several" coin flips. Rather, for increasing even values; for odd values we can never have exactly half the flips be heads.

If the coin is weighted a tiny bit towards heads, then maybe it becomes more likely that 100 flips will yield 51 heads instead of 50. But it will still yield, say, between 46 and 56 heads most of the time, and 75 or more heads much less often.

The game against our nemesis is the same, except that although we are guessing nemesis' coin from our perspective, we are a (possibly weighted) coin from nemesis' perspective. So if we try to exploit nemesis, we become exploitable as well. If nemesis decided to stick to a 50/50 strategy no matter what, then it would not matter what we do. But if nemesis is thinking, then anything we do other than 50/50 allows nemesis to change to 100/0 (or 0/100) and take advantage. If we try to re-exploit that, then... well, eventually it will balance out and we both get stuck with 50/50. There's only so much thinking you can do usefully in a game this simple.

The less I read, the more sense you make. Hopefully I read enough to figure out what you're trying to say.

its so late ill pick this up tomorow but,

i tought since we knew the coin would weighted to a 50/50 scenario and cannot be exploitable due to his randomness, i tough the coin facing 2 opponent ( me and my friend) that try to beat each other using the coin results , the coin could of somekind be treated has the nemesis since he coulnt be exploited . Because if the coin could be exploited, in turn i could exploited my friends if i knew how to exploited the coin strats by knowing the coin mix strategy...

since the coin has no strategy beside an unexploitable one, wich i tought be considered a nemesis strat that give in the end a 50% head or tail, then i figured by using a pure strategy of 100% tell or heads it would of accomplished the same thing has in the first matrix conclusion in MOP.
saying has soon has u try to play an exploitive startegy by playing more then 50%x, the nemesis response was pure strategy by 100%y and wins.

i was thinking the game with the coin vs 2 players has the coin being the nemesis....tought using pure startegy would of worked great because :
1....i cant loose vs the coin ( using by default a 50/50 mixed startegy) and
2. if my friends doesnt use an optimal strategy of 50/50 or a pure strategy like if i choose 100x he should choose 100y .
if my friends use a mixed strategy like 70% tails(x) and 30% heads(y), , then i should i think win vs him and not loosing vs the nemesis... being 50/50 vs the nemesis using a pure strats and winning hugely with pure strategy vs my friends mix strategy of 70%x...

but seem i mix something up here ? since each flip of coin is restarting the matrix or something similar like halftilt is saying??
see i suck...i need some order in my head to comprehend this, i cant go forward if i dont catch all of this
tought my thinking wasnt to much flawed but i guess im a bit lost and mixing a lot of things right...

make sense?

ty