a game theory calculation
I haven't got any education in math so I have made this from what i think is right. Hope some of you can tell me if it does what it is supposed to.
It is a calculation of a poker situation - with one card to come. I call the player "Hero" and the opposition "Villian". It is supposed to calculate break even point of expected value as in how low can e.g. X be if zyw is ... and give 0 loss/profit.
- I have put the current pot as 1000
- X - is the % (e.g. 30% = 0.3) Villian needs to fold the bet to be "profitable=0"
- outs * 0.02174 - is the number of cards Hero can hit on the last card - which will win him the pot - * the % of any one card coming. Eg. theres is 2.2% chance of ace of hearts hitting as the last card.
- FvRB is villians fold % when hero hits his cards and bets the last round. So if this is 100% he will never call and 0% he will call all the extra bets Hero bets on the last round when he hits his cards.
- Villianraise is the % of times villian raises on the initial round forcing Hero to fold, and lose his 750 bet immediately with no chance of winning anything.
Here is the math:
0 = x * 1000 + (1-x) * ([(outs*0.02174)*(1-(villianraise/(1-x))]*(1000+750+(1-FvRB)*1875) - ((1 - (outs * 0.02174) * 750) - (([outs * 0.02174] - ((outs * 0.02174)* (villianraise / (1 - x))))*750))
It is split into 2 different groups:
- x * 1000 = is the % villian folds and Hero earns the 1000 pot [Plus 2]
- (1-x) * (2a-((2b)+(2c))) = the remaining % of hands where villian doesn't fold
2a. Outs*0.02174)*(1-(villianraise/(1-x))]*(1000+750+(1-FvRB)*1875) = is the % of hands hero hits, where he wins 1000 pot + 750 call. He also wins 1875 * 1-villians fold % - so if villian folds 70% of the time - he will win 0.3*1850. This is the part i have some trouble with - When villian raises Hero folds, so i have made this 1-(villianraise/(1-x)) - this should give me the number of raises villian makes of the hands he doesn't fold: Like if he folds 50% and Raises 50% - it would be 100% of the remaining hands villian raises. If i fill in the "blanks" it should give me e.g. X = the minimum % villian needs to fold for this to break even. Can anyone help me to see if my logic is flawed.
2b. (1 - (outs * 0.02174) * 750) = the % of hands where villian doesn't fold and hero doesn't hit = a loss of the initial 750 bet and subtracted from the winnings in 2a.
2c. [outs * 0.02174] - ((outs * 0.02174)* (villianraise / (1 - x))))*750) = the hands where Hero would have won, but was obstructed by Villians raise in 2a - this is also subtracted from the winnings in 2a.